Quantitative Investing

Ibbotson Asset Allocation Conference

Robert LittermanMarch, 2008

Clearly Articulated Investment Beliefs Should Drive Investment Strategy

Our Investment Beliefs (an example)

1) There is only one basic source of long run wealth creation, the growth of the economy.

2) In equilibrium the investment portfolios of all individuals should reflect that source of wealth. The portfolios would all have weights proportional to market capitalizations which would reflect the economy’s expected future productive capacity.

3) The world is clearly (given, among other indications, the diversity of portfolios) not in equilibrium.

4) The market as a whole has shown itself to be subject to extended periods of overreaction. Nonetheless, capital markets are competitive, and though not entirely efficient, are becoming more efficient over time.

Clearly Articulated Investment Beliefs Should Drive Investment Strategy (continued)

Our Investment Beliefs (an example)

5) Deviations from equilibrium provide opportunities for some disciplined investors with superior skills and information and typically a longer than average investment horizon to outperform the market return on a risk adjusted basis.

6 ) The key to superior investment performance is superior fundamental research through which we can identify disequilibrium phenomena.

7) Systematically capturing returns from such phenomena requires rigorous objective research, state of art risk measurement and portfolio construction, efficient trading, and patience.

Risk Is a Scarce Resource

Risk provides the energy that creates returns

However, risk also creates the opportunity for losses

Losses should be limited in a bad scenario

Thus, risk appetite is limited

How much pain is too much?

Imagine a very bad economic scenario:

Equity markets decline globally by 50%

This decline reflects extensive defaults and depressed economic activity for several years

In this environment long term investors should be increasing their allocation to equity.

Will the investor be able to?

How much can an individual afford to lose? (10%, 20%, …?)

The answer to this question is the most important determinant of long term asset allocation.

An Optimal Portfolio

Maximizes return for a given level of risk

For illustrative purposes only.

The Mathematics of Risk & Return

The Utility Function (Expected Return) is Linear

The Constraint Function (Risk) is Nonlinear

(And Depends on the Correlation of Returns)

A

C B

A = Old Portfolio B = New Investment C = New Portfolio

A

C

B

correlation = .6

correlation = .2

correlation = -.2

Different Levels of Portfolio AggregationCan Highlight Different Dimensions of Risk

In understanding the sources of risk and return at times it may be useful to focus on:

Each cash flow

Individual securities

However, the most important determinants are:

Asset class allocations

Factors driving overall valuations

In particular, beta, the exposure to global market returns

When Is a Portfolio Optimal?

A portfolio is optimal when, at the margin the following ratio is identical for each asset or other investment activity:

Change in Expected Excess Return

Change in Portfolio Risk

Why Should This Be True?

If not, the fund can be improved:

Take funds from the lowest (per unit of contribution to portfolio risk) returning activity

Move funds into a higher returning activity

Adjust cash to keep portfolio risk constant

Focus on the Risk / Return Frontier

Por

tfol

io E

xpec

ted

Ret

urn

Portfolio RiskFor illustrative purposes only.

The Bottom Line

Ultimately there is a risk budget

Every decision depends on:

Expected excess return

And the marginal impact on portfolio risk

Efficient allocations require this ratio to be the same at every margin

Quantitative Models Measure Marginal Contribution to Risk

The marginal contribution to risk of each asset

Depends on:

The covariance of that asset with every other asset

The amounts invested in each asset

Can be calculated given:

Portfolio holdings

Volatilities and correlations

The Marginal Risk Contribution Determines “Implied Views”

If a portfolio is optimal, the implied expected excess returns must be proportional to the marginal contribution to portfolio risk

We refer to these expected excess returns for which the portfolio is optimal as the “implied views” of the portfolio

We call this a “risk based” approach to asset allocation because risk is measurable and risk measurement implies a set of views for which any portfolio is optimal.

Are those implied views reasonable?

Implied Views Guide Behavior

If these “implied views” conform with current expectations

Portfolio structure is appropriate

Otherwise

Adjustments should be made to increase expected portfolio return

Consider increasing investments in assets with expected returns above the implied views; decreasing those below

Equilibrium Theory provides a neutral starting point for Expected Returns

Modern Investment Management An Equilibrium Approach

Institutional investors are adjusting to an environment of low interest rates and reduced expected returns from equities.

What does the equilibrium theory suggest?

