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Wealth and Investment ManagementGlobal Research & Investments

February 2013

White Paper

Asset allocation at Barclays

Wealth and Investment Management Global Research & Investments

Asset allocation at Barclays February 2013 1

Contents

Introduction 3

Why asset allocation? ................................................................................................................. 3

Meeting clients’ needs ............................................................................................................... 3

Diversification ................................................................................................................................ 3

We expand the range of asset classes............................................................................ 4

We use sophisticated risk measurement and management techniques............ 4

Accessibility.................................................................................................................................... 4

Incorporating long-term views ................................................................................................ 4

Section 1: Overview 6

What asset classes should be included in a client portfolio? ........................................ 6

How should a portfolio be divided between these assets? ........................................... 6

How do you allocate to suit an individual? .......................................................................... 7

What makes our asset allocation process unique? .......................................................... 7

Section 2: Our roster of nine asset classes 9

Cash and Short-maturity Bonds ............................................................................................. 9

Risk-adjusted returns: Sharpe Ratio and desirability ............................................... 10

Developed Government Bonds ............................................................................................ 10

Investment Grade Bonds........................................................................................................ 11

High Yield and Emerging Markets Bonds ......................................................................... 12

Developed Markets Equities.................................................................................................. 12

Emerging Markets Equities.................................................................................................... 13

Commodities .............................................................................................................................. 14

Real Estate ................................................................................................................................... 14

Alternative Trading Strategies .............................................................................................. 15

Some of the things we haven’t included .......................................................................... 16

Section 3: How much of each 17

The optimal mix......................................................................................................................... 17

The asset allocation process ................................................................................................. 17

Forward-looking returns ......................................................................................................... 18

The Black-Litterman model: a starting point ............................................................. 18

The logic of Black-Litterman ................................................................................................. 19

The importance of views .................................................................................................. 20

Trading off risk and return ..................................................................................................... 21

Personalising risk ................................................................................................................. 21

Reducing dependence on historical data .................................................................... 21

Section 4: From model SAAs to customised portfolios 24

Section 5: What’s different? 26



Mathematical appendix:

the Strategic Asset Allocation process, step by step 27

Step 1: Assemble the input data on excess returns and estimate market

weights in the Global Capital Market portfolio ................................................ 28

Step 2: Calculate the implied equilibrium returns and collect Barclays’ strategic

long-term views .......................................................................................................... 29

Step 3: Combine the expected equilibrium returns with Barclays’ strategic long-

term views .................................................................................................................... 30

Step 4: Combine the resulting blended returns with investors’ risk

characteristics to produce optimised portfolios .............................................. 32

The investors’ utility function ............................................................................................... 32

Re-sampling ................................................................................................................................ 36

Step 5: Present five strategic asset allocation portfolios, along with

accompanying risk measures ................................................................................ 37

Risk and performance.............................................................................................................. 38



Introduction Dear clients and colleagues:

Barclays’ Investment Philosophy is the cornerstone of our offering to our Wealth and Investment Management clients. Through it, we aim to understand the unique needs of each of our clients and to provide them with personalised investment portfolios that enable them to achieve sustainable growth and risk management through diversified investments across multiple asset classes.

Why asset allocation? Whether we think in these terms or not, every investor has an asset allocation. Holding nothing but cash is an asset allocation (though it dramatically sacrifices long-term returns for short-term comfort). Holding only individual investments also results in a de facto asset allocation (one that places a huge bet on concentration and investment skill at the expense of diversification and risk reduction).

The question is not whether you have an asset allocation, but rather whether the one you have is efficient, sensible, and rewards you for the risks you’re taking … or not. We believe that a thoughtfully designed diversified asset allocation is the optimal approach to achieving your long-term goals.

When we set out to create the asset allocation process that lies at the heart of our Investment Philosophy, we followed four basic principles. The asset allocation must (1) meet clients’ needs, (2) provide diversification to minimise risk, (3) be comprised of asset classes that are generally accessible to investors, and (4) incorporate our long-term macroeconomic and market views as well as our behavioural finance expertise.

Meeting clients’ needs The first principle is that our asset allocations should meet clients’ needs. To do this, our Strategic Asset Allocations (SAAs) incorporate how investors psychologically perceive long-term risk, and our five (SAA) model portfolios are linked directly to client Risk Tolerance (measured by our Financial Personality Assessment™). They reflect our fundamental thinking about how financial markets work and our views on long-term trends in asset values, combined to reflect the optimal long-term risk-return trade-offs appropriate to investors with different levels of Risk Tolerance.

Diversification The second principle is that clients should benefit fully from diversification within their portfolio.1 In order to achieve maximum risk-adjusted efficiency, an investment portfolio needs to include not only stocks, bonds and cash but also other asset classes such as Commodities, Real Estate and Alternative Trading Strategies.

The idea that introducing imperfectly correlated assets to a portfolio can both decrease risk and enhance opportunities for return is well established in the academic literature and among investment managers. This concept, however, came under attack during the 2008–2009 financial crisis when most asset classes moved in one direction (down) and

1 Diversification does not guarantee a profit or protect against a loss.

Kevin Gardiner Chief Investment Officer,

Europe

Tom Lee Co-Head, Global Research

and Investments

Hans Olsen Chief Investment Officer,

Americas

Benjamin Yeo Chief Investment Officer,

Asia and Middle East



most short-term correlations strengthened for a time. We believe that this attack is largely misguided. What a diversified portfolio seeks to achieve is protection over the long term, in the form of a counterweight, to the uncertainty associated with a single asset class’ performance.2

Post-financial crisis scepticism aside, the principle of diversification remains a key building block of every good asset allocation.

We expand the range of asset classes

In applying diversification, we expand our range of asset classes to include the full universe of investible assets available to individual investors, including Commodities and Real Estate in addition to cash, bonds and equities. And we introduce the notion of Alternative Trading Strategies (ATS) as an asset class. Hedge funds and other alternative investment vehicles can play a variety of roles in a portfolio – one of which, we believe, is to generate attractive risk-adjusted returns that are weakly correlated with other asset classes because of the trading strategies involved.

We use sophisticated risk measurement and management techniques

In creating diversified allocations, we use sophisticated risk measurement and management techniques to account for the fact that asset returns do not follow a Normal (bell-shaped) distribution, tending instead to be asymmetrical and have ‘fat tails’.3

More generally, when analysing asset class returns, we are careful not to rely on a simplistic interpretation of data, and also not to assume that the future will look like the past, a common (if surprising) forecasting bias. Important insights emerge from this approach to asset returns. For example, traditional asset allocations suggest a much higher allocation to bonds than we believe advisable. Given the long-term bull market in bonds, we believe that future performance is likely to be different and our allocation should reflect that.

Accessibility Our third principle relates to the accessibility of investments: We seek for our clients a truly diversified, optimised portfolio that is also practically accessible. Thus, we have sought to ensure that our asset allocation models recommend broad categories of investible assets, ones that are both potentially attractive and accessible to all investors, rather than specific products. So, for example, we do not consider private equity to be a separate asset class, but rather a particular type of broader classes, such as Developed Markets Equities or High Yield and Emerging Markets Bonds.

Incorporating long-term views The fourth principle is that our asset allocation should incorporate our long-term (five-year) macroeconomic and market views as well as our behavioural finance and quantitative expertise.

Members of both our investment management as well as research and investment strategy teams participate in a rigorous annual process to determine our long-term views on asset classes (and meet every two weeks to determine shorter-term views).

2 See Compass February 2013 for a greater more in-depth discussion on the topic. 3 Skewness describes the asymmetry of distributions and should be zero for symmetric distributions, such as the Normal distribution. Excess kurtosis measures the higher probability in the tails of a distribution (that is, the ‘thickness’ of the tails), and has a value of 0 for the Normal distribution.

http://www.barclayswealth.com/Images/compass-feb-2013.pdf



We also incorporate behavioural finance to help us understand what is important to our clients, their perceptions of long-term risk and their preferences of balancing it with expected return. Quantitative analysis integrates these, bringing together our market expertise and our understanding of clients, in order to best meet clients’ needs.

We are proud of our asset allocation process, and believe that it contains many significant improvements to past practice in the wealth management industry. But we are determined to keep on improving this process – and we do each year, building further on our investment knowledge and skills.

Sincerely yours,

Kevin Gardiner Chief Investment Officer, Europe

Tom Lee Co-Head, Global Research and Investments

Hans Olsen Chief Investment Officer, Americas

Benjamin Yeo Chief Investment Officer, Asia and Middle East



Section 1: Overview The process in summary: selecting asset classes; allocating

investments between asset classes; and customising allocation to

investor needs.

Asset allocation – the appropriate mix of stocks, bonds, cash, real estate, commodities and other asset classes – is the cornerstone of the investment advice Barclays offers its clients. The appropriate allocation over the long-term aims to fully reward investors for the risks they take; to ensure that they don’t take unnecessary risks; and to deliver a combination of risk and expected return that is optimal for their level of Risk Tolerance.

Crafting the right allocation for any particular individual, family or entity calls upon all the skills we possess as investment professionals: finance theory, economic analysis, market savvy and psychological insight. To design our approach to asset allocation, we have drawn upon the many facets of our organisation.

Getting asset allocation right can be a difficult business. It involves asking some simple sounding questions, and getting some complicated responses. In this white paper, we let these questions guide the explanation of our processes. Our answers highlight how our approach to asset allocation is distinct from our competitors’.

What asset classes should be included in a client portfolio?

Diversification and investment accessibility are the broad themes that underpin our decisions about which asset classes should be included in a client portfolio.

In Section 2, we explain the rules that guide our selection and why we believe that the following nine asset classes are appropriate for most portfolios: Cash and Short-maturity Bonds, Developed Government Bonds, Investment Grade Bonds, High Yield and Emerging Markets Bonds, Developed Markets Equities, Emerging Markets Equities, Commodities, Real Estate and Alternative Trading Strategies (ATS), often found in funds that actively take long and short positions in a variety of markets. Note our explicit focus on emerging markets, which we believe will account for an increasing share of global market capitalisation, and the separation of Alternative Trading Strategies.

How should a portfolio be divided between these assets?

The answer is infinitely variable as it depends on individual client circumstances, needs and preferences. But for each client, we start from our core strategic asset allocation, which is designed to deliver the best long-term risk-adjusted returns for a given investor’s Risk Tolerance.

Section 3 explains how we define our strategic allocation. We take an established method of creating an optimal asset allocation, the Black-Litterman model,4 and seek to improve it by addressing some of its inherent limitations.

4 Black F. and Litterman R.: Global Portfolio Optimization, Financial Analysts Journal, September 1992, pp. 28–43.

Antonia Lim

Global Head of Quantitative Research

+44 (0)20 3555 3296

[email protected]

Greg B Davies

Head of Behavioural and

Quantitative Finance

+44 (0)20 3555 8395

[email protected]



We develop our own long-term views on expected returns for each asset class through a top-down, building-block process. Using the Black-Litterman model, we combine these views with those implied by market conditions and historical data to generate a blended expected return. We address limitations to the model in two ways. First, we employ a sophisticated risk measure (Behavioural Risk5) that doesn’t simply equate risk with volatility, but instead aligns with how investors actually view long-term risk. Specifically, we give greater weight in the risk measure to progressively worse downside scenarios as investors tend to view worse-than-expected as risk (negative outcomes add to risk), but allow better-than-expected returns to reduce the risk measure (positive outcome reduce risk). Thus, when we minimise risk in our optimisations, we reduce the chance of bad outcomes occurring, without simultaneously penalising good outcomes. Second, we use an advanced statistical technique called re-sampling. By enabling us to take into account many different future scenarios using the same historical data, this technique reduces the likelihood that a model’s allocation is biased toward protecting against a specific past market event.

The five Strategic Asset Allocation (SAA) model portfolios created through this process offer a baseline mix of assets that, if held on average over a five-year period, will in our view provide the most desirable combination of risk and return for an investor’s degree of Risk Tolerance.6

How do you allocate to suit an individual?

It is important to note that we use these SAA model portfolios as a starting point. Rather than serving as the recommended investments for any particular investor at any particular point in time, the models help guide the building and managing of customised investment portfolios.

We begin with one of the five SAAs and tailor it for what makes a client unique: overall wealth, specific financial situation and needs, as well as attitudes about, and approach to, investing. This process may involve tactical shifts from one asset class to the other.7

What makes our asset allocation process unique?

