asset allocation at barclays · asset allocation at barclays august 2017 1 ... the black-litterman...

Asset allocation at Barclays

White Paper l August 2017

Asset allocation at Barclays August 2017 1

Contents

Introduction 2

Why Asset Allocation? ........................................................................................................ 2

Meeting Client Needs ......................................................................................................... 2

Diversification ...................................................................................................................... 2

We Expand the Range of Asset Classes .................................................................... 3

We Use Sophisticated Risk Measurement and Management Techniques ........ 3

Accessibility .......................................................................................................................... 3

Incorporating Long-Term Views ...................................................................................... 3

Section 1: Overview 5

Which Asset Classes Should be Included in a Client Portfolio? ............................ 5

How Should a Portfolio be Divided Between These Assets? ................................. 5

What Makes Our Asset Allocation Process Unique? ............................................... 6

Section 2: Our Roster of Asset Classes 7

Cash and Short-Maturity Bonds ...................................................................................... 7

Developed Government Bonds ........................................................................................ 8

Investment Grade Bonds ................................................................................................... 8

High Yield and Emerging Markets Bonds ...................................................................... 9

Developed Markets Equities ............................................................................................. 9

Emerging Markets Equities ............................................................................................. 10

Commodities ......................................................................................................................11

Real Estate ...........................................................................................................................11

Alternative Trading Strategies .........................................................................................11

Some of the Things We Haven’t Included ................................................................... 12

Section 3: How Much of Each 14

The Optimal Mix ............................................................................................................... 14

The Asset Allocation Process .......................................................................................... 14

Forward-Looking Returns .................................................................................................15

The Black-Litterman Model: A Starting Point ..........................................................15

The Logic of Equilibrium Returns ................................................................................... 16

The Importance of Views ........................................................................................... 16

Trading Off Risk and Return .............................................................................................17

Personalising Risk ..........................................................................................................17

Reducing Dependence on Historical Data .............................................................. 18

Section 4: From Asset Allocations to Customised Portfolios 19

Section 5: What’s Different? 21


Introduction Dear clients and colleagues,

Barclays’ Investment Philosophy is the cornerstone of our client offering. Based on our clients’ unique needs, it is designed to provide personalised investment portfolios, delivering sustainable growth and risk management through diversified investments across multiple asset classes.

Why Asset Allocation?Every investor has an asset allocation, whether they think in those terms or not. Holding nothing but cash is an asset allocation, in this case dramatically sacrificing long-term returns for short-term comfort. Holding only individual equity investments is also an asset allocation, albeit a highly concentrated one with limited diversification benefits.

So the question is not whether you have an asset allocation or not, but rather if your asset allocation is in line with your needs and rewards you enough for the risk you are taking. We believe that a thoughtfully designed, diversified asset allocation is the best foundation for achieving your long-term goals.

When we created our strategic asset allocation process, that lies at the heart of our Investment Philosophy, we followed four basic principles. The asset allocation must (1) meet client needs, (2) provide diversification to help manage risk, (3) comprise asset classes that are generally accessible to investors, and (4) incorporate our long-term macroeconomic and market views, as well as our insights in behavioural and quantitative finance.

Meeting Client NeedsTo meet our clients long-term investment needs, they must be able to invest in portfolios that align to their Risk Profile – determined by their Risk Capacity (as established by a review of total wealth) and their Risk Tolerance (measured by our Financial Personality Assessment™) – and be comfortable to hold this portfolio over a long time horizon.

To satisfy this requirement, we have developed five Strategic Asset Allocations, (SAAs), from Low to High risk, taking into account how investors psychologically perceive risk, which tends to be more focused on poor outcomes than on just volatility.

More generally, our SAA model portfolios reflect how we think financial markets work and our long-term views on economic and market variables as well as asset class valuations. We combine this to generate optimal long-term risk-return trade-offs for investors with different Risk Profiles.

DiversificationTo benefit from diversification and enhance portfolio efficiency, an investment portfolio should include several asset classes and ideally go beyond the traditional set of stocks, bonds and cash.1 The idea that introducing diversifying assets to a portfolio can both help decrease risk and enhance opportunities for return is well established in the

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

Arne Hassel

Chief Investment Officer

+44 (0)20 3134 1681

[email protected]


academic literature and among investment managers. However, the concept came under attack during the global financial crises in 2008–2009, when most asset classes sold off at the same time, resulting in elevated short-term correlations. We believe that this attack is largely misguided, as it focuses on the shorter term instead of on the benefits over the longer term compared to the uncertainty associated with single asset class performance.