A book by Bob Litterman and 22 Goldman Sachs

Asset Management investment professionals

A re-examination of investment strategy with a focus on alpha vs. beta

Sources of Total Return in a $1 Million Portfolio:

There are Three FundamentalSources Of Portfolio Return

1 Real Risk Free Rate

Risk free rate = 4.5%

$ 45,000

2 Market Risk Premium

20% Equity Allocation0.82% ER3.6% Vol

70% Equity Allocation2.58% ER9.6% Vol

3 Active Manager Return

100% Indexed0.0% ER

1.5% Tracking Error at IR = 0.5

Beta

Alpha

$ 8189 $ 25,779

$ 0 $ 7500

For illustrative purposes only.

And Three Sources of Portfolio Risk

Interest rate risk, usually from liabilities:

Uncompensated risk

Can be hedged via derivatives or bonds

Market risk:

Basically available for free (no fees)

Has relatively low expected return per unit of risk

Active risk:

Uncorrelated risk implies low impact on portfolio risk

Skill-based

Opportunities require deviations from equilibrium

Active management fees

Which Risks Should Be Compensated?

An answer was provided by the capital asset pricing model: an equilibrium model

When all investors maximize expected return subject to a risk constraint and markets are efficient

Expected excess return (the equilibrium risk premium) is proportional to the beta of an asset

Why?

Beta measures the marginal impact of increasing asset weight on the risk of the market portfolio

Why Focus on Equilibrium?

The world is not “in equilibrium”

The academic theory is nonetheless relevant for investors

Deviations from equilibrium provide opportunities

But investors taking advantage of these opportunities push the capital markets back toward equilibrium and greater efficiency

So the equilibrium framework helps investors to identify opportunities…it provides the hurdle rate, the required expected return for taking additional risk

Equilibrium Expected Excess Returns

There are several versions of Global CAPM Equilibrium

We focus on a particularly simple one: Fischer Black’s “Universal Hedging”

An assumption on risk aversion determines:

A constant degree of currency hedging

A risk premium or excess return on all assets

Fischer’s model is calibrated to long run market returns

Forward Looking Equilibrium Risk Premia Lead to Better Behaved Optimal Asset Allocations

Equilibrium risk premia justify market capitalization portfolio weights

Asset ClassMarket Capitalization

Equilibrium Risk Premium

US Equity 23.7% 3.53%

Non-US Developed Equity 26.3% 3.51%

Non-China Emerging Equity 4.8% 4.08%

China Equity 0.9% 4.51%

Global Fixed Income 42.5% 0.03%

High Yield 1.7% 1.27%

Private Equity 0% 4.69%

Real Estate 0% 2.63%

Hedge Funds 0% 0.48%Market Cap above as of Sept 30th, 2007. All numbers reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are hypothetical indications of a broad range of possible returns. Please see p68 for a summary of the assumptions.Expected returns are estimates of hypothetical average returns of economic asset classes derived from statistical models. There can be no assurance that these returns can be achieved. Actual returns are likely to vary. Please see additional disclosures.

Current Estimates of Global CAPM Equilibrium Risk Premia

All numbers reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are hypothetical indications of a broad range of possible returns. Please see p68 for a summary of the assumptions.Expected returns are estimates of hypothetical average returns of economic asset classes derived from statistical models. There can be no assurance that these returns can be achieved. Actual returns are likely to vary. Please see additional disclosures.

0.00%

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1.50%

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2.50%

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3.50%

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5.00%

Private Equity China Equity Non-ChinaEmerging

Equity

US Equity Non-USDeveloped

Equity

Real Estate High Yield Hedge Funds Global FixedIncome

Strategic Asset Allocation provides a long term neutral anchor for fund investment policy

Steps toward a Strategic Asset Allocation

Specify the liability structure or fund objective: e.g. maximize real wealth creation

Determine a risk tolerance

Start with global equilibrium risk premia

Tilt in the direction of long-term views

Optimize

The Equity Allocation Drives the Overall Level of Risk

China Equity

US Equity

Emerging Equity ex-China

Global Aggregate Fixed Income

Developed Equity ex-US

Global High Yield China Equity

US Equity

Emerging Equity ex-China

Global Aggregate Fixed Income

Developed Equity ex-US

Global High Yield

Market Capitalization Weights Risk¹ Decomposition

1 The risk decomposition is the contribution of each asset class to the total portfolio variance. All numbers reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are hypothetical indications of a broad range of possible returns. Please see p68 for a summary of the assumptions.For illustrative purpose only

Black-Litterman Model combines Market Equilibrium with Investor Views

Incorporating Views In PortfoliosStep 1. Define What a View Is

A simple view:

UST yields will decline 50 bps in six months

Equivalently the Expected Return UST = 3.3%

If the view is uncertain:

UST = 3.3% + UST

where

UST = Expected Return

UST = Uncertainty in the Expected Return

USTN Measures Uncertainty

A more complicated view:

Globally bonds will outperform stocks by about 3%

Equivalently: FI - MSCI = 3.0% +

Or: (1, -1) * (FI , MSCI ) = 3.0% +

In general a view is represented as:

pv * = q+

where the weights pv define the “view” portfolio.