We have nine asset classes in order to provide a diverse portfolio of easily accessible investments. Our macroeconomic and market views are fed seamlessly into our investment recommendations. Our focus on total wealth adds an extra degree of consideration, particularly for investors with low Risk Tolerance.

Sophisticated statistical techniques help improve the conventional asset allocation process, while our innovative approach allows us to seek to mitigate investors’ risk in a way that is consistent with what matters most to them: the chance of bad outcomes. And we tailor our SAA portfolios to meet specific investor needs.

5 See the Mathematical Appendix for the definition of Behavioural Risk. 6 It provides the best possible risk-adjusted returns, i.e., the highest expected returns over and above the return that each investor requires to compensate him or her for the risk they take. 7 Take, for example, an investor’s overall wealth. Many individuals have a sizable portion of their non-investible wealth in personal real estate (their house, vacation homes, etc.). While it’s right that such Personal Holdings are considered as to be outside their Investment Portfolio, the existence of these assets often provides a good reason not to double up on exposure to real estate in the asset allocation. As another example, take an investor who, based on our insights from the use of Behavioural Finance, we understand has low ‘Belief in Skill’. We should be ready to adjust our baseline SAA portfolios by, for instance, reducing or cutting out altogether their exposure to skill-based asset classes, such as ATS. Belief in Skill is one of six dimensions measured by our behavioural finance-based Financial Personality Assessment™ (FPA). It reveals how much an investor is inclined to believe in the potential success of active management. Contact your Barclays representative to learn more about our FPA or visit http://www.investmentphilosophy.net/.

http://www.investmentphilosophy.net/



Each of these areas of difference has an important effect on our asset allocations. For example, as a result of considering a client’s total wealth, our SAA model portfolios suggest that investors, particularly those with low and medium-low Risk Tolerance, should hold more in cash and short-term bonds than advocated in conventional strategic asset allocations. We learned from the 2008–2009 financial crisis that under very adverse market conditions, cash and short-term bonds constitute the only reliable store of value – and we believe that a sound investment strategy needs to provide some protection against a recurrence of such events.

As another example, the result of incorporating our long-term views is that our SAAs are very much oriented toward benefiting from continuing growth in emerging markets. Thus, compared to most of our competitors, we have a relatively large strategic asset allocation to emerging markets equities and bonds.8

8 For example, the 2013 Moderate Risk SAA allocates around 17% to emerging markets equities and bonds, compared to an average of approximately 8% at more than 35 wealth managers.



Section 2: Our roster of nine asset classes Why we think investors should consider holding nine asset classes

in their portfolio – and why we don’t recommend some others.

An asset class is a good candidate for routine inclusion in an investment portfolio to the extent that:

It is likely to provide competitive risk-adjusted returns, and

It offers unique risk or return characteristics, and

It is efficiently accessible by affluent and wealthy individual investors, and

Adding this asset class does not unnecessarily complicate the overall portfolio.

There is no single ‘right’ answer for how many asset classes investors should consider holding in their portfolio, as there is a trade-off between having as many different asset classes as possible and choosing only those that make sufficient difference when included. After analysing a broad range of candidates we concluded that, unless there is a good reason to do otherwise, investors should hold some combinations of the following nine asset classes in their portfolios at almost all times. We explain our approach and the rationale behind each asset class below.

Cash and Short-maturity Bonds9 This asset class plays a unique and essential role in SAAs, especially for the most risk-averse investors. It is the only investment that fulfils the objective: ‘Make sure I retain my capital long term.’ For this reason cash and short-term bonds are often referred to as the ‘risk-free’ asset. This is, however, misleading. Bank deposits, money market fund shares, and short-maturity government bonds might be considered ‘risk-free’ investments in some senses, but not others. They are almost ‘risk free’ in the sense that the investor is reasonably assured of receiving back the face amount of the investment, on or by a certain date; however, some investments, such as money market funds, may carry a very small though not immaterial credit risk that makes the return of capital extremely likely, but not guaranteed. Moreover, as an asset class held in an investment portfolio over a long period of time, Cash and Short-maturity Bonds are not ‘risk free’ because the return or yield may not be high enough to maintain the purchasing power of the money invested. In particular, the purchasing power of funds invested in this asset class will decline over time if, on average, the return or yield on Cash and Short-maturity Bonds falls below the rate of inflation, as it has in, say the US or Europe, recently.

Many investors distinguish between Cash – defined as a fixed-income investment with a final maturity of one year or less – and Short-maturity Bonds – defined as debt with maturities above one year and below three years. The two types of investments are, however, very similar and should, in our view, be categorised as a single, very low-risk asset class, with the average maturity of the cash and short-term bond mix varying over time depending on the level and outlook for short-term interest rates and the timing of potential liquidity needs.

9 These bonds should be rated AA- or higher.



Risk-adjusted returns: Sharpe Ratio and desirability Historical risk-adjusted return has traditionally been measured through the Sharpe Ratio. This is defined as:

Excess Return

Volatility

Where Excess Return is the average annual return generated by an asset class in excess of a risk-free-like rate such as the return of US Treasury Bills and Volatility is the annualised standard deviation of returns over the same period. The Sharpe Ratio tells us the additional excess return we get on an investment for each additional unit of volatility. For example, over the 20 years ending in September 2012, Alternative Trading Strategies (ATS) and Developed Markets Equities generated very similar (excess) returns, but since stock returns were more volatile on a month-to-month basis, ATS’ Sharpe Ratio was much higher than the stocks’: 0.6 versus 0.3. That is, over the past 20 years ATS produced better risk-adjusted returns than developed equities.

Despite being widely used in the investment community, the Sharpe Ratio is not a perfect measure of risk-adjusted returns, particularly for individual investors; they need to be able to optimally allocate their total wealth, which usually includes cash, to get the best overall risk-return trade-off. There is a huge difference between choosing an efficient portfolio, or allocating only 20% of your wealth to this portfolio, and leaving the rest in cash – and yet these two options have exactly the same Sharpe Ratio! In fact, all such blends that include cash have the same Sharpe Ratio, regardless of how much cash is used. The Sharpe Ratio cannot be used to select the best total wealth allocation including the amount left in cash.

Moreover, the Sharpe Ratio uses volatility as a measure of risk. This is unsuitable in two ways. First, risk is about the chance of low portfolio values in the long term, whereas volatility is about fluctuations along the journey. The latter only really matters to a long-term investor insofar as it increases anxiety and the temptation to deviate from good long-term investing decisions. Second, even if we were concerned about volatility, rather than risk, this should not be measured (as the Sharpe Ratio does) through standard deviation, because it does not adequately reflect that downside volatility is what really matters to investors (better-than-expected positive returns are not typically what worry investors). We understand these failings and try to address them by introducing a new measure of risk-adjusted returns called Desirability, which can be thought of as the returns remaining after the investor has been compensated for taking on risk.10

Developed Government Bonds We define Developed Government Bonds as fixed income instruments with maturities of three years and above, issued by sovereigns with credit ratings of AA- or better. Most such bonds pay fixed coupon rates, but inflation-indexed issues are also considered.

Developed Government Bonds play an important role in an investment portfolio as they tend to stabilise its value in two different ways.

First, in general, their inclusion in a portfolio tends to make the returns on that portfolio less volatile, as government bonds tend to fluctuate in value less than equities and other risky assets.

10 See the Mathematical appendix for further details.



Second, Developed Government Bonds provide diversification benefits as, usually, bond prices tend to move in the opposite direction from stock prices. This is mainly due to the evolution of interest rates, the main determinant of government bonds returns, during the business cycle. In general, when the economy is strong and stocks are rising, interest rates tend to increase, pushing down bond prices and reducing bond returns. In contrast, when economic growth is weak and stock prices are falling, interest rates tend to decrease, driving bond prices up and enhancing bond returns. This negative relationship between stock and bond price movements is far from perfect, and tends at times to break down, in particular when inflation turns out to be much higher or lower than anticipated. But overall it is sufficiently strong11 to justify the inclusion of Developed Government Bonds in a portfolio as a distinct asset class. Figure 1, for instance, highlights how they provided portfolio smoothing benefits during the 2008–2009 financial crisis and the recent euro area debt crisis.

Figure 1: Price changes through the curve

50

60

70

80

90

100

110

120

130

140

Sep-08 Sep-09 Sep-10 Sep-11 Sep-12S&P 500 30-year US Treasury

September 12, 2008 = 100

Onset of financial crisis

Euro crisis and subsequent repercussions

Source: Datastream. Indices: S&P 500 Composite Price Index, USD; US Treasury Benchmark Bond 30 Years.

Investment Grade Bonds We define Investment Grade Bonds as fixed-income securities with maturities greater than one year issued by corporations with credit ratings of BBB- or higher and by governments with credit ratings between BBB- and A+.

The reasons for including Investment Grade Bonds in a diversified portfolio are the same as for government bonds: stable and somewhat countercyclical returns. But the differences between the two markets are sufficient to justify separating them into two distinct asset classes. A diversified portfolio should include some of both.

In particular, returns on Investment Grade Bonds are determined by the level and change in interest rates and the level and change in the amount of additional yield, or ’spread’, paid to compensate investors for the risk that the company or government may default. Most of the time the extra yield earned as compensation for credit risk enhances the return on corporate bonds relative to governments; for this reason, most well-constructed bond portfolios include a substantial allocation to investment grade issues. Issuers do occasionally default on the debt that had an investment grade rating immediately prior to the event, but changes in the actual volume of bankruptcies is not

11 For instance, over the five years to September 2012, the correlation between Developed Government Bonds and Developed Market Equities was -0.27.



the primary driver of returns on these bonds. Rather, it is changes in yield spreads between investment grade and government bonds, reflecting changing market expectations about the frequency of future defaults, that determine these returns. If spreads narrow (or ‘tighten’), then the return on corporate bonds will be higher than on comparable maturity government bonds and vice versa. Issuer credit quality tends to improve and spreads tend to tighten when the economy is growing, so it frequently happens that Investment Grade Bonds produce much better returns than government bonds at times when interest rates are rising and government bond prices are declining.

High Yield and Emerging Markets Bonds We decided to group global high yield credit and emerging markets bonds under a single asset class called High Yield and Emerging Markets Bonds. High yield credit refers to fixed-income instruments issued by companies with low credit ratings (BB+ or lower). Emerging markets bonds refers to fixed-income instruments issued by sovereigns, government-related agencies and corporations with a rating of BB+ and lower denominated in major currencies (US dollar, euro, yen, or sterling) and local currencies. In particular, emerging markets bonds denominated in local currencies have become increasingly important in terms of both market capitalisation and potential contribution to portfolio risk-adjusted returns.

We group these instruments under a single asset class because while high yield credit and emerging markets bonds may have different risk-adjusted returns over the short term, they display similar risk-return characteristics over the long term. So separating them out into two separate asset classes would not make enough difference in a portfolio context.

As with Investment Grade Bonds, the return on this asset class is mainly determined by changes in the level of interest rates, the level of yield spreads, and the volume of defaults. But the proportionate impact of each of these factors differs enough from investment-grade debt for them to be considered as a different asset class. Additionally, the inclusion of emerging markets debt issued in local currency offers another potential source of higher risk-adjusted returns: currency appreciation as these economies mature.

Developed Markets Equities12 Over long periods of time, common stocks of European, North American and Pacific Rim companies have created more wealth, by orders of magnitude, for investors than any other liquid asset class (Figure 2). It is not just that the return on equities has compensated investors for the additional risk incurred relative to bonds or cash. Over long periods of time, equities’ risk-adjusted return has been substantially higher than bonds’. Put simply, if an investor is willing to take risk in one and only one asset class, Developed Markets Equities should be the choice, based on the longest track record of high risk-adjusted returns.

The performance of equities since the end of the ‘90s (Figure 2) has called this conclusion into question in some minds since over this period bond returns have been much higher than stock returns. An investment of $10,000 in the S&P 500 in December 1999, with all dividends reinvested in the same index, would have been worth about $12,400 in September 2012.13 The same $10,000 invested in the 30-year US Treasuries

12 As defined by their inclusion in the MSCI World Index. (Western Europe, the United States, Canada, Japan, Australia, New Zealand, Hong Kong, Singapore and Israel, as of January 2013.) 13 S&P 500 Total Return Index is used to calculate return. Source: Bloomberg. An investment cannot be made directly in an index.



over the same period would have been worth $17,900.14 15 However, it is important to be careful about what one does and does not infer from recent historical experience.