We strongly believe that diversification should play a key role in all asset allocations and still urge you to not ‘put all your eggs in one basket.’

To achieve 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 also introduce the notion of Alternative Trading Strategies (ATS) as an asset class. We believe that hedge funds and other alternative investment vehicles can play a variety of roles in a portfolio, including the generation of attractive risk-adjusted returns with strategies that have low correlation to other asset classes.

To create diversified allocations, we use sophisticated risk measurement and management techniques to account for the fact that asset returns do not follow an abstract Normal (bell-shaped) distribution, tending instead to be asymmetrical and have ‘fat tails’.2

More generally, when analysing asset class returns, we are careful not to rely on a simplistic interpretation of data, and also avoid the assumption that the future will look like the past, a surprisingly common forecasting bias.

Accessibility To make sure our clients are truly diversified, we have to provide an optimal portfolio that is also practically accessible. That is why we recommend broad categories of investible assets, both potentially attractive and accessible to all investors, rather than specific areas or products. For example, we do not consider private equity to be a separate asset class, but typically a particular expression of the broader asset class Developed Markets Equities.

Incorporating Long-Term ViewsOur final principle is that we seek to incorporate our long-term macroeconomic and market views, as well as our insight in behavioural finance. We combine historical market data with our investment experts’ views on economic and market variables going forward. We also incorporate behavioural finance to help us understand what is important to our clients, their perceptions of long-term risk and their preferences when balancing risk with expected returns. Using quantitative analysis, we combine our behavioural insights and understanding of clients with our market expertise, to best meet the long-term investment needs of our clients.

2 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.


We are proud of our strategic asset allocation process and believe that it contains many significant improvements to past practices in the investment management industry. However, we continue to be focused on improving and updating our process, which is why we regularly conduct a deep dive into our inputs and methodology, all to maximise our chances of delivering strong long-term investment returns in line with our clients’ goals.

Warmest regards,

Arne Hassel Chief Investment Officer


Section 1: OverviewA brief tour of our asset allocation methodology.

Asset allocation – the appropriate mix of stocks, bonds, cash, real estate, commodities and other asset classes – is the cornerstone of how Barclays builds client portfolios. 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 them.

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’.

Which 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 principles 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).

How Should a Portfolio be Divided Between These Assets?

The answer depends on individual client circumstances, needs and preferences. For each client, we start from one of our core Strategic Asset Allocations, which are designed to deliver the best long-term risk-adjusted returns for a given investor’s long-term objectives.

Section 3 explains our Strategic Asset Allocation (SAA) methodology in detail. We begin by forecasting the average returns for each asset class, using a blend of objective estimates implied by market data, and subjective projections made by our investment strategists.

Then, we acknowledge the uncertainty of the future by simulating many different possible scenarios for each asset class. This ensures that the resulting portfolios are well-diversified, because large allocations to an asset class which might have performed well in the past are balanced by simulations showing potentially weaker performance in the future.

In determining what we consider an ‘optimal’ portfolio for each Risk Profile, we try to maximise long-term expected returns whilst penalising risk in a unique, intuitive way. Our risk measure focuses more on poor outcomes – as is sensible, and not the case in the commonly-used measure of risk known as volatility. This means the portfolios we consider to be optimal have less exposure to asset classes with a tendency to crash sharply in value.

Antonia Lim

Global Head of Quantitative Research

+44 (0)20 3555 3296

[email protected]


The SAAs created through this process offer a baseline mix of assets that, if held on average over the long term, will in our view provide a most desirable trade-off of risk and return for an investor’s Risk Profile.3

What Makes Our Asset Allocation Process Unique?

Though we make use of sophisticated statistical techniques, our focus is to ensure that, at every stage, we are building the portfolios our clients would want to build for themselves.

As mentioned above, our risk measure is in tune with how people naturally perceive risk. And we marry this with simulations of the future which preserve the rare-but-extreme ‘tail risk’ characteristics of each asset class. This means that our Strategic Asset Allocations are not only equipped with a healthy caution towards investments prone to sudden lurches in value – they are also prudently diversified.

Furthermore, we don’t target a specific level of risk regardless of the market outlook. Instead, in conjunction with our future views of expected returns, we strive to achieve the best balance of risk and return, i.e. we will only take on risk to the extent that we think it will be rewarded.