Incorporating Views In PortfoliosStep 2. Create a General Representation

Views Can Reflect Long-Run or Short-Run Opportunities

In forming a Strategic Benchmark, views should reflect long-term deviations from equilibrium

Examples:

Emerging markets will outperform developed markets

Infrastructure returns will exceed their beta

Excess returns to commodities will be positive

Tactical Views

In forming a Tactical Asset Allocation, views should reflect short-term deviations from equilibrium

Examples:

Global stock markets will outperform global bond markets by only 2 percent this year (a relatively bearish view on stocks)

Real estate will underperform US equities by 5 percent this year

Chinese equities will outperform other emerging markets by 5 percent this year

Incorporating Views in PortfoliosStep 3. The Black-Litterman Model

Start with neutral expected returns derived from the global CAPM equilibrium

Add a set of views:

p1 * = q1+ 11N 1

p2 * = q2+ 2 2N 2

p3 * = q3+ 33N 3

Black-Litterman combines the views with equilibrium and provides as output

BL = Black-Litterman Expected Returns

An Example: Using the Black-Litterman model

Asset ClassSymbol

VolatilityEquilibrium Risk Premium

China Equity C 35.7% 4.51%

US Equity US 14.5% 3.53%

Non-US Developed Equity DE 14.3% 3.51%

Non-China Emerging Equity EE 22.0% 4.08%

Global Fixed Income GFI 3.0% 0.03%

High Yield HY 8.4% 1.27%

Private Equity PE 20.9% 4.69%

Real Estate RE 16.0% 2.63%

Hedge Fund Portfolio HF 3.6% 0.48%

In this example there are nine assets.

We start with the equilibrium risk premia -- a set of expected excess returns that are for each asset proportional to the beta of that asset with the global market portfolio:

All numbers reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are hypothetical indications of a broad range of possible returns. Please see p68 for a summary of the assumptions.Expected returns are estimates of hypothetical average returns of economic asset classes derived from statistical models. There can be no assurance that these returns can be achieved. Actual returns are likely to vary. Please see additional disclosures.

Equilibrium Risk Premia Provide a Reasonable Starting Point for Asset Allocation Exercises

Equilibrium Expected Excess Returns

Optimizer maximizes expected return for a given level of risk

Implies Market Capitalization

Weights

Equilibrium Risk Premia

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1%

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5%

6%

7%

C US DE EE GFI HY PE RE HF

Market Cap Weights

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5%

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45%

C US DE EE GFI HY PE RE HFMarket Cap above as of Sept 30th, 2007. All numbers reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are hypothetical indications of a broad range of possible returns. Please see p68 for a summary of the assumptions.Expected returns are estimates of hypothetical average returns of economic asset classes derived from statistical models. There can be no assurance that these returns can be achieved. Actual returns are likely to vary. Please see additional disclosures.

Suppose you have the view described below.How would you adjust your expected returns?

1. Global stock markets will outperform global bond markets by only 2 percent this year

One approach is to make adjustments directly to the expected excess returns that drive an asset allocation exercise.

Another approach is to use the Black-Litterman Global Asset Allocation Model.

The direct adjustment of expected excess returns is a complex and often frustrating exercise

0.0%

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1.5%

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2.5%

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3.5%

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C US DE EE GFI HY PE RE HF

Equilibrium Adjusted

Equilibrium expected returns above reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are hypothetical indications of a broad range of possible returns. Please see p68 for a summary of the assumptions.Expected returns are estimates of hypothetical average returns of economic asset classes derived from statistical models. There can be no assurance that these returns can be achieved. Actual returns are likely to vary. Please see additional disclosures.For illustrative purposes only.

The optimal portfolio does something strange:It allocates 10 percent to real estate

Optimal Portfolio Weights

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70%

C US DE EE GFI HY PE RE HF

Market Cap Adjusted

?

Market Cap above as of Sept 30th, 2007. For illustrative purposes only.