Take, for example, the year 1999, which saw the last phase of an unprecedented run-up in stock prices and valuations to levels that were patently overvalued. An investor would have been mistaken to look back on the previous decade from that vantage point and conclude that stocks were ‘a sure thing’. Similarly, we believe it would be a mistake to view the last decade’s poor performance and decide to avoid equities. Instead, what one should learn from the post-1999 period is that the volatility of stock market returns seems to have ratcheted up in recent decades, as a quick glance at Figure 2 suggests. For a variety of reasons this asset class seems to have become more vulnerable to bubbles and busts than it had been for most of the previous 50 years. The conclusion we draw is this: While in the past the developed countries’ stocks were clearly the very best and, perhaps, the only good place to take investment risk, in the future these markets will be one among several worthwhile places to take risk.

Emerging Markets Equities16 Although the correlation between emerging and developed equity market returns is high and has been increasing, we believe it makes sense to separate ‘global equities’ into two distinct asset classes – developed and emerging – for several reasons.

First, emerging equity markets tend to be newer, smaller, less transparent and less liquid than developed country equity markets. For these reasons, investments in this asset class have been a great deal more risky over the past 20 years than Developed Markets Equities.

Second, these markets are maturing rapidly, becoming larger, more transparent and more liquid. Early investors have benefited and earned higher returns than in developed equity markets over a 20-year period.

14 Source: Bloomberg. US Generic Treasury 30-Year Yield is used to calculated return. 15 Data which may be found in this document are based on quantitative research and analysis of historic data using previous and current asset weightings and proprietary projections of expected returns and estimates of future volatility. The data do not reflect actual trading, liquidity constraints, fees and other costs. They should not be taken as a forecast or estimate of likely future returns. As illustrations do not take into account fees and commissions, or taxation, the actual performance of any investment might be more or less than is stated in any illustration. 16 As defined by the countries included in the MSCI Emerging Markets Index.

Figure 2: Cumulative returns Figure 3: Emerging Markets’ share of total global equity

0

10000

20000

30000

40000

50000

60000

70000

1950 1960 1970 1980 1990 2000 2010

January 1, 1950 = 100

S&P 500

Long-term Bonds

0

2

4

6

8

10

12

14

16

Jan-88 Jan-92 Jan-96 Jan-00 Jan-04 Jan-08 Jan-12

MSCI Emerging Markets as percentage of MSCI All World

Percentage Points (%)

Source: Prof. Robert J. Shiller, http://www.econ.yale.edu/~shiller/data.htm S&P 500: S&P 500 Composite Price Index + monthly dividend data Long-term bonds: 10-year Treasury Constant Maturity Rate, monthly. Past performance is not a guarantee of future results. An investment cannot be made directly in an index.

Source: FactSet.

http://www.econ.yale.edu/~shiller/data.htm



Third, the emerging economies have been, and are likely to remain, the most dynamic in the world. As a consequence, these countries’ stock markets have been accounting for an ever-increasing share of total global market capitalisation – from around 4% ten years ago to around 13% today (Figure 3) – and we expect this trend to continue. All of these reasons justify singling out this asset class for separate consideration.

Commodities Commodities are physical assets like gold, oil or corn and as such are not typically direct investments held in an investor’s financial portfolio. They can – and should – be accessed through diversified instruments like funds or notes issued by an intermediary.

Our main reason for concluding that most investors should have some allocation to commodities at most times is diversification. There have been, and in the future could be, periods when returns on commodities are high and positive while real returns on stocks, bonds, and cash are large and negative. In particular, when inflation turns out to be substantially higher than investors had anticipated, then both stock and bond prices tend to decline and real (inflation-adjusted) yields on cash are often negative. Under the same circumstances, commodity prices are likely to rise.

The last time high inflation consistently surprised investors over a prolonged period started 40 years ago, in the 1970s. A near-term repetition of that episode is looking increasingly unlikely. If we thought that commodities produced competitive risk-adjusted returns only during periods of high and rising inflation, we would not treat them as a strategic asset class. We have seen, however, that even during periods of declining inflation, commodities have delivered unique risk-adjusted returns. Our conclusion is that it is sensible to hold a diversified portfolio of commodities during most periods and that an allocation to this asset class could provide important portfolio smoothing benefits under some unpredictable circumstances.

Real Estate Real estate as an investment asset class can take a variety of forms, and compared with the equity and bond markets, the real estate markets are much more heterogeneous. This asset class qualifies as a strategic holding on several counts. For many investors, real estate is the most important ‘real’ asset. This is due both to their everyday experience and to the size of the market. Real estate is therefore often the focus of investment decisions aimed at increasing diversification (of the overall portfolio and of its ‘real’ part) and achieving a certain degree of inflation protection while targeting high returns. Taxation considerations also play an important role in defining real estate as a separate asset class.

Real estate can be accessed in several ways. One of the most easily accessible of these is through indirect investments, such as a Real Estate Investment Trust (REIT) – companies (or groups of companies) that provide a tax-efficient, liquid way to invest in commercial and residential property. They also allow investors to overcome high management and transaction costs, and avoid concentration risk. In our analysis, we have therefore represented this asset class with an index for REITs. However, the tradability and leverage associated with REITs means they are subject to factors such as market sentiment: They are effectively part of the quoted equities universe, and so can be correlated with it.



For clients with the right liquidity profile and preference, direct real estate is the purest representation of the asset class. It can reward with an illiquidity premium but benefits greatly from diligent fund and manager selection. However, this method is harder to access and potentially carries higher concentration risk than an indirect investment.

Alternative Trading Strategies Alternative Trading Strategies (ATS) aim to generate profits for investors by actively taking long and short positions in a wide range of markets. Many, but not all, hedge funds fit into this asset class. Investors can also access ATS through mutual funds in the US; UCITS funds in the European Union; and through a variety of structured notes.

ATS fund managers tap into a range of sources of return. Some systematically aim to exploit common market anomalies, such as the tendency for:

Momentum to drive markets upward or downward much further than is justified by the fundamental facts,

Market prices of convertible bonds to add up to less than the value of the sum of the security’s component parts, or

Stock markets to underestimate the likelihood that announced acquisition deals will close.

Other ATS managers rely solely on their skill in anticipating market moves and on efficiently expressing their views in a variety of global markets.

Hedge funds should not be viewed only as an implementation of the Alternative Trading Strategies asset class. In fact, many hedge funds are not what we at Barclays would consider ATS. For example, if an investment vehicle exhibits a strong tendency to do well when equity markets are rising and to lose money when they’re declining (what we would deem to be a heavily beta-driven strategy), then that investment may be considered as part of equities. Thus, we may categorise some equity long-short hedge funds as a component of an investor’s Developed or Emerging Markets Equities allocation. Similarly, we might characterise a hedge fund that produced returns highly correlated with, say, the high yield bond market as part of the allocation to that asset class.

What an investor ultimately does by investing in ATS is to ‘buy’ the managers’ skills, seeking to achieve seek better risk-adjusted performance. The inclusion of ATS in an investment portfolio is justified not only by the fact that ATS managers operate along different dimensions than ‘traditional’ buy-and-hold managers, but also by ATS managers’ unique risk-return characteristics. For the most part, ATS’ returns have mid-to-low long-term correlations with returns on other asset classes. While this benefits portfolios over the long term, it does not mean that such assets will protect in every event along the way. For example, when markets freeze up as they did in 2008, ATS may have large, negative returns along with stocks, commodities, corporate bonds and real estate.

It is important to underscore the wide dispersion of results across managers in this asset class. As allocation to ATS is largely an allocation to skill, it needs to be approached with care. The successful inclusion of ATS within a portfolio depends on a rigorous and continuing selection and monitoring process.



Some of the things we haven’t included In the process of selecting these nine asset classes, we rejected a number of other candidates. A detailed accounting for all the reasons and decisions is beyond the scope of this white paper, but a few are worth mentioning.

We do not break out Developed Markets Equities into regional sub-asset classes. Returns on US equities, European equities and Japanese equities are highly correlated and a large proportion of the each of these markets’ total capitalisation consists of multinational companies. This does not mean that it never makes sense to favour one developed market rather than another; often it does. But we believe that unless there is a good temporary reason to do otherwise, this asset class should include a broad representation of companies with headquarters all over the developed world.

We do not distinguish between public equity (common stocks) and private equity on the strategic asset class level. Instead, we recommend categorising investments in private equity funds as part of either the developed or emerging equities market asset classes. Although returns on private and public equity are only weakly correlated on a month-to-month or year-to-year basis, over longer periods of time the same basic economic factors drive returns to both. Our asset allocations are designed to optimise long-term risk-return characteristics, rather than to beat the markets in the short term. Further, we believe that only the best, ‘top-quartile’, private equity funds reliably generate high enough returns to compensate investors for the extreme illiquidity of these investments; but such investments are not readily available to investors in all wealth categories. So although we believe that private equity funds can enhance portfolio performance, especially for risk-tolerant, highly composed investors with high Belief in Skill, we decided not to single out this category as a strategic asset class.17

We do not break down commodities into sub-sectors such as ‘precious metals’, ‘industrial metals’, ‘grains’, etc. despite their different risk-return characteristics. And, in particular, we don’t single out gold as a separate strategic asset class. This has to do with the degree of granularity that we want to be reflected in our portfolio. In normal circumstances, a diversified portfolio of commodities should include some allocation to gold and all of the commodities sub-sectors.

17 Composure, one of six dimensions measured by our Financial Personality Assessment™, reveals how much an investor engages with and is responsive to short-term investment performance. For more on Belief in Skill, see Section 4, “From model SAAs to customised portfolios”.



Section 3: How much of each The ways in which we’ve made the conventional approach to

asset allocation better – and why we generate five separate

model portfolios.

The optimal mix In a world of uncertainty, the optimal mix of assets for an investor to hold at the start of a time horizon is the one that provides the best weighted-average subjective outcome at the end of the period, across the full range of possible states of the world. Some focus on each of the key words in this definition is worthwhile.

Outcome: This can be defined as the end point value of the portfolio.

Weighted Average: We do not know in advance, of course, what will occur over the next five years. We do, however, have some idea of the range of possible outcomes and estimates of the probabilities of each outcome. The average used is the sum of all of possible outcomes weighted by the probability of that outcome occurring.

Time Horizon: Strategic asset allocation is defined as the mix of assets one plans to hold on average over a relatively long period of time before planned withdrawals. For our purposes here, we have a five-year horizon in mind. This is not to say that we expect clients to reserve judgment on the performance of our investment advice for that long. We aim to give good advice about what investments to make with much shorter time horizons in mind, from overnight to a few years. Having a five-year investment horizon in mind also does not mean that the portfolio does not change during this period. Not only do we rebalance portfolios regularly to adjust for events as they occur, but we also re-evaluate and update our five-year views every year and we take tactical positions that tilt these five-year views to account for the prevailing economic and political environment and shorter-term forward views.

Subjective: Some investors judge given outcomes differently to others. The subjective evaluation of the portfolio value at any given horizon depends in part on how much in real purchasing power the portfolio is worth at the time, but not wholly. A 20% increase is not twice as good from a particular investor’s point of view as a 10% increase, and different investors will place different values on any given percentage change. In particular, risk-averse investors will respond much more negatively to a loss (say 10%) than more risk-tolerant investors.

The asset allocation process Once we’ve identified the right set of asset classes, and defined what we mean by ‘optimal mix’, the process of defining recommended strategic asset allocations has two steps: (i) estimating the forward-looking statistical distribution of asset class returns and (ii) solving for the optimal mix of assets for investors with different degrees of risk tolerance. We believe that the approach to both of these steps presented in this White Paper represents an improvement over previous best practice in the field of wealth management.



In particular, the main innovation of our approach to portfolio construction comes from taking the individual client as a starting point and recognising that the way they trade off risk and return is different than usually assumed. Standard practice in the wealth management industry has been to consider deviations from the mean on either side as contributing equally to risk. In contrast, we recognise that this is not the case and that there is an asymmetry to how investors subjectively evaluate different outcomes since they focus on restricting the chance of lower-return-than-expected outcomes, but not higher-return-than-expected outcomes.