Whether it’s how we measure risk, or how we avoid a rear-view mirror approach – at every stage, we’ve designed our SAAs from our clients’ perspective.

3 Through aiming towards the best 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.


Section 2: Our Roster of Asset ClassesWhy 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:

nn It is likely to improve the portfolio’s risk-adjusted returns, and

nn It offers unique risk or return characteristics, and

nn It is efficiently accessible by affluent individual investors, and

nn 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 combination of the following nine asset classes in their portfolios. We explain our approach and the rationale behind each asset class below.

Cash and Short-Maturity Bonds4

This asset class plays a unique and essential role in SAAs, especially for the most risk-averse investors. Cash and short-term bonds are often referred to as ‘risk-free’ assets. This is, however, misleading. Bank deposits, money market funds, 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 falls below the rate of inflation, as it has in many developed markets in the years following the 2008 financial crisis.

That being said, Cash & Short-Maturity Bonds still play a crucial role in a portfolio as the safest ‘safe haven’ available; without it, low risk portfolios would otherwise be exposed to more credit or interest rate risk than might be prudent. And whilst other asset classes can act as sources of liquidity, they can suddenly become unavailable just when they are required – nothing can replace cash for this vital role.

4 These bonds should be rated AA- or higher and with a remaining maturity of up to three years.


Developed Government BondsWe define Developed Government Bonds as bonds issued by sovereigns with credit ratings of AA- or higher. Most of these 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.

Second, Developed Government Bonds provide diversification benefits as, usually, bond prices tend to move in the opposite direction to stock prices in the short term. This is mainly due to the evolution of interest rates, the main determinant of government bond 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 strong5 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 euro area debt crisis. The distinction between these and other bond asset classes are detailed in later sections.

Figure 1: Stock market and government bond reactions during crises

!S&P 500 30-year US Treasury

180

160

140

120

100

80

60

402008 2009 2010 2011 2012 2013 2014 2015 2016 2017

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

Past performance of investments is not a reliable indicator of their future performance.

Investment Grade BondsWe define Investment Grade Bonds as fixed income securities issued by corporations with credit ratings of BBB- or higher, or by governments with credit ratings between BBB- and A+.

5 For instance, over the five years to the end of 2016, the correlation between Developed Government Bonds and Developed Markets Equities was -0.3.


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 are not the primary driver of returns on these bonds. Rather, it is changes in the difference in yields (the ‘spread’) 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, during that period, 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 securities issued by companies with low credit ratings (BB+ or lower). Emerging markets bonds refers to bonds 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) or in local currencies. In particular, over the last couple of decades, 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. Separating them out into distinct 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 Equities6

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 of our other traditional liquid asset classes (Figure 2). It is not just that the return on equities has compensated investors for the additional risk incurred relative to bonds or cash.

6 As defined by their inclusion in the MSCI World Index.


Over very long periods of time, equities’ risk-adjusted return has been substantially higher than bonds’. Put simply, if an investor is willing to take high risk in one and only one asset class, Developed Markets Equities would be the choice, based on the longest track record of high risk-adjusted returns.

The performance of equities in the previous decade has called this conclusion into question in some minds since, over this period, stock markets experienced both the tech crash of 2000 and the financial crisis of 2008. 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 an unprecedented run-up in stock prices to levels that were patently (in hindsight) 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’.7

Emerging Markets Equities8

Although the correlation between emerging and developed equity market returns has historically been strongly positive, 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 and warrant separate treatment.

Second, these markets are maturing rapidly, becoming larger, more transparent and more liquid, and so increasing their attractiveness and accessibility to investors.

7 Data in this document are based on quantitative research and analysis of historical 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.8 As defined by their inclusion in the MSCI Emerging Markets Index.

Figure 2: Long term inflation-adjusted returns7

!

100,000

10,000

1,000

100

101925 1950 1975 2000

US Cash US Bond US Equity

Source: Barclays Equity Gilt Study 2016. Past performance is not a guarantee of future results. An investment cannot be made directly in an index.

Figure 3: Emerging markets’ share of total global equity

!

16%

14%

12%

10%

8%

6%

4%

2%

0%1990 1995 2000 2005 2010 2015

MSCI EM as percentage of MSCI All Country World

Source: FactSet.


Third, 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 increasing share of total global market capitalisation (Figure 3) and despite recent ructions, we expect this trend to continue. All of these reasons justify singling out this asset class for both inclusion and separate consideration.