The Black-Litterman Model converts the views into a set of consistent expected excess returns…

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C US DE EE GFI HY PE RE HF

Equilibrium Black-Litterman

One not entirely obvious implication of stocks doing poorly is

that real estate is likely to do less well

Equilibrium expected returns above reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are hypothetical indications of a broad range of possible returns. Please see p68 for a summary of the assumptions.Expected returns are estimates of hypothetical average returns of economic asset classes derived from statistical models. There can be no assurance that these returns can be achieved. Actual returns are likely to vary. Please see additional disclosures.For illustrative purposes only.

One can also specify higher or lower degrees of confidence in a view

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1.5%

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2.5%

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3.5%

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C US DE EE GFI HY PE RE HF

Equilibrium Less confident view

Equilibrium expected returns above reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are hypothetical indications of a broad range of possible returns. Please see p68 for a summary of the assumptions.Expected returns are estimates of hypothetical average returns of economic asset classes derived from statistical models. There can be no assurance that these returns can be achieved. Actual returns are likely to vary. Please see additional disclosures.For illustrative purposes only.

The Black-Litterman expected excess returns lead to a well behaved optimal portfolio

0%

10%

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30%

40%

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60%

70%

C US DE EE GFI HY PE RE HF

Market Cap Black-Litterman BL with a Less Confident View

Market Cap above as of Sept 30th, 2007. For illustrative purposes only.

In fact, in the simplest context the deviations from the market cap portfolio are the view portfolio

Deviations from market cap portfolio weights

-8.00%

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-4.00%

-2.00%

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6.00%

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C US DE EE GFI HY PE RE HF

The bearish equity view is expressed in the Black-Litterman model as the following equation:

1.7%*C + 42.6%*US + 47.2% * DE + 8.6% * EE = GFI + 2.0

For illustrative purposes only.

More generally, the Black-Litterman modelallocates risk to a combination of view portfolios

In the absence of:

A benchmark

Constraints

Transactions costs

The optimal portfolio is a linear combination of the market and the view portfolios

PBL = 0 x M + 1 x p1 + 2 x p2 + 3 x p3

Where is the Value Added?

In this simplest context the optimal portfolio is intuitive and obvious:

Tilt away from the market portfolio

Tilt toward an optimal combination of the view portfolios which we call the OTP, or “Optimal Tilt Portfolio”

Black-Litterman determines these optimal weights

The value added also shows up in more complex environments

When transactions costs matter

Or when there are constraints

In more complicated contexts the optimal portfolio is not so obvious

Here we show the optimal portfolio, based on three views, and with and without a constraint on the allocation to Private Equity

-10%

0%

10%

20%

30%

40%

50%

60%

C US DE EE GFI HY PE RE HF

Market Cap No constraint on PE PE constrained

When private equity

is constrained the

allocations to public

equity increase

Market Cap above as of Sept 30th, 2007. For illustrative purposes only.

The Role of Active Management

Adding Active Risk Can Dramatically Shift the Portfolio Frontier Upward

Note: Simulated performance results do not reflect actual trading and have certain inherent limitations. Please see appendix for further disclosures.

Adding exposure to active risk can boost long-run expected returns without meaningfully increasing fund volatility.

Sharpe Ratio improves with the addition of market independent return

Excess Return (%)

Volatility (%)

SharpeRatio

Original Portfolio (50% equity) 1.7 8.1

Additional Market Risk (25% equity) 0.8 3.9

New Portfolio 2.5 11.8 0.21

Original Portfolio (50% equity) 1.7 8.1

1.5% Active Risk (assumed IR = 0.5) .7 1.5

New Portfolio 2.4 8.2 0.29

Benefit from Diversification – (0.2)

Benefit from Diversification – (1.4)

Active risk typically makes a very small contribution to overall portfolio volatility

For illustrative purposes only.Simulated performance results do not reflect actual trading and have inherent limitations. Please see additional disclosures.

0%

2%

4%

6%

8%

10%

12%

0 0.5 1 1.5 2 2.5

Active Risk

Contribution from Active Risk Portfolio Volatility

The Active Risk Puzzle: Why do funds have such modest expectations?

Optimal Risk Allocations Reveal Modest IR Expectations

Volatility = 6.0%

Volatility = 9.0%

Source: Goldman Sachs Asset Management.

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Aggregate Active Risk Information Ratio

Op

tim

al A

llo

cati

on

to

Act

ive

Ris

kAllocations to active risk of typical funds range between 50 and 200 basis points

Possible Explanations: • Funds may be unsure of their ability to select skilled managers• Career risk• Governance restrictions• Active risk and strategic asset allocation have historically been linked

For illustrative purposes only.Simulated performance results do not reflect actual trading and have inherent limitations. Please see additional disclosures.