By specifying more realistic long-term risk-return client preferences, and by using a more sophisticated risk measure (Behavioural Risk)18 that goes beyond the mere association of risk with volatility, we are able to take into account some observed features of asset returns, such as the potential for extreme negative events. Moreover, to make sure that such asset return characteristics are reflected during our portfolio construction process, we use our improved measure of risk together with an advanced statistical technique called re-sampling.19

Good asset allocation advice must be based on reliable estimates of future asset class returns. Strategic asset allocation is based on estimates of returns over relatively long periods of time, say, five years or more. Also, to give good advice, we need reliable estimates not only of the expected future average return on each asset class, but also of the future risk or uncertainty surrounding each return estimate and the statistical relationships among returns on the different strategic asset classes, such as the correlations. The following discussion presents a purely verbal description of our process for estimating these numbers. The “Mathematical appendix: the Strategic Asset Allocation process, step by step” presents the methodology in mathematical terms.

Forward-looking returns One method for estimating future returns that we do not want to use is a naïve process of taking the average of asset class returns, risks and correlations over some historical period and projecting these into the future. To see why this is wrong consider the past 20 years, when bonds have produced about the same average annual returns as stocks with much less risk. A ‘rear-view mirror’ approach would suggest that investors should hold a lot of bonds and very few stocks going forward. But consider that the reason bonds have done well is that interest rates have been declining on average over the past 20 years and have reached a point where, for many maturities in many countries, they are essentially at 0% and can’t get much lower. Although bonds have an important role to play in an asset allocation, as discussed above, it is logically impossible for bonds to produce high returns in the future.

The Black-Litterman model: a starting point

The approach we take for estimating future returns begins with current standard industry best practice, the Black-Litterman model, and modifies that to correct some of this model’s more restrictive assumptions.

In order to apply the Black-Litterman model to our nine asset classes, we need estimates of the total amount of each asset available in the market. This is relatively straightforward for stocks and bonds, for which such data are readily and reliably available. Estimating the market capitalisation of the other asset classes is harder. For instance, the amount invested in commodities and ATS is not limited by a fixed amount available.

18 See the Mathematical appendix for the definition of Behavioural Risk measure. 19 See the Mathematical appendix for further details about our asset allocation process.



The logic of Black-Litterman The Black-Litterman model, developed more than 20 years ago by Robert Litterman and the late Fisher Black, starts with the observation that every asset in the market has to be owned by someone at all times. Therefore, unless there is a good reason to expect otherwise, the expected relative returns on different investments will tend toward their ‘equilibrium’ values. The equilibrium expectation for any asset is the relative level of return that must be anticipated – given how risky that investment is and how returns on that investment relate to returns on other assets – to induce investors to hold the total market value of the asset. For example, to induce investors to hold all of the government bonds available on the market, the expected return on government bonds does not have to be particularly high relative to returns on other investments. This is because government bonds are not particularly risky investments and returns on government bonds tend to be negatively correlated with returns on riskier assets such as stocks or commodities. By contrast, the expected return on developed equities does need to be relatively high because stocks are relatively risky and because stock returns are positively correlated with returns on other risky assets.

Figure 4: Basic Black-Litterman estimates of asset class capitalisation, return, and risk

Asset class

Estimated market

capitalisation (USD, trillions)

Forward-looking Black-Litterman

equilibrium return*

Risk (probability of a negative return over a

one-year horizon)

Cash and Short-maturity Bonds 6 1.5% 0%

Developed Government Bonds 23 1.5% 5%

Investment Grade Bonds 7 2.4% 8%

High Yield and Emerging Markets Bonds 4 4.9% 18%

Developed Markets Equities 25 7.9% 28%

Emerging Markets Equities 4 10.4% 35%

Commodities 3 4.9% 28%

Real Estate 1 8.3% 29%

Alternative Trading Strategies (ATS) 2 3.3% 15%

*Assumes 1.5% Equilibrium Yield on Cash and Short-maturity Bonds. Risk is based on rolling one-year returns based on data from November1991 to September 2012. Source: Barclays. There is no guarantee that these estimates will be achieved.

The volume of commodities futures contracts is determined by the willingness of buyers and short-sellers to open contracts. And the aggregate investment in Alternative Trading Strategies (ATS) is not limited by the volume of any given asset but rather by the willingness of investors to pay the fees that the managers of these funds charge. Because Black-Litterman is only the starting point of our process, we have decided to use a series of adequate, if imperfect, measures of asset class capitalisation for commodities (a notional value of futures positions), and ATS (industry’s assets under management).

With these estimates of market capitalisation and historical measures of asset class risks and correlations, we can estimate the forward-looking equilibrium expected excess returns (over cash) for each of our asset classes. These are listed, along with their probability of a negative return in any one year, in Figure 4. Note that although Cash and Short-maturity Bonds have not given a negative return in this period, that does not preclude them doing so in the future, even if it’s very unlikely. Standard practice would



be to call the process of estimating forward-looking equilibrium returns complete and proceed immediately to the next step of the process, namely, calculating the optimal strategic portfolios across investor risk-tolerance levels.

There are good reasons, however, to be dissatisfied with these estimates of forward-looking equilibrium returns as a basis for strategic asset allocation advice.

The importance of views

Once we have estimated the forward-looking equilibrium returns, the Black-Litterman model allows us to express our strategic views on excess returns in a clear and flexible way and to combine these two sources of information together. Indeed, the Black-Litterman model does not assume that the world is always in equilibrium, but rather that when expected returns move away from equilibrium, imbalances in markets will tend to push them back. Investors can therefore profit by combining their views about returns in different markets with the information contained in equilibrium prices and returns. Equilibrium returns can therefore be seen as a ‘centre of gravity’ for expected returns; investors’ views determine the extent of the deviations from equilibrium.

We start the development of our five-year views on future returns for each of our nine asset classes by eliciting the input of a wide range of research and investment professionals across Barclays globally. Our process then uses a top-down, building-block approach in which the building blocks for each asset class include the key macroeconomic variables that drive that asset class’ return, as well as the price, valuation and market fundamentals relevant to its performance. This ensures that views across asset classes are grounded and consistent.

One thing that’s particularly relevant right now, for instance, is that short-term interest rates in the US, the UK, Europe and Japan are very close to 0%. While in theory, and practice, they could become negative, they are in our view unlikely to fall much further. This means that the prices of many bonds in the market cannot go much higher; in practice, they are more likely to go down. (By how much and how soon this might happen is, of course, a matter of uncertainty.) In such a situation, a model that assumes that risks of a bond portfolio are symmetric because they always have been would not provide proper guidance.

In our SAA process, we have incorporated our expectations about a small number of long-term trends that we are confident are likely to continue over the next five years or longer. In particular, our recommended strategic asset allocations reflect two high-conviction views.

First, as noted above, we believe bond yields are, on average, much more likely to rise than to fall over the next five years. Therefore, allocations to fixed-income asset classes are much less likely to serve as high-return, low-risk investments than they have in the past.

Second, we expect that many of the large emerging economies will continue to outpace the developed world in terms of economic growth and financial market development. One implication of this expectation is that we are confident in our belief that, on average, investments in emerging equity markets will continue to produce superior risk-adjusted returns over the next five years.

We blend these long-term views with the expected equilibrium returns to create our forward-looking returns. The main impacts of these views on our model strategic asset allocations are straightforward. First, we recommend that investors hold smaller proportions of their portfolios in Developed Government Bonds and larger proportions in



Cash and Short-maturity Bonds than a view-free application of Black-Litterman would suggest. Second, our recommended allocation to Emerging Markets Equities is larger than these markets’ current proportion of total global market capitalisation would suggest.

Trading off risk and return

Personalising risk

Once we have used Black-Litterman to create our blended forward-looking returns, this is the point at which we depart from the next step in a typical Black-Litterman process. Usually that step would be optimising between the forward-looking returns and a standard technical measure of risk, such as volatility. However, volatility is problematic as a risk measure: It penalises positive deviations from the expected outcome as much as it does negative deviations. This is not what ‘risk’ means to investors. The chance that you could get 5% more than you expect is not a risk to be suppressed in the optimisation, but a desirable outcome to be encouraged.

So instead of using volatility as risk, we use our own Behavioural Risk measure. This measure penalises potential negative deviations from expected outcomes by weighting progressively worse potential outcomes more heavily (because from an investor’s point of view they add to risk), but treats potential positive deviations by giving them negative weight (because they reduce an asset’s risk from an investor’s point of view). That way, when our optimisation procedure minimises risk, it’s not aimed at the same time at eliminating the chance of great outcomes. This is much more closely connected to our behavioural understanding of risk, and links directly to the Risk Tolerance scale in our Financial Personality Assessment™. It also means that our risk measure accounts for ‘fat tail’ events and asymmetry of asset returns, which can’t be accommodated in the standard risk measures.

Subsequently, from optimising return against this more realistic and personalised view of risk, the investor should feel more comfortable with their portfolio allocation. We generate five SAA model portfolios corresponding to five different tolerances of ‘risk’.

Reducing dependence on historical data

Basic return estimates rely on statistics that don’t precisely measure what we need to know. We have already noted that the estimates of asset class capitalisation vary in quality, and some are shaky. Even for the asset classes where reliable data are available, the notion of using total market capitalisation at one point in time as a basis for advice regarding multi-year investment strategies is problematic. If, for example, bond prices rise for a period of years and stock markets decline, the total market capitalisation of the fixed-income asset classes will increase and that of equities will decline. If we’re using market capitalisation as the basis for strategic asset allocation, our process would lead us to increase our allocation to bonds and decrease the equity allocation. But doing exactly the opposite is more likely to be the right advice because after the price moves that led to this outcome, stocks are probably cheap and bonds expensive.

While it makes sense to ground the modelling on a concept of market equilibrium in which relative returns reflect market capitalisation and asset class relative riskiness, the resulting optimised allocations may be distorted by a given market event or period, and biased toward protecting against specific past events. The historical data are all we have, but they reflect experience over only one particular period of time, while investors can draw on what is known about other historical epochs and about how the future may differ from the past when they assess asset class risk.



To address this problem, we apply a statistical technique called ‘re-sampling’. Essentially this involves viewing the actual asset class capitalisation, historical variance and correlation data as one of many possible and equally likely hypothetical histories, where the number of histories can be seen as a measure of the amount of confidence an investor has in their investment information going into the optimisation process.

This technique can be viewed as generating a number of different scenarios that together reflect all of the information we have about the past without assuming that what actually occurred is the only possible history. Rather than use a typical single optimisation on one history, we generate many model portfolios matching different scenarios. The result of combining these multiple models is enhanced diversification and reduced sensitivity to one set of data.

The result of this process – modifying the Black-Litterman model to incorporate our views on forward-looking returns; introducing our more personalised and fuller risk measure, along with re-sampling – defines the asset class weights for model strategic allocations across a range of investor risk tolerances (Figures 5 and 6).

Figure 5: Model strategic asset allocations (SAAs )

Model Portfolio 1 Model Portfolio 2 Model Portfolio 3 Model Portfolio 4 Model Portfolio 5

Asset Class Low Risk Medium-Low Risk Moderate Risk Medium-High Risk High Risk

Cash and Short-maturity Bonds 46% 17% 7% 3% 2%

Developed Government Bonds 8% 7% 4% 2% 1%

Investment Grade Bonds 6% 9% 7% 4% 2%

High Yield and Emerging Markets Bonds 6% 10% 11% 10% 8%

Developed Markets Equities 16% 28% 38% 45% 50%

Emerging Markets Equities 3% 6% 10% 14% 18%

Commodities 2% 4% 5% 6% 5%

Real Estate 2% 3% 4% 6% 7%

Alternative Trading Strategies (ATS) 11% 16% 14% 10% 7%

Source: Barclays.



Figure 6: Our five model strategic asset allocations

Risk Profile 1: Low Risk

Risk Profile 2: Medium-Low Risk

46%

8%6%

6%

16%

3%2%

2%

11%

17%

7%

9%

10%

28%

6%

4%

3%

16%

Risk Profile 3: Moderate Risk

Risk Profile 4: Medium-High Risk 7%

4%

7%

11%

38%

10%

5%

4%

14%

3% 2%4%

10%

45%

14%

6%

6%

10%

Risk Profile 5: High Risk

2% 1% 2%8%

50%

18%

5%

7%

7%

Cash and Short-maturity Bonds

Developed Government Bonds

Investment Grade Bonds

High Yield and Emerging Markets Bonds

Developed Markets Equities

Emerging Markets Equities

Commodities

Real Estate

Alternative Trading Strategies

Source for all charts on this page: Barclays.



Section 4: From model SAAs to customised portfolios How we tailor asset allocations to suit individual investor needs,

and to incorporate tactical adjustments to portfolios.

