quantitative investing ibbotson asset allocation conference robert litterman march, 2008
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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%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
4.50%
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
0%
1%
2%
3%
4%
5%
6%
7%
C US DE EE GFI HY PE RE HF
Market Cap Weights
0%
5%
10%
15%
20%
25%
30%
35%
40%
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%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
4.0%
4.5%
5.0%
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
0%
10%
20%
30%
40%
50%
60%
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…
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
4.0%
4.5%
5.0%
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
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
4.0%
4.5%
5.0%
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%
20%
30%
40%
50%
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%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
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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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1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
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9.00%
0 0.1 0.2 0.3 0.4 0.5 0.6
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.