CommoditiesCommodities 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. Despite their run of poor performance from 2012-2015, 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 over 40 years ago, in the 1970s. Near-term repetitions of that episode are looking unlikely, but nonetheless as a source of potential return Commodities are quite unlike any other asset class. 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. Tax 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 and can benefit greatly from diligent fund and manager selection. However, this method is harder to access and potentially carries higher concentration risk than via REITs.


Alternative Trading StrategiesAlternative Trading Strategies (ATS) aim to generate profits for investors by actively taking long and short positions in a wide range of markets. The asset class tends to exhibit low-to-moderate long-term correlations with returns on other asset classes and lower risk than traditional collective equity investments. As a result, ATS offers investors the potential to dampen the overall risk of the portfolio.

What an investor ultimately does by investing in ATS is to ‘buy’ the manager’s skill, seeking to achieve enhanced risk-adjusted performance. The inclusion of ATS in an investment portfolio is justified not only by the fact that ATS managers are able to profit from a wider variety of outcomes than ‘traditional’ long-only managers, but also by ATS managers’ unique risk-return characteristics.

These characteristics can vary widely from fund to fund and, as an 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.

ATS fund managers are able to provide diversifying returns by tapping into a range of sources of return which are typically unavailable to investors via traditional investments. Some examples of typical strategies and their sources of returns are:

nn Long-Short Equity – Taking long positions in (buying) stocks that are expected to appreciate and short positions in (selling) stocks that are expected to decline

nn CTA – The tendency for momentum to drive markets upward or downward much further than is justified by the fundamental facts

nn Convertible Arbitrage – Often market prices of convertible bonds add up to less than the value of the sum of the security’s component parts, or

nn Merger arbitrage – Stock markets tend to underestimate the likelihood that announced acquisition deals will close.

At Barclays, we access ATS managers through a UCITS-regulated structure which ensures investors are provided with minimum levels of liquidity, transparency and diversification. ATS strategies within this type of structure are often also referred to as ‘Liquid Alternatives’.

Some of the Things We Haven’t IncludedIn the process of selecting these nine asset classes, we rejected a number of other candidates. A detailed account of 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 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 typically categorise investments in private equity funds as part of either the developed or emerging equities asset classes, depending on the nature of the investment. 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 all investors. So, although we believe that private equity funds can enhance portfolio performance, we decided not to single out this category as a strategic asset class. For highly composed9 investors with a long enough time horizon, private equity funds could form part of their overall asset allocation.

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.

9 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. See Section 4, “From Asset Allocations to Customised Portfolios”.


Section 3: How Much of EachThe ways in which we’ve made the conventional approach to asset allocation better – and why we generate five separate portfolios.

The Optimal MixIn 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 preferred probability-weighted 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.

Probability-weighted: We do not know in advance, of course, what will occur over the next decade. We do, however, have some idea of the range of potential outcomes and estimates of the probabilities of each outcome. The overall ‘expectation’ is the sum of all of possible outcomes weighted by the probability of each 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 complete market cycle in mind. This is not to say that we expect clients to reserve judgement 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 a few weeks to a few years. Having a long 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 views every 12-18 months, and we take tactical positions around the SAA weights to account for the prevailing economic and political environment and shorter-term opinions.

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. It also depends upon perceptions of return. Getting an extra 1% return, which improves your overall return from 1% to 2%, would add more to an investor’s happiness than if that extra 1% had changed overall return from 21% to 22%. Additionally, relative happiness with returns also differs among investors. In particular, risk-averse investors will respond much more negatively to a loss (say -10%) than more risk tolerant investors.

The Asset Allocation ProcessOnce 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 Risk Profiles. 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 between risk and return is different than usually assumed. Standard practice in the wealth management industry has been to consider deviations from the mean return in both directions (i.e. both better and worse returns) as contributing equally to risk. In contrast, we appreciate that this is not the case and that there is an asymmetry to how investors subjectively evaluate different outcomes; they focus on restricting the chance of unpleasant eventualities.

By specifying more realistic long-term risk-return client preferences, and by using a more sophisticated risk measure (Behavioural Risk) that goes beyond the association of risk merely 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.

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, a full market cycle. 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.

Forward-Looking ReturnsOne 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 flawed consider the past 25 years when bonds have produced roughly 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 25 years and have reached a point where, for many maturities in many countries, they are essentially at 0% or even below 0%, which means that they are unlikely to 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 such high returns for so long 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 model10.