These model Strategic Asset Allocations (SAAs) are not necessarily the recommended holdings for any particular investor at any particular time. Two further steps are necessary to get to something that we would recommend that investors hold.

The first step we need to take is to understand that an SAA, whether model or customised, represents what we believe the investor should hold on average over the subsequent multi-year period. This particular mix may not be the right allocation to hold at every point in time during that period, and we may recommend incorporating small tactical shifts from one asset class to the other, to reflect short-term views. The difference between the SAA – either model or customised – and the recommended portfolio is our Tactical Asset Allocation (TAA). This will be of interest to many, but not all, investors as we shall see below.

Second, the SAA needs to be customised to reflect two categories concerning the investor’s specific circumstances: (a) their financial situation and (b) their financial personality. The model portfolios are optimised to help meet the long-term risk-return preferences of five different levels of Risk Tolerance, but otherwise suppose that the investors are unhindered by other financial constraints, and are concerned only with the long-term financial efficiency of their portfolio. This allows these portfolios to have the broadest possible application; but there are aspects of individual investors’ circumstances which may require some customisation of these model portfolios.

As examples of financial constraints or circumstances, we might consider what other concentrated positions an investor may hold in a business, property or company stock, and what cash flow is needed by the investor to pay for lifestyle needs and future expenses. Many individuals, for instance, have a sizable portion of their non-investible wealth in personal real estate (their house, vacation homes, etc.). While it’s entirely right that such Personal Holdings are left outside their Investment Portfolio, the existence of these assets often provides a good reason not to double up on exposure to real estate in the asset allocation. For these clients, the right asset allocation is a variant on the model SAA that uses all the technology discussed in this paper to provide the optimal risk-adjusted returns, but without the Real Estate asset class.

The other crucial aspect of investors’ circumstances we need to consider is their Financial Personality.20 Traditional approaches to asset allocation assume that investors have only one objective: maximising long-term risk-adjusted returns. Unfortunately this takes an extremely narrow view that is simply not accurate. Investors ultimately don’t care so much about risk-adjusted returns, as they do about anxiety-adjusted returns. We do not live in the long term. We live in the present. Our experiences along the

20 Our unique behavioural finance-based Financial Personality Assessment™ (FPA) measures an investor’s attitudes toward risk, reactions to investing and preferences for financial decision making along six dimensions. To learn more about our FPA, contact your Barclays representative or visit http://www.investmentphilosophy.net/.

http://www.investmentphilosophy.net/



investment journey are important because they influence how we feel about our investments. And, perhaps more crucially, these experiences are important because our anxiety along the journey leads us to seek emotional comfort – in order to reduce this anxiety – typically in ways that are costly to our ‘optimal’ long-run returns.

Reducing volatility does reduce anxiety, but also tends to drag down long-term returns appropriate to an investor’s Risk Tolerance level. Fortunately, there are cheaper, more targeted, and more efficient ways of attaining the optimal anxiety-adjusted returns than simply reducing risk further than desirable for an investor’s long-run goals. Investors acquire emotional comfort along the journey in many ways: phasing investments slowly over time; choosing products that smooth the short-term journey; or simply monitoring investments less frequently. Which strategies are most effective for an investor depends on their own unique Financial Personality.

There are also changes we can make to the asset allocation to address this need for comfort. For example, some investors have innately high Belief in Skill, which determines whether they are comfortable with taking on the additional risk and potential return of having investment specialists try to beat the market on their behalf. For those high on this scale, the chance of additional returns more than offsets the costs and risks of active management, taking tactical positions, and including inherent skill-based asset classes, such as ATS. But for clients who have a low Belief in Skill, such positions merely increase anxiety and discomfort, thus decreasing anxiety-adjusted returns. In these cases, we deliberately stick to more passive index-based building blocks, follow the SAA rather than the TAA adjustments, and may amend the model SAAs to eliminate the ATS asset class. We believe all of these things make the investor both more comfortable and, therefore, ultimately better off.



Section 5: What’s different? At the start of this white paper, we laid down the four basic principles at the heart of our asset allocation process: meeting clients’ needs, portfolio diversification, accessibility of investments, and the incorporation of our long-term market views as well as our expertise in behavioural finance.

Our asset allocation process represents the culmination of a long-term program of innovation, to allow us to apply these principles to what we do.

In particular, we have focused on:

Expanding the range of asset classes to include Commodities, Real Estate and Alternative Trading Strategies, and then determining the optimal size of these allocations in a way that is consistent with the treatment of stocks, bonds and cash

An investor’s total wealth, which results in many investors with low Risk Tolerance holding more in cash and short-term bonds than advocated in conventional strategic asset allocations

Improving the standard Black-Litterman asset allocation process by using sophisticated statistical techniques that allow us to incorporate uncertainty around the risk-return estimates and to help reduce the sensitivity of the optimised portfolios

Measuring and seeking to mitigate risk in a way that is consistent with what matters to investors: the chance of bad outcomes. Features of asset returns, such as fat tails and asymmetries, are then accounted for

An integrated research and strategy department, so that our views on future macroeconomic developments feed seamlessly into our investment recommendations

Building an innovative approach to measuring individual investor needs – in multiple dimensions – so that we can present the most appropriate Strategic Asset Allocation (SAA) as a starting point

The ability to tailor our model SAA portfolios to help meet investor needs, and, where desired, apply short-term tactical tilts on the portfolio to benefit clients

Our approach to strategic asset allocation at Barclays is one important part of our overall Investment Philosophy. It is a component of the advice we provide clients, but not the whole package. The latter includes substantial tailoring of the implementation to help meet the specific needs of individual clients, both financial and emotional, and also tactical recommendations about where to deploy funds at a particular point in time and how quickly to shift investments from one market to another. Good advice includes recommendations about how to implement one’s asset allocation at any point in time using a combination of managed accounts, structured products, funds and individual securities, selected in light of each investor’s long-term goals and financial personality.



Mathematical appendix: the Strategic Asset Allocation process, step by step In this appendix, we elaborate on the technical details of the

strategic asset allocation methodology discussed in our “Asset

Allocation at Barclays” white paper. By necessity, this section

contains mathematical formulae and notation, however, we do

hope that all readers will be interested in how we incorporate our

behavioural analysis and strategic investment views into the

allocation process.

For an online glossary of mathematical terms, we would suggest visiting: http://mathworld.wolfram.com/

Our Strategic Asset Allocation (SAA) methodology takes the Black-Litterman21 model as a starting point and builds upon it by reducing estimation error or parameter uncertainty in optimisation inputs through re-sampling (see Step 4). Figure 1 shows a schematic explanation of the process, which is described in greater detail in the remainder of the appendix.

Figure 1: Schematic representation of Barclays’ Strategic Asset Allocation methodology

Multiple Scenario Optimization (step 4)

1. Sample a time-series of N years from adjusted historical data

2. Optimize portfolio based on Behavioural Finance utility

3. Repeat several times over

Global Capital Market Risk

Premium (step 1)

Covariance Matrix from

Historical Data (step 1)

Market Capitalization

Weights(step 1)

Strategic Views(step 2)

Implied Equilibrium Returns(step 2)

New Blended Returns(step 3)

SAA Model Portfolios for Total Wealth (step 5)

43%

10%3%4%

16%

4%

2%

7%

11% 15%

13%

4%

7%

29%

7%

4%

5%

16% 8%

9%

4%

8%

38%

10%

5%

4%

14% 5%6%

3%

8%

45%

13%

6%

3%

11% 4% 4%2%

6%

51%

17%

6%

2%8%

Risk Tolerance T(Risk Profiles: 1,…,5)

Utility Function

FPA

Source: Barclays.

21 Black, F. and Litterman, R., “Global Portfolio Optimization”, Financial Analysts Journal, Sep/Oct 1992; 48,5. pp 28-43.

Quantitative Research Team:

Antonia Lim

Global Head of

Quantitative Research

[email protected]

+44 (0)20 3555 3296

Ricardo Feced

Senior Quantitative Analyst

[email protected]

+44 (0)20 3555 8417

Paul Wesson

Senior Quantitative Developer

[email protected]

+44 (0)20 3555 56598

Shweta Agarwal

Junior Quantitative Analyst

[email protected]

+44 (0)20 3555 3096

Will Morris


[email protected]

+44 (0)20 3134 0476

Jessica Pok


[email protected]

+852 2903 2058

Christian Theis

Macro

[email protected]

+44 (0)20 3555 8409

http://mathworld.wolfram.com/



Step 1: Assemble the input data on excess returns and estimate market weights in the Global Capital Market portfolio The first step involves collecting and estimating the necessary inputs to derive the implied equilibrium returns. These include: the historical excess returns time series to calculate the historical covariance matrix, the Global Capital Market risk premium, and the market capitalisation weights.

Using Bloomberg and FactSet, we collected the historical, end-of-month, closing prices time series for each of the nine asset classes (spanning September 1992 – September 2012). The excess returns were then calculated by subtracting the cash return (3-month LIBOR) from the total returns. Figure 2 is a summary of key historical statistics for each asset class, while Figure 3 shows the historical correlation matrix. Along with the mean excess returns and annualised volatilities, we show skewness22 and excess kurtosis23. The aim of this is to highlight how most of the asset classes under consideration depart from the ‘standard’ assumption of ‘normal distribution’, and exhibit negative skewness and positive excess kurtosis.

Figure 2: Market weights and summary statistics for our nine asset classes (Sep 1992 – Sep 2012)

Market weight

Annualised historical excess

return

Annualised historical volatility Skewness

Excess kurtosis

Cash and Short-maturity Bonds 8% -0.4% 0.2% 0.2 2.7

Developed Government Bonds 30% 2.5% 3.0% -0.1 0.2

Investment Grade Bonds 9% 2.9% 4.5% -0.6 3.1

High Yield and Emerging Markets Bonds 6% 5.7% 9.7% -1.8 9.1

Developed Markets Equities 34% 4.1% 15.4% -0.7 1.6

Emerging Markets Equities 5% 7.8% 24.2% -0.7 1.9

Commodities 4% 3.0% 15.6% -0.6 2.4

Real Estate 1% 7.7% 19.0% -0.8 4.0

Alternative Trading Strategies 3% 3.6% 6.3% -0.8 4.7

Source: Barclays. Past performance is no guarantee of future results.

Figure 3: Correlation matrix for our nine asset classes (Sep 1992 – Sep 2012)

Cash and

Short-maturity

Bonds

Developed Government

Bonds




Emerging Markets Equities Commodities

Real Estate

Alternative Trading

Strategies

Cash & Short-maturity Bonds 1.00 0.37 0.30 0.08 -0.02 -0.08 -0.01 0.10 -0.01

Developed Government Bonds 0.37 1.00 0.68 0.12 -0.14 -0.15 -0.12 0.02 0.01

Investment Grade Bonds 0.30 0.68 1.00 0.56 0.31 0.25 0.20 0.41 0.36

High Yield & Emerging Markets Bonds 0.08 0.12 0.56 1.00 0.72 0.76 0.38 0.74 0.58

Developed Markets Equities -0.02 -0.14 0.31 0.72 1.00 0.80 0.42 0.78 0.61

Emerging Markets Equities -0.08 -0.15 0.25 0.76 0.80 1.00 0.45 0.74 0.64

Commodities -0.01 -0.12 0.20 0.38 0.42 0.45 1.00 0.42 0.46

Real Estate 0.10 0.02 0.41 0.74 0.78 0.74 0.42 1.00 0.55

Alternative Trading Strategies -0.01 0.01 0.36 0.58 0.61 0.64 0.46 0.55 1.00

Source: Barclays. Past performance is no guarantee of future results.

22 Skewness describes the asymmetry of distributions and should be zero for symmetric distributions, such as the Normal distribution. 23 Excess kurtosis measures the excess of probability weight in the tails of the distribution (that is, the ‘thickness’ of the tails), and has a value of 0 for the Normal distribution.



A key characteristic of our asset allocation methodology is its ability to capture these stylised features and allows us to include asset classes that are not normally distributed in our portfolios. This is because, instead of merely using volatility as a measure of risk, we consider a more sophisticated measure that takes into account all the higher moments of the distribution and therefore explicitly captures the total risks of each distribution. In particular, to ensure that these non-normal features are fully reflected in our methodology we construct a non-parametric distribution by bootstrapping24 and re-sampling from the historical return time series (see Step 4).