Alternative investments encompass a diverse range of strategies and are a good source of active risk

Private Equity

Real Estate

Hedge Funds

Commodities

Overlays such as GTAA (Global Tactical Asset Allocation) and Active Currency Management

What Makes Alternative Investments Attractive?

Attributes of Alternative Investments include:

Historically attractive absolute returns versus traditional asset classes

Lower correlations that can provide protection in bear markets

Therefore may provide excess returns above the equilibrium hurdle rate

Appendix

Strategic Long-Term AssumptionsRisk and Return characteristics

All tracking error assumptions reflect GSAM Global Investment Strategies estimates for above-average active managers and are based on a historical study of the results of active management [see Active Risk Budgeting in Action: Evaluating Historical Characteristics of Traditional Managers by Yoel Lax, Tarun Tyagi, and Kurt Winkelmann (GSAM Strategic Research, October 2003)], which is available upon request. Expected returns are estimates of hypothetical average returns of economic asset classes derived from statistical models. There can be no assurance that these returns can be achieved. Actual returns are likely to vary. Please see additional disclosures. All numbers reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are hypothetical indications of a broad range of possible returns. Please see additional disclosures.

Asset Class Asset Class Symbol Volatility

Equilibrium Risk

PremiumChina Equity MSCI China Index C 35.7% 4.51%US Equity MSCI USA Index US 14.5% 3.53%Non-US Developed Equity MSCI ex US Index DE 14.3% 3.51%Non-China Emerging Equity MSCI Emerging Market ex-China EE 22.0% 4.90%Global Fixed Income Lehman Global Aggregate Index GFI 3.0% 0.03%High Yield Lehman Global High Yield Index HY 8.4% 1.27%Private Equity Modeled as an equal weighted blend of Venture Capital,

Large US Buyout, Small US Buyout, and European Buyout Sectors. PE 20.9% 4.69%

Real Estate FTSE/NAREIT Global Index (unhedged) RE 16.0% 2.63%Hedge Fund Portfolio Modeled as a customized blend of Event Driven, Relative

Value, Equity Long/Short, and Tactical Trading Hedge Funds HF 3.6% 0.48%

All numbers reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are hypothetical indications of a broad range of possible returns. Please see additional disclosures.

Strategic Long-Term AssumptionsCorrelations

China Equity US Equity

Non-US Developed Equity

Non-China Emerging Equity

Global Fixed Income High Yield

Private Equity

Real Estate

Hedge Fund Portfolio

China Equity 1.00 0.40 0.42 0.34 (0.04) 0.21 0.37 0.46 0.22 US Equity 0.40 1.00 0.77 0.51 (0.01) 0.44 0.79 0.50 0.52 Non-US Developed Equity 0.42 0.77 1.00 0.63 (0.13) 0.46 0.79 0.52 0.42 Non-China Emerging Equity 0.34 0.51 0.63 1.00 (0.09) 0.53 0.53 0.54 0.28 Global Fixed Income (0.04) (0.01) (0.13) (0.09) 1.00 0.13 (0.06) 0.15 (0.00) High Yield 0.21 0.44 0.46 0.53 0.13 1.00 0.41 0.51 0.24 Private Equity 0.37 0.79 0.79 0.53 (0.06) 0.41 1.00 0.47 0.43 Real Estate 0.46 0.50 0.52 0.54 0.15 0.51 0.47 1.00 0.27 Hedge Fund Portfolio 0.22 0.52 0.42 0.28 (0.00) 0.24 0.43 0.27 1.00

Appendix

The currency market affords investors a substantial degree of leverage. This leverage presents the potential for substantial profits but also entails a high degree of risk including the risk that losses may be similarly substantial. Such transactions are considered suitable only for investors who are experienced in transactions of that kind. Currency fluctuations will also affect the value of an investment.

Emerging markets securities may be less liquid and more volatile and are subject to a number of additional risks, including but not limited to currency fluctuations and political instability.

High-yield, lower-rated securities involve greater price volatility and present greater credit risks than higher-rated fixed income securities.

An investment in real estate securities is subject to greater price volatility and the special risks associated with direct ownership of real estate.

The portfolio risk management process includes an effort to monitor and manage risk, but does not imply low risk.