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.

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


The Logic of Equilibrium ReturnsThe Capital Asset Pricing Model (CAPM), developed more than 50 years ago by William Sharpe, 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.

Figure 4: Illustrative estimates of Asset Class Capitalisation and Risk

Asset Class

Estimated Market

Capitalisation (USD, trillions)

Market Capitalisation

Portfolio Weight

(Rounded)

Estimated Frequency of Negative One-Year Return*

Cash and Short-Maturity Bonds 5 6% 0%

Developed Government Bonds 23 29% 2%

Investment Grade Bonds 8 10% 6%

High Yield and Emerging Markets Bonds 5 6% 20%

Developed Markets Equities 30 38% 31%

Emerging Markets Equities 3 4% 38%

Commodities 2 2% 43%

Real Estate 1 2% 27%

Alternative Trading Strategies (ATS) 3 3% 23%

* Based on rolling one-year returns based on monthly data from the end of December 1996 to the end of December 2016. 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 equilibrium returns are 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 unlikely.

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 as a robust union of objective and subjective expertise. 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 long-term 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. Our process then uses a top-down approach in which the building blocks for each asset class include key macroeconomic variables as well as the price, valuation and market fundamentals relevant to its performance. This helps views across asset classes to be 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% or even negative. In our view they are unlikely to fall much further, which means that the prices of many bonds in the market cannot go much higher and 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, valuation measurements influence our long-term return expectations. For example, for fixed income asset classes, we consider the current yield of the representative benchmark and compare that to the expected yield at the end of the next ten years, and similarly the P/E ratio for equity asset classes. By updating the SAA each year with new views, we ensure that our long-term asset allocations are positioned intelligently with regard to valuations.

Finally, we blend our long-term views with the expected equilibrium returns to create our forward-looking returns. As a result expensive assets, such as currently many of the fixed income asset classes, will have lower expected returns and therefore smaller weights in our portfolios than the historical and equilibrium returns 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 trying to eliminate the chance of very good outcomes. This is much more closely aligned to our innate 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.


Consequently, by optimising return with this more realistic and personalised view of risk in mind, the investor should feel more comfortable with their portfolio allocation. We generate SAAs 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. 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, 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 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 portfolios matching different scenarios. The result of incorporating many different portfolios is enhanced diversification and reduced sensitivity to one set of data.

The result of this process – modifying the Black-Litterman model to integrate our views on forward-looking returns; introducing our more personalised and natural risk measure, along with re-sampling – defines the asset class weights for strategic asset allocations across a range of investor Risk Profiles.


Section 4: From Asset Allocations to Customised PortfoliosHow we tailor asset allocations to suit individual investor needs, and incorporate tactical adjustments to portfolios.

These 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 investors hold.

The first step we need to take is to understand that an SAA 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 tactical shifts between and within asset class, to reflect short-term views. The difference between the SAA 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 portfolios are optimised to help meet the long-term risk-return preferences of five different Risk Profiles, but otherwise suppose that the investors are unhindered by other financial constraints, have no plans to spend the money in their portfolio, have no income requirement, and are concerned only with the long-term financial efficiency of their portfolio. This allows these portfolios to have the broadest possible application to meet long-term investment needs, but there are aspects of individual investors’ circumstances which may require some customisation of these 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. Many individuals, for instance, have a sizable portion of their non-investible wealth in personal real estate (their house, holiday 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 of the 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.11 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 investment journey are important because they influence how we feel about our investments.

11 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 www.investmentphilosophy.com.


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. The Composure dimension of our Financial Personality Assessment™ measures this propensity towards anxiety.

Reducing volatility does reduce anxiety, but also tends to drag down long-term returns appropriate to an investor’s Risk Profile. 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 can 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.


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 client needs, portfolio diversification, accessibility of investments, and the incorporation of our long-term market views as well as our expertise in behavioural and quantitative finance.

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

In particular, we have focused on:

nn 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

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

nn 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

nn 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

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

nn 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

nn The ability to tailor our 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 an appropriate asset allocation at any point in time12 in light of each investor’s long-term goals and financial personality.

12 https://wealth.barclays.com/content/dam/bwpublic/global/documents/wealth_management/the-science-and-art-of-manager-selection.pdf

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.