Figure 2 also presents the market capitalisation weights for each of our nine asset classes. The information on market capitalisation is readily available for equities and bonds but some assumptions need to be made for alternative asset classes. The global market value for the equity and bonds asset classes was drawn from MSCI and Barclays indices, respectively. The weight for Commodities is the notional positions in the futures commodities market (as reported by BIS). Market weight for ATS was calculated from the assets under management by the hedge fund industry (as estimated by BarclayHedge). Finally, the weight for Real Estate was drawn from the FTSE EPRA/NAREIT index.

Step 2: Calculate the implied equilibrium returns and collect Barclays’ strategic long-term views The Black-Litterman methodology begins with the hypothesis that the Global Capital Market portfolio is the optimal mean-variance portfolio of risky assets.25 To understand why this portfolio can be considered ‘optimal’ one has to assume that markets are in equilibrium. This means that the asset prices, and their corresponding aggregate market value, reflect the homogeneous expectations of the performance of the asset classes. If investors have the same expectations about the performance of the different asset classes, but tolerance to risk varies among them, each investor will optimally hold a mixture of the same model portfolio plus a certain amount of cash (or leverage) to match their risk profile. When we aggregate across all investors, we should obtain the Global Capital Market portfolio, which has to be optimal in equilibrium.

By performing a reverse optimisation, we can infer the expected returns that would be required in order to make the Global Capital Market portfolio optimal. These are the equilibrium returns that are calculated from the Capital Asset Pricing Model (CAPM) equation:

ei mktwµ λ= Ω (1)

where eiµ is the implied excess returns equilibrium vector, λ is a scaling parameter, Ω

is the covariance matrix of historical excess returns, and mktw is the vector of market

capitalisation weights corresponding to the Global Capital Market portfolio. The scaling factor was estimated assuming a risk premium of 6.4% for developed equities, a value

24 Bootstrapping is a statistical method for estimating the sampling distribution of a random variable on the basis of observed data when the probability distribution of the observed sample is unknown. The sampling distribution is estimated by sampling with replacement from the observed data, and is often used as a robust alternative to inference based on parametric assumptions when those assumptions are in doubt, or where parametric inference is impossible or requires very complicated formulas for the calculation of standard errors. It is also used frequently for the purpose of deriving robust estimates of standard errors and confidence intervals of a population parameter like a mean, median, proportion, odds ratio, correlation coefficient or regression coefficient. It may also be used for constructing hypothesis tests. 25 We know that such an assumption is imperfect because, as noted above, many asset classes do not have a normal distribution. But it gives us a simple and transparent way to a reasonable starting point. Statistical techniques such as re-sampling, discussed below, are used to advance from there.



proposed by our investment management, research and investment strategy teams to reflect the equilibrium risk premium of the asset class.

The equilibrium excess returns are presented in Figure 4. As we can see from equation (1), equilibrium returns follow from risk premium assumption, market capitalisation weights, volatility and correlation among the asset classes. Their values can be regarded as fair values of expected returns for the assets given their long-term risk characteristics, as argued in the CAPM methodology. Note, however, that historical returns may differ from their equilibrium values as some asset classes may have exhibited anomalous returns with respect to their risk levels in the recent past.

We have calculated the equilibrium excess returns from a mean-variance optimisation argument, so these equilibrium returns should also be considered an approximate starting point. However, if investors’ views deviate from the expected equilibrium market returns, they will hold a portfolio that is slightly different from the Global Capital Market portfolio. Similarly, the size of the active position will depend on the degree of confidence in these views. Barclays’ Research and Strategy team periodically produces a five-year strategic view on all the main asset classes. These forward-looking views, shown in Figure 4, are used in our asset allocation process to tilt our portfolios away from the equilibrium Global Capital Market portfolio solutions, with the objective of enhancing performance.

As shown in Figure 4, in particular, Barclays’ views for the next five years are sub-zero on Developed Government Bonds, and positive on Emerging Markets Equities, and High Yield and Emerging Markets Bonds.

Figure 4: Equilibrium excess returns and Barclays’ views* for our nine asset classes

Equilibrium

excess returns Barclays’ views

on excess returns

Cash and Short-maturity Bonds 0.0% 0.0%

Developed Government Bonds 0.0% -1.6%

Investment Grade Bonds 0.9% -0.3%

High Yield and Emerging Markets Bonds 3.4% 3.8%

Developed Markets Equities 6.4% 6.4%

Emerging Markets Equities 8.9% 11.0%

Commodities 3.4% 2.6%

Real Estate 6.8% 3.8%

Alternative Trading Strategies 1.8% 3.8%

* Barclays’ views on excess returns, for the next five years. There is no guarantee that these returns will be achieved. Source: Barclays.

Step 3: Combine the expected equilibrium returns with Barclays’ strategic long-term views Our next objective is to calculate forward-looking returns that incorporate both the current market view (equilibrium returns) and Barclays’ long-term views for each asset class (strategic views). The forward-looking returns will be a weighted average of the equilibrium excess returns and the strategic views, where the relative weights depend on our degree of confidence in the views. We have assumed a low confidence on all our views – so that the final expected returns remain grounded in those implied by the equilibrium analysis, and need only to be tweaked toward our forward assessments.



The mixing process follows a Bayesian analysis.26 The prior distribution for the assets returns is assumed to be Gaussian,27 with a mean equal to the equilibrium returns, and covariance proportional to the historical covariance:

, ~ (0, )ei i ir Nµ ε ε= + Ω (2)

where eiµ is the implied excess returns equilibrium vector, i the asset class, ε a vector

of Gaussian residuals, and Ω is the historical covariance matrix. Assuming that our

views vµ are on average correct (i.e., expected values are equal to r) – with an

uncertainty proportional to the volatility of each asset class and weighted by our confidence on the particular view – we can write:

, ~ (0, )vi i i ir Nµ η ζ ζ= + Ω (3)

Where ζ is the vector of Gaussian residuals independent of ε , η is a vector that

measures our confidence in the views. Other assumptions are possible for combining equilibrium and subjective views, but this is a simple and reasonable approach. Small values for iη should be used when our confidence on the view for asset i is high (i.e., low

uncertainty), while a high value for iη will indicate low confidence (i.e., high

uncertainty).

Following the Bayesian analysis, the posterior distribution ( | )vf r µ can be calculated in

terms of the prior ( )f r and the conditional distribution ( | )vf rµ as:

( | ) ( )( | )

( | ) ( )

vv

v

f r f rf r

f r f r drµµµ

=∫

(4)

The expected returns of the posterior distribution are the Black-Litterman blended or tilted returns. If we stack the confidence vector η in the diagonal of a square matrix (let us still call it η), the blended expected returns are calculated as:

( ) ( )11 1 1 1 1 1 1 1BL e vµ η η µ η η µ−− − − − − − − −= Ω + Ω Ω + Ω (5)

The Barclays investment committee decided to have low confidence on all the views. As confidence levels increase the portfolio will be tilted according to our views. We checked for sensitivity of the asset allocation to various levels of confidence and found that as the confidence level increases the allocation favours ATS over bonds, without significantly affecting the equity content.

Since we would like to consider the full distribution for the asset excess returns in the optimisation process, we ‘shift’ the historical time series of excess returns so that their mean values coincide with Black-Litterman blended expected returns as follows:

( ) ( )BL h BLi i i ir t r t µ µ= − + (6)

where hµ is a vector of mean historical excess returns. The adjusted historical time series

have forward-looking expected returns that correspond to the Black-Litterman blended

26 Bayesian analysis is a statistical procedure which endeavours to estimate parameters of an underlying distribution based on the observed distribution or update a prior distribution in the light of new, relevant information. In practice, it is common to assume a suitable parametric distribution over the appropriate range of values for a prior distribution. For more information see: http://mathworld.wolfram.com/BayesianAnalysis.html

27 In statistics, a Gaussian (or Normal) distribution is a distribution of the form: −= −

2

2

( )( )

2x b

f x aec

The shape of a Gaussian function is the characteristic symmetric “bell curve” shape that quickly falls off towards plus/minus infinity. For more information see: http://mathworld.wolfram.com/NormalDistribution.html

http://mathworld.wolfram.com/BayesianAnalysis.html

http://mathworld.wolfram.com/NormalDistribution.html



returns, and distributions, correlations and risk characteristics that correspond to the last 20 years of historical performance.

Step 4: Combine the resulting blended returns with investors’ risk characteristics to produce optimised portfolios Once we’ve obtained the adjusted historical time series returns (6), we can proceed with the optimisation process. The objective of this process is to find the possible combination of the nine asset classes that maximises the expected utility (Desirability) of investors with given Risk Tolerance T and a target horizon of one year, thereby finding the portfolio that optimises the trade-off between risk and return. The optimisation steps are summarised in Box 1.

Box 1: Optimisation process

1. We sample a time series of N years consisting of N annual excess returns from the vector of adjusted historical (monthly) time series BLr

2. For a given year k and a given portfolio w, its excess annual log-return is calculated:

( , ) log(1 ( ))i iir k w w R k= + Σ

where i is the asset class index, k is the year index (1 to N) and ( )iR k is the vector of one-year excess returns for each of the assets.

3. We generate the optimal portfolio ( optw ) that maximises the investor’s utility function:

2 r(k,w)-

k

1U(r) ( ) 1- e

NTw = ∑

and calculate the required compensation for risk and Desirability for the investor with Risk Tolerance level T.

4. We repeat this process several (M) times (re-sampling) to reduce the sensitivity of the portfolios to small input changes.

The solution for the final optimal portfolio ( optfinalw ) will be a function of the length of

the time series of adjusted excess returns (N) and the number of times the process is repeated (M). In our simulations, we consider a moderate value for N and a value for M that ensures relative stability in the portfolio weights.

Two important innovations of our approach to portfolio optimisation are the use of the Behavioural Finance Utility function and the regularisation of the optimisation outcomes through re-sampling. We now describe these two aspects of the optimisation process in greater detail.

The investors’ utility function A key input into our optimisation process is the investor’s utility function. When thinking about all the factors that influence peoples’ financial decisions, we believe that stable, rational preferences for outcomes in the long run should form the core of any optimisation process. We express these preferences in the form of a concave (risk-averse) utility function, which penalises negative financial outcomes while rewarding positive outcomes. The use of this function captures attitudes to risk that are more sophisticated than simply trading off the mean and variance of a portfolio. This



specifically allows us to consider asset classes with non-normal returns distributions (i.e., with skewness and excess kurtosis) and to incorporate comprehensive downside risk attitudes rather than solely attitudes to volatility.

Different functions have different implications for how risk attitudes change across the range of returns. We believe that a CRRA (constant relative risk aversion) utility function is most appropriate to model long-term risk/return preferences. It is in line with evidence that risk attitudes, relative to total wealth, are fairly consistent on average across wealth levels, and remain so over prolonged periods of time. More importantly, we have no accurate way of predicting how the attitudes of an individual client will change as their wealth changes. When determining the optimal attitude to long-term risks it is better to assume that these will be constant, however, it is vital to regularly review the client’s risk attitude and adjust the optimal portfolio accordingly.

The only functional forms that satisfy CRRA, when log returns are used, are the exponential functions. The exponential utility function is equivalent to the better known power utility function when applied to wealth levels rather than returns. Since we are aiming to optimise allocations over the client’s entire investment portfolio, it is important to gauge risk, relative to total wealth (considering risk attitudes for much smaller investments may lead to highly inaccurate assessments). Using a utility function over log returns enables us to apply the same function regardless of the wealth level of the clients. It is concerned with relative returns on total wealth, regardless of the specific starting wealth level. The utility function is parameterised by means of a Risk Tolerance parameter calibrated to our proprietary Risk Tolerance scale28, and grounded in knowledge of behavioural finance, to ensure that the totality of the ‘risk’ of portfolios (and not just volatility) is reflected. The precise form of the utility function is:

2

-U(r) 1-e

rT= (7)

where r are 1-year excess log-returns for the portfolio and T is the Risk Tolerance parameter. The lower the degree of Risk Tolerance (low T) the more the function will penalise negative potential outcomes, and the more risk will be avoided in the portfolio as a whole. The values for the Risk Tolerance parameter selected for the different risk profiles are calibrated with a few principles in mind:

They need to reflect rational long-term preferences for risk and return, relative to total wealth. They need to exclude short-term behavioural or emotional risk attitudes that might distort the risk-return optimisation appropriate to a long-term rational investor. (It is our job to help clients overcome irrational investment decision making, not to replicate it.)