Indices are unmanaged. The figures for the index reflect the reinvestment of dividends but do not reflect the deduction of any fees or expenses which would reduce returns. Investors cannot invest directly in indices.

References to indices, benchmarks or other measures of relative market performance over a specified period of time are provided for your information only and do not imply that the portfolio will achieve similar results. The index composition may not reflect the manner in which a portfolio is constructed. While an adviser seeks to design a portfolio which reflects appropriate risk and return features, portfolio characteristics may deviate from those of the benchmark.

Appendix

There may be conflicts of interest relating to the Alternative Investment and its service providers, including Goldman Sachs and its affiliates, who are engaged in businesses and have interests other than that of managing, distributing and otherwise providing services to the Alternative Investment. These activities and interests include potential multiple advisory, transactional and financial and other interests in securities and instruments that may be purchased or sold by the Alternative Investment, or in other investment vehicles that may purchase or sell such securities and instruments. These are considerations of which investors in the Alternative Investment should be aware. Additional information relating to these conflicts is set forth in the offering materials for the Alternative Investment.

Past performance is not indicative of future results, which may vary. The value of investments and the income derived from investments can go down as well as up. Future returns are not guaranteed, and a loss of principal may occur.

Effect of Fees

The following table provides a simplified example of the effect of management fees on portfolio returns. Assume a portfolio has a steady investment return, gross of fees, of 0.5% per month and total management fees of 0.05% per month of the market value of the portfolio on the last day of the month. Management fees are deducted from the market value of the portfolio on that day. There are no cash flows during the period. The table shows that, assuming all other factors remain constant, the difference increases due to the compounding effect over time. Of course, the magnitude of the difference between gross-of-fee and net-of-fee returns will depend on a variety of factors, and this example is purposely simplified.

Gross NetPeriod Return Return Differential1 year 6.17% 5.54% 0.63%2 years 12.72 11.38 1.3410 years 81.94 71.39 10.55

Appendix

Alternative Investments such as hedge funds are subject to less regulation than other types of pooled investment vehicles such as mutual funds, may make speculative investments, may be illiquid and can involve a significant use of leverage, making them substantially riskier than the other investments. An Alternative Investment Fund may incur high fees and expenses which would offset trading profits. Alternative Investment Funds are not required to provide periodic pricing or valuation information to investors. The Manager of an Alternative Investment Fund has total investment discretion over the investments of the Fund and the use of a single advisor applying generally similar trading programs could mean a lack of diversification, and consequentially, higher risk. Investors may have limited rights with respect to their investments, including limited voting rights and participation in the management of the Fund.

Alternative Investments by their nature, involve a substantial degree of risk, including the risk of total loss of an investor's capital. Fund performance can be volatile. There may be conflicts of interest between the Alternative Investment Fund and other service providers, including the investment manager and sponsor of the Alternative Investment. Similarly, interests in an Alternative Investment are highly illiquid and generally are not transferable without the consent of the sponsor, and applicable securities and tax laws will limit transfers.

Strategic Long Term AssumptionsThe data regarding strategic assumptions has been generated by GSAM for informational purposes. As such data is estimated and based on a number of assumptions; it is subject to significant revision and may change materially with changes in the underlying assumptions. GSAM has no obligation to provide updates or changes. The strategic long-term assumptions shown are largely based on proprietary models and do not provide any assurance as to future returns. They are not representative of how we will manage any portfolios or allocate funds to the asset classes.

Appendix

These examples are for illustrative purposes only and are not actual results.  If any assumptions used do not prove to be true, results may vary substantially.

This material is provided for educational purposes only and should not be construed as investment advice or an offer or solicitation to buy or sell securities.

Simulated Performance

Simulated performance is hypothetical and may not take into account material economic and market factors that would impact the adviser’s decision-making.  Simulated results are achieved by retroactively applying a model with the benefit of hindsight. The results reflect the reinvestment of dividends and other earnings, but do not reflect fees, transaction costs, and other expenses, which would reduce returns. Actual results will vary.

Views and opinions expressed are for informational purposes only and do not constitute a recommendation by GSAM to buy, sell, or hold any security. Views and opinions are current as of the date of this presentation and may be subject to change, they should not be construed as investment advice.

Opinions expressed are current opinions as of the date appearing in this material only. No part of this material may, without GSAM’s prior written consent, be (i) copied, photocopied or duplicated in any form, by any means, or (ii) distributed to any person that is not an employee, officer, director, or authorized agent of the recipient.

Copyright © 2007, Goldman, Sachs & Co. All rights reserved.