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 offers wealth and investment management products and services to its clients through Barclays Bank PLC and its subsidiary companies. Barclays Bank PLC is registered in England and authorised by the Prudential Regulation Authority and regulated by the Financial Conduct Authority and the Prudential Regulation Authority. Registered No. 1026167. Registered Office: 1 Churchill Place, London E14 5HP.

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 FCA peut être contrôlée sur le site internet www.orias.fr), prestataire de service d’investissement de droit anglais agréé par the Financial Conduct Authority (FCA), autorité de tutelle britannique qui a son siège social 25 The North Colonnade, Canary Wharf, Londres E14 5HS. (www.fca.org.uk), FCA register n° 122702 La Succursale française de Barclays Bank PLC, est autorisée par le FCA à recourir à un Agent lié, Barclays Patrimoine SCS. Gibraltar – Barclays offers banking, wealth and investment management products and services to its clients through Barclays Bank PLC and its subsidiaries. Barclays Bank Plc is authorised by the Gibraltar Financial Services Commission to conduct banking and investment business in Gibraltar. Guernsey – 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 Number: 396330. Registered Office: Two Park Place, Hatch Street, Dublin 2. Calls may be recorded for security and other purposes. Isle of Man – Barclays Bank PLC, Isle of Man Branch is licensed by the Isle of Man Financial Services Authority. 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, IM99 1AJ. Italy – Barclays Bank PLC – Via della Moscova. 18 – 20121 Milan – Italy, is a branch of Barclays Bank PLC and is registered with the Register of Banks Milan n° 4862. Company Register Milan n° 80123490155 – R.E.A. Milan 1040254 – Fiscal Code n° 80123490155 – Registered VAT n° 04826660153. Jersey – Barclays Bank PLC, Jersey Branch is regulated by the Jersey Financial Services Commission. Barclays Bank PLC, Jersey Branch is regulated by the Guernsey Financial Services Commission under the Protection of Investors (Bailiwick of Guernsey) Law 1987, as amended. Barclays Bank PLC, Jersey Branch has its principal business address in Jersey at 13 Library Place, St Helier, Jersey JE4 8NE, Channel Islands. Monaco – Barclays Bank PLC – Monaco is a branch of Barclays Bank PLC with its offices in the Principality of Monaco at 31 Avenue de la Costa, MC 98000 Monaco – Tel. +377 93 15 35 35. Registered with the Monaco Chamber of Commerce and Industry under No° 68 S 01191. Registered VAT No° FR 40 00002674 9. Nigeria – Barclays Group Representative Office (NIG) Ltd. Registered Company No: RC41757 and its mailing address is Barclays Group Representative Office (NIG) Ltd, Courier Department, 3rd Floor, 1 Churchill Place, London, E14 5HP. Portugal – Barclays Bank PLC activity in Portugal is supervised by Banco de Portugal (BoP) and Comissão de Mercado de Valores Mobiliários (CMVM). Switzerland – Barclays Bank (Suisse) SA is a Bank registered in Switzerland and regulated and supervised by FINMA. Registered No. CH-660.0.118.986-6. Registered Office: Chemin de Grange-Canal 18-20, P.O. Box 3941, 1211 Geneva 3, Switzerland. Registered branch: Beethovenstrasse 19, P.O. Box, 8027 Zurich. Registered VAT No. CHE-106.002.386. Barclays Bank (Suisse) SA is a subsidiary of Barclays Bank PLC registered in England, authorised by the Prudential Regulation Authority and regulated by the Financial Conduct Authority and the Prudential Regulation Authority. It is registered under No. 1026167 and its registered office is 1 Churchill Place, London E14 5HP. United Arab Emirates – Barclays Bank PLC (DIFC Branch) (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. Related financial products or services are only available to Professional Clients as defined by the DFSA. Principal place of business in the DIFC: Dubai International Financial Centre, The Gate Village Building No. 10, Level 6, PO Box 506674, Dubai, U.A.E.

This item can be provided in Braille, large print or audio by calling: +44(0)1624 684 444* (or via TextDirect if appropriate).

*Lines are open 24 hours a day, 7 days a week, except 25 December when lines are closed.

Call costs may vary – please check with your telecoms provider. Calls may be recorded so that we can monitor the quality of our service and for security purposes.

wealth.barclays.com UK0048/CP 57361-17. Updated August 2017

asset allocation at barclays · asset allocation at barclays august 2017 1 ... the black-litterman...

Documents