When applied to simple naïve portfolios that are combinations of bonds and equities, with relatively normal returns distributions (following the same returns distributions as the methodology above), they should result in portfolio proportions that are in accordance with accepted industry norms in terms of the risk exhibited for low-, medium- and high-risk portfolios.

They need to result in risk-return trade-offs that feel intuitive when considering long-term investments with the total investment portfolio.

They need to be spread out so as to maximise the differences between consecutive risk profiles, enabling our allocations to cover the range of client Risk Tolerance with as few portfolios as possible.

28 Which can be assessed for any individual, along with five other dimensions of financial personality, by completing Barclays’ Financial Personality Assessment™ (FPA).



In the following Figure 5, we observe the utility function for three values of the T parameter, for risk profiles 1, 3, and 5 respectively:

Figure 5: The utility function for three values of the T factor

-100%

-80%

-60%

-40%

-20%

0%

20%

40%

60%

80%

100%

-25% -15% -5% 5% 15% 25%

Risk Profile 1

Risk Profile 3

Risk Profile 5

Utility

Log returns

Source: Barclays.

As we’ve already pointed out, these utility functions allow us to construct a more comprehensive and accurate measure of risk, incorporating individual preferences for skewness and kurtosis in addition to variance. This measure, which we call ‘Behavioural Variance’ ( 2

Bσ ) is given by:

( )2 ( )2

2 ln2

E r r

TB

TE eσ

− =

(8)

where E(r) is the expected return. The risk measure can be approximated in a more

useful form that explicitly shows how it accounts for skewness and kurtosis:

2

2 22

21

3 3B skew kurtT Tσ σσ σ

≈ − +

(9)

This shows that, if the distribution is normal, Behavioural Variance reduces to the variance of the distribution as skewness and kurtosis are both zero. However, if the distribution is not normal, this new measure adjusts the variance to account for the specific preferences for skewness and kurtosis that would be showed by an investor with the exponential utility function and Risk Tolerance of T. Specifically, positive skewness reduces the risk of the investment; and positive kurtosis (‘fat tails’) increases the risk of the investment. For most of our nine asset classes – which show negative skewness and positive kurtosis – this demonstrates that variance understates the true risk of the asset class.

More importantly, compared to the standard mean-variance analysis, Behavioural Variance allows us to determine, in a simpler and more intuitive way than the standard mean-variance analysis, how a specific investor trades-off risk and return. The total excess return of an investment or portfolio breaks down simply into two components. The first is the cost of the risk for the individual investor – and more risk tolerant investors will naturally require lower compensation for taking on an equivalent amount of risk. The second is the remainder, the psychological ‘profit’ in the investment after the investor has been compensated for taking on risk. We term this latter piece the Desirability of the investment – the returns that remain after compensating the



investor for the risks taken. The trade-off between risk and return for each risk profile, then, is accurately expressed by

2

( ) BE R DTσ

= + (10)

The compensation required for the risk of the investment is given by 2B

Tσ

, the Behavioural

Variance divided by Risk Tolerance. The Desirability (D) is what is left over.

An investor will choose to invest in any portfolio that has positive Desirability – it has positive returns after deducting the compensation for taking on the risk – while investments with negative Desirability will be rejected in favour of cash. In optimising a portfolio, we seek not just to achieve positive Desirability, but to maximise it. The portfolio with maximum expected utility is exactly the same as that which optimises Desirability, although Desirability is more readily interpretable since it is measured in units of returns (the surplus return after compensating for risk). So our SAAs are optimised to provide the maximum possible returns after deducting risk costs.

This can be illustrated using a simple example. Imagine a portfolio with expected excess returns of 5%, and volatility of 10%. If the returns distribution is normal then the true behavioural risk measure for any individual will be the same as the variance, so

( )22 2 10% 1%Bσ σ= = = . A client with a Risk Tolerance parameter of T=1 would require 2 1%

1%1

B

Tσ

= = to compensate them for taking on this risk. The Desirability of this

investment is thus 2

5% 1% 4%BD rTσ

= − = − = . The investor would be very happy to

hold this investment since the psychological cost of risk is only 1% out of total excess returns of 5%. By contrast, an investor with very low Risk Tolerance of T=0.2 would have

a risk cost of 2 1%

5%0.2

B

Tσ

= = for the same investment. This means they would not

consider this investment worth holding. This cautious investor would be indifferent about holding this investment and holding cash, despite the 5% excess returns.

The framework is shown graphically in Figure 6. The curve shows the accept/reject line for an investor with Risk Tolerance T. All investments above this line have positive Desirability. Our portfolio optimisation is designed to find the combination of asset classes that give this investor the highest possible Desirability. The advantage of this approach is that it makes explicit the cost of risk to each investor, and does so in a way that can be measured directly in terms of returns.

Figure 6: ‘Desirability’ and the trade-off between risk and return

Risk free return

r

fr

Bσ

Reject

Accept

Desirability

Risk compensation

2Br

Tσ

=Maximum Desirability

Source: Barclays.



Re-sampling The optimal portfolio found in Step 3 of the optimisation process is likely to exhibit great sensitivity to the input parameters such as the forward-looking expected returns assumptions and the Risk Tolerance of the investors. The portfolios may not evolve smoothly across risk profiles. They may vary dramatically when we change, even marginally, some of the assumptions that led to the blended expected returns (these may include the composition of the market portfolio or our views on the assets). This sensitivity is an inherent problem of portfolio optimisation, which seeks to exploit as much as possible any inconsistencies or arbitrage opportunities in the input data. In fact, one of Black and Litterman’s main motivations was to find a solution to this sensitivity problem.

The statistical technique we use to deal with this problem and to regularise the outcome of the optimisation was introduced by Richard O. Michaud29 and is generically known as re-sampling. One of the benefits of the technique is that it enhances diversification30 in the portfolios and provides a smooth evolution in the allocation across different risk profiles. Re-sampled portfolios are also generally less sensitive to changes in assumptions.

The idea behind this technique is essentially to repeat the optimisation process a number (M) of times and to average the weights of the optimal portfolios obtained in each simulation. The final optimal portfolio ( opt

finalw ) for each risk profile can thus be

written as:

1

1 Mopt optfinal j

j

w wM =

= ∑ (11)

where optjw is the optimal portfolio obtained in simulation j.

The outcome of the optimisation will depend on the number of simulations (M) and the length of the sampled time series of adjusted excess returns (N). The parameter M should be large enough so that the optimisation reaches convergence, while the parameter N should be selected according to the degree of desired regularisation. Small values of N are equivalent to imprecise estimations of the assets’ expected returns. These lead to greater variety among the optimisation outcomes – hence, to a more diversified final portfolio and lower sensitivity to input parameters. In contrast, when N becomes very large, all the optimisations will essentially yield similar results and the effect of averaging will be diminished. In our simulations, we considered a moderate value for N and a value for M that ensured convergence in the portfolio weights.

29 Michaud, R. and Michaud, R. (2008), “Estimation Error and Portfolio Optimization: a Re-sampling Solution”, Journal of Investment Management, Vol. 6, No. 1, pp. 8-28. 30 Diversification does not guarantee a profit or protect against loss.



Step 5: Present five strategic asset allocation portfolios, along with accompanying risk measures

Allocation

The strategic asset allocation portfolios finally calculated are summarised in Figure 7:

Figure 7: Strategic Asset Allocation portfolios

Risk profile

Asset class 1 2 3 4 5

Cash and Short-maturity Bonds 46% 17% 7% 3% 2%

Developed Government Bonds 8% 7% 4% 2% 1%

Investment Grade Bonds 6% 9% 7% 4% 2%

High Yield and Emerging Markets Bonds 6% 10% 11% 10% 8%

Developed Markets Equities 16% 28% 38% 45% 50%

Emerging Markets Equities 3% 6% 10% 14% 18%

Commodities 2% 4% 5% 6% 5%

Real Estate 2% 3% 4% 6% 7%

Alternative Trading Strategies 11% 16% 14% 10% 7%

Source: Barclays.

The aggregated allocation for Equities, Fixed Income and Alternatives is:

Figure 8: Aggregated broad asset class strategic allocation

Risk profile Equity Fixed income Alternatives Total

1 19% 66% 15% 100%

2 34% 43% 23% 100%

3 48% 29% 23% 100%

4 59% 19% 22% 100%

5 68% 13% 19% 100%

Source: Barclays.

Figure 9: Asset allocation for different risk levels

0%

20%

40%

60%

80%

100%

1 2 3 4 5

Cash and Short-maturity Bonds

Real Estate

Alternative Trading Strategies

Commodities



Developed Government Bonds

Emerging Markets Equities


Allocation

Risk level Source: Barclays.



Risk and performance Behavioural Variance, and consequently Behavioural Volatility ( Bσ ), constitutes a more

comprehensive and accurate measure of risk than volatility. However, volatility – expressed as the annualised standard deviation of the portfolio excess returns – is still widely used and can provide a useful and familiar measure of the risk level.

Standard risk and return measures for the five SAA model portfolios are shown in Figure 10:

Figure 10: Excess return, volatility and the Sharpe ratio* for the five portfolios

Risk profile Excess return

(annual) Volatility (annual) Sharpe Ratio

1 2.0% 4.6% 0.43

2 3.4% 8.0% 0.43

3 4.5% 10.5% 0.43

4 5.3% 12.5% 0.43

5 5.9% 13.9% 0.42

Source: Barclays. *The Sharpe Ratio (William Sharpe) is a risk-adjusted financial measure which uses an investment’s excess return and standard deviation as a measure of risk to determine the reward per unit of risk. It is given by:

σ−

=( )rfr r

s where r is the investment return, rrf is the risk-free return and σ is the standard deviation of the

investment’s returns. For more information see: http://mathworld.wolfram.com/SharpeRatio.html.

The risk-return trade-off is captured by the efficient frontier, which plots the volatility for the different risk profiles against their forward-looking excess returns (Figure 11).

Figure 11: The efficient frontier

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0%

Volatility (annual)

Excess Returns (annual)

Source: Barclays.

The behavioural risk and return measures described in Step 4 (corresponding to our Strategic Asset Allocation portfolios) are shown in Figure 12.

http://mathworld.wolfram.com/SharpeRatio.html



Figure 12: Behavioural-adjusted risk and return measures for the five portfolios

Risk profile Behavioural

volatility Log excess

returns Risk

compensation Desirability

1 4.7% 1.9% 0.9% 0.9%

2 8.2% 3.1% 1.4% 1.7%

3 10.8% 3.9% 1.6% 2.3%

4 12.9% 4.5% 1.7% 2.8%

5 14.3% 4.9% 1.7% 3.2%

Note: Figures are based on monthly returns from October 1992 to September 2012. Source: Barclays.

We can examine the breakdown of total returns for each of these portfolios into the components of compensation for risk and Desirability (Figure 13). Each degree of Risk Tolerance T implies a specific trade-off between risk and return, and the optimal portfolio for each risk profile gives the maximum possible Desirability for investors with that degree of Risk Tolerance (they provide the greatest surplus return after compensating that investor for risk). The implication of this is that investors in each risk profile have the portfolio that is optimal for their level of T, and they should prefer this portfolio to any of the others. Note that the risk compensation values given here are only appropriate for the investors in that risk profile. Investors in other risk profiles will have different values for T, and thus require different compensation for the same risks. They will also, therefore, have lower Desirability for each of the portfolios other than their optimal one.

Figure 13: Desirability and excess returns for the five portfolios

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00%

Risk Compensation

Desirability

Excess Returns

Excess Returns (annualised log)

Behavioural Volatility (Annual) Source: Barclays.

Barclays believes the information contained herein to be reliable but cannot guarantee its accuracy. The figures used in the charts above are assumptions and may not be representative of actual investment results.

Simulated, modeled, or hypothetical performance results have certain inherent limitations. No representation is being made that any client will or is likely to achieve the hypothetical returns represented above. Such results are hypothetical and do not represent actual trading, and thus may not reflect material economic and market factors, such as liquidity constraints, that may have had an impact on Barclays actual decision making. Actual returns may vary. Scenarios are for illustrative purposes only.

This document has been prepared by the wealth and investment management division of Barclays Bank plc (“Barclays”), for information purposes only. Barclays does not guarantee the accuracy or completeness of information which is contained in this document and which is stated to have been obtained from or is based upon trade and statistical services or other third party sources. Any data on past performance, modelling or back-testing contained herein is no indication as to future performance. No representation is made as to the reasonableness of the assumptions made within or the accuracy or completeness of any modelling or back-testing. All opinions and estimates are given as of the date hereof and are subject to change. The value of any investment may fluctuate as a result of market changes. The information in this document is not intended to predict actual results and no assurances are given with respect thereto.

The information contained herein is intended for general circulation. It does not take into account the specific investment objectives, financial situation or particular needs of any particular person. The investments discussed in this publication may not be suitable for all investors. Advice should be sought from a financial adviser regarding the suitability of the investment products mentioned herein, taking into account your specific objectives, financial situation and particular needs before you make any commitment to purchase any such investment products. Barclays and its affiliates do not provide tax advice and nothing herein should be construed as such. Accordingly, you should seek advice based on your particular circumstances from an independent tax advisor. Neither Barclays, nor any affiliate, nor any of their respective officers, directors, partners, or employees accepts any liability whatsoever for any direct or consequential loss arising from any use of or reliance upon this publication or its contents, or for any omission. Past performance does not guarantee or predict future performance. The information herein is not intended to predict actual results, which may differ substantially from those reflected.

The products mentioned in this document may not be eligible for sale in some states or countries, nor suitable for all types of investors. This document shall not constitute an underwriting commitment, an offer of financing, an offer to sell, or the solicitation of an offer to buy any securities described herein, which shall be subject to Barclays’ internal approvals. No transaction or services related thereto is contemplated without Barclays’ subsequent formal agreement. Unless expressly stated, products mentioned herein are not guaranteed by Barclays Bank plc or its affiliates or any government entity.

This document is not directed to, nor intended for distribution or use by, any person or entity in any jurisdiction or country where the publication or availability of this document or such distribution or use would be contrary to local law or regulation, including, for the avoidance of doubt, the United States of America. It may not be reproduced or disclosed (in whole or in part) to any other person without prior written permission. You should not take notice of this document if you know that your access would contravene applicable local, national or international laws. The contents of this publication have not been reviewed or approved by any regulatory authority.

Barclays Capital Inc., Member SIPC, Barclays Bank plc and / or their affiliated companies and/or the individuals associated therewith (in various capacities) may already have or intend to: (i) seek investment banking or other business relationships for which they already receive or will receive compensation from the companies that are the subject of this publication (“Researched Companies”), such as underwriting, advising, and lending – as such, it is possible that Barclays Capital Inc., Barclays Bank plc or their affiliated companies may have managed or co-managed a public offering of securities for any issuer mentioned in this document within the last three years.; (ii) have an interest in the Researched Companies by acting making a market or dealing as principal in securities issued by Researched Companies or in options or other derivatives based thereon, or otherwise hold personal interests in the Research Companies; (iii) appoint employees or associates as directors or officers of the Researched Companies; (iv) act upon the contents of this publication prior to your having received it; (v) effect transactions which are not consistent with the recommendations given herein.

Cyprus – Barclays Bank PLC is registered in England and is authorised and regulated by the Financial Services Authority. Registered No. 1026167. Registered Office: 1 Churchill Place, London E14 5HP. Barclays Bank PLC is authorised by the Central Bank of Cyprus to conduct banking and investment business. France – Barclays Bank PLC, Succursale en France - Principal établissement : 32 avenue George V - 75008 Paris - RCS Paris B 381 066 281 - C.C.P. 62-07 Paris - Siège social à Londres E14 5HP, Angleterre, 1, Churchill Place - Reg N° 1026167 - Capital autorisé 3 040 001 000 de Livres Sterling. BARCLAYS BANK PLC est un établissement de crédit, intermédiaire en assurance (l’immatriculation auprès du FSA peut être contrôlée sur le site internet www.orias.fr), prestataire de service d’investissement de droit anglais agréé par the Financial Services Authority (FSA), autorité de tutelle britannique qui a son siège social 25 The North Colonnade, Canary Wharf, Londres E14 5HS. (www.fsa.gov.uk), FSA register n° 122702 La Succursale française de Barclays Bank PLC, est autorisée par le FSA à recourir à un Agent lié, Barclays Patrimoine SCS. Gibraltar – Barclays Bank PLC is registered in England and authorised and regulated by the Financial Services Authority. Registered No. 1026167. Registered Office: 1 Churchill Place, London E14 5HP. Barclays Bank PLC is authorised by the Gibraltar Financial Services Commission to conduct banking and investment business in Gibraltar. Guernsey – Barclays Bank PLC is registered in England and is authorised and regulated by the Financial Services Authority. Registered Number: 1026167. Registered Office: 1 Churchill Place, London E14 5HP. Barclays Bank PLC, Guernsey Branch is licensed by the Guernsey Financial Services Commission under the Banking Supervision (Bailiwick of Guernsey) Law 1994, as amended, and the Protection of Investors (Bailiwick of Guernsey) Law 1987, as amended, Barclays Bank PLC, Guernsey Branch has its principal place of business at Le Marchant House, St Peter Port, Guernsey, GY1 3BE. Ireland – Barclays Bank Ireland PLC is regulated by the Central Bank of Ireland. Registered in Ireland. Registered Office: Two Park Place, Hatch Street, Dublin 2. Registered Number: 396330. In the provision of certain corporate, investment banking and wealth products and services, Barclays Bank Ireland PLC acts as agent for Barclays Bank PLC. Barclays Bank PLC. Registered in England. Registered Number: 1026167. Registered Office: 1 Churchill Place, London, E14 5HP. Barclays Bank PLC is authorised and regulated by the Financial Services Authority. Calls will be recorded for quality and security purposes. Isle of Man – Barclays Bank PLC is registered in England and is authorised and regulated by the Financial Services Authority. Registered Number: 1026167. Registered Office: 1 Churchill Place, London E14 5HP. Barclays Bank PLC, Isle of Man Branch is licensed by the Isle of Man Financial Supervision Commission. Barclays Bank Plc, Isle of Man Branch has its principal business address in the Isle of Man at Barclays House, Victoria Street, Douglas, Isle of Man. Italy – Barclays, attraverso Barclays Bank PLC e le sue controllate, offre ai propri clienti servizi e prodotti di wealth management e di gestione degli investimenti. Barclays Bank PLC è iscritta nel Regno Unito ed è soggetta all’autorizzazione ed alla regolamentazione della Financial Services Authority. Il rispettivo numero di registrazione è 1026167 e la sua sede legale è in Churchill Place, Londra E14 5HP. Barclays Bank PLC – Via della Moscova 18 – 20121 Milano è iscritta all’albo delle banche n. 4862, Registro Imprese Milano n. 80123490155 R.E.A. Milano n. 1040254 – Cod. Fiscale 80123490155 Partita IVA 04826660153 Le informazioni presenti in questo documento non costituiscono una raccomandazione, una sollecitazione o un invito all’acquisto o alla vendita di alcuno strumento finanziario né costituiscono una consulenza strumentale all’investimento in strumenti finanziari. I rendimenti conseguiti in passato non sono garanzia di rendimenti futuri. Monaco – Barclays Bank PLC is registered in England and authorised and regulated by the Financial Services Authority. Registered No. 1026167. Registered Office: 1 Churchill Place, London E14 5HP. Barclays Bank PLC, Succursale en Principauté de Monaco - 31, avenue de la Costa, MC 98000 Monaco - is a branch of Barclays Bank PLC, and registered with the Monaco Chamber of Commerce and Industry under no 68 S01191. Registered VAT No FR 40 00002674 9. Nigeria – Barclays Bank PLC is registered in England and authorised and regulated by the Financial Services Authority. Registered No.1026167. Registered Office: 1 Churchill Place, London E14 5HP. Barclays Group Representative Office (Nigeria) Ltd. Registered Company No: RC41757 and its mailing address is Barclays Group Representative Office (Nigeria) Ltd, Courier Department, 3rd Floor, 1 Churchill Place, London, E14 5HP. Portugal – Barclays Bank PLC is registered in England and authorised and regulated by the Financial Services Authority. Registered No. 1026167. Registered Office: 1 Churchill Place, London E14 5HP. Barclays Bank PLC activity in Portugal is supervised by Banco de Portugal (BoP) and Comissão de Mercado de Valores Mobiliários (CMVM). Qatar – Barclays Bank PLC is registered in England and is authorised and regulated by the Financial Services Authority. Registered No. 1026167. Registered Office: 1 Churchill Place, London E14 5HP. Barclays Bank PLC in the Qatar Financial Centre (Registered No. 00018) is authorised by the Qatar Financial Centre Regulatory Authority. Barclays Bank PLC QFC Branch may only undertake the regulated activities that fall within the scope of its existing QFCRA authorisation. Principal place of business in Qatar: Qatar Financial Centre, Office 1002, 10th Floor, QFC Tower, Diplomatic Area, West Bay, PO Box 15891, Doha, Qatar. This information has been distributed by Barclays Bank PLC. Related financial products or services are only available to Business Customers as defined by the QFCRA. Saudi Arabia – Barclays offers wealth and investment management products and services to its clients through Barclays Bank PLC and its subsidiary companies. Barclays Saudi Arabia is a closed joint stock company with its registered office at Level 18, Al Faisaliah Tower, King Fahad Road, Riyadh 11311, Saudi Arabia. Authorised and regulated by the Capital Market Authority (CMA Licence No. 09141-37). Commercial Registration Number 1010283024. South Africa – Barclays offers wealth and investment management products to its clients through Barclays Bank PLC and its subsidiaries. Absa Bank Limited t/a ABSA Private Bank. Registration number: 1986/004794/06. Authorised financial services Licence No 523 and registered credit provider NCRCP7. Spain – Barclays Bank, S.A.U. es un banco español regulado por el Banco de España e inscrito en el registro de bancos y banqueros del Banco de España con el nº 0065. Domicilio social: Plaza de Colón, 1 28046 Madrid. Inscrito en el R.M. Madrid, T. 3755, F.1, Hoja M62564, I. 1381. NIF: A47001946. Barclays Bank, S.A.U. es una filial de Barclays Bank PLC, autorizado y regulado por la Autoridad de los Servicios Financieros, e inscrito en Inglaterra con el no: 1026167. Domicilio social 1 Churchill Place, London, E14 5HP. Switzerland – Barclays Bank (Suisse) SA - Switzerland. Barclays Bank (Suisse) SA is a Swiss Bank regulated and supervised by FINMA. Registered in Switzerland. Registered No. 1381/1986. Registered Office: Chemin de Grange-Canal 18-20, P.O. Box 3941, 1211 Geneva 3, Switzerland. Registered VAT No. 288 787. Barclays Bank (Suisse) SA is a subsidiary of Barclays Bank PLC registered in England and authorised and regulated by the Financial Services Authority. Registered number is 1026167 and its registered office is 1 Churchill Place, London E14 5HP. United Arab Emirates – Barclays Bank PLC is registered in England and authorised and regulated by the Financial Services Authority. Registered No. 1026167. Registered Office: 1 Churchill Place, London E14 5HP. Barclays Bank PLC in the UAE is regulated by the Central Bank of the U.A.E. and is licensed to conduct business activities as a branch of a foreign bank in the UAE ( Dubai Licence No.: 13/1844/2008, Registered Office: Building No. 6, Burj Dubai Business Hub, Sheikh Zayed Rd, Dubai City) and Abu Dhabi (Licence No.: 13/952/2008, Registered Office: Al Jazira Towers, Hamdan Street, PO Box 2734, Abu Dhabi). United Arab Emirates (Dubai International Financial Centre) – Barclays Bank PLC is registered in England and authorised and regulated by the Financial Services Authority. Registered No. 1026167. Registered Office: 1 Churchill Place, London E14 5HP. Barclays Bank PLC in the Dubai International Financial Centre (Registered No. 0060) is regulated by the Dubai Financial Services Authority. Barclays Bank PLC DIFC Branch may only undertake the financial services activities that fall within the scope of its existing DFSA licence. Principal place of business: Wealth and investment management, Dubai International Financial Centre, The Gate Village Building No. 10, Level 6, PO Box 506674, Dubai, UAE. This information has been distributed by Barclays Bank PLC DIFC Branch. Related financial products or services are only available to Professional Clients as defined by the DFSA. Barclays Bank PLC is registered in England and authorised and regulated by the Financial Services Authority. Registered No. 1026167. Registered Office: 1 Churchill Place, London E14 5HP.

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Updated July 2013UK0036/CP41760-13

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