litterman asset allocation

8/8/2019 Litterman Asset Allocation

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Quantitative Investing

Ibbotson Asset Allocation Conference

Robert Litterman

March, 2008


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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 economys expected future

productive capacity.

3) The world is clearly (given, among other indications, the diversity ofportfolios) 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.


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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 rigorousobjective research, state of art risk measurement and portfolio construction,

efficient trading, and patience.


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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


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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.


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An Optimal Portfolio

Maximizes return for a given level of risk

For illustrative purposes only.


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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


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Different Levels of Portfolio Aggregation

Can 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


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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


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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


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Focus on the Risk / Return Frontier

PortfolioExpec

tedR

eturn

Portfolio RiskFor illustrative purposes only.


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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


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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


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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?


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Implied Views Guide Behavior

If these implied views conform with current expectations

Portfolio structure is appropriate

Otherwise

Adjustments should be made to increase expected portfolioreturn

Consider increasing investments in assets with expected

returns above the implied views; decreasing those below


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Equilibrium Theory providesa neutral starting point for Expected Returns


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Modern Investment ManagementAn 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


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Sources of Total Return in a $1 Million Portfolio:

There are Three Fundamental

Sources Of Portfolio Return

1 Real Risk Free Rate

Risk free rate = 4.5%

$ 45,000

2 Market Risk Premium

20% Equity Allocation

0.82% ER

3.6% Vol

70% Equity Allocation

2.58% ER

9.6% Vol

3 Active Manager Return

100% Indexed

0.0% ER

1.5% Tracking Error

at IR = 0.5

Beta

Alpha

$ 8189 $ 25,779

$ 0 $ 7500



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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


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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


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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 thecapital markets back toward equilibrium and greater efficiency

So the equilibrium framework helps investors to identify

opportunitiesit provides the hurdle rate, the required expected

return for taking additional risk


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Equilibrium Expected Excess Returns

There are several versions of Global CAPM Equilibrium

We focus on a particularly simple one: Fischer Blacks Universal Hedging

An assumption on risk aversion determines:

A constant degree of currency hedging A risk premium or excess return on all assets

Fischers model is calibrated to long run market returns


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Forward Looking Equilibrium Risk Premia Lead to

Better Behaved Optimal Asset Allocations

Equilibrium risk premia justify market capitalization portfolio weights

Asset Class MarketCapitalization

Equilibrium RiskPremium

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 aresubject 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 beno assurance that these returns can be achieved. Actual returns are likely to vary. Please see additional disclosures.


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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 aresubject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are


4.50%

5.00%


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Strategic Asset Allocation providesa long term neutral anchor for

fund investment policy


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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


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The Equity Allocation Drives the Overall Level of Risk

Market Capitalization Weights Risk 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 assumptionsare 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


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Black-Litterman Model combinesMarket Equilibrium with Investor Views


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Incorporating Views In Portfolios

Step 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

UST N( 0, ) Measures Uncertainty


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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 Portfolios

Step 2. Create a General Representation


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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


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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


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Incorporating Views in Portfolios

Step 3. The Black-Litterman Model

Start with neutral expected returns derived from the global CAPM

equilibrium

Add a set of views:

p1 * = q1 + 1 1 N( 0, 1 )

p2 * = q2 + 2 2 N( 0, 2 )

p3 * = q3 + 3 3 N( 0, 3 )

Black-Litterman combines the views with equilibrium and provides

as output

BL = Black-Litterman Expected Returns


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An Example: Using the Black-Litterman model

Asset Class Symbol Volatility Equilibrium RiskPremium

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 aresubject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are



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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

5%

6%

7%

45%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 aresubject to high levels of uncertainty regarding future economic and market factors that may affect future performance. They are



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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 theexpected excess returns that drive an asset allocation

exercise.

Another approach is to use the Black-Litterman Global Asset

Allocation Model.


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The direct adjustment of expected excess returns

is a complex and often frustrating exercise

4.5%

5.0%

Equilibrium expected returns above reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategiclong-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect futureperformance. 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 beno assurance that these returns can be achieved. Actual returns are likely to vary. Please see additional disclosures.For illustrative purposes only.


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The optimal portfolio does something strange:

It allocates 10 percent to real estate

70%

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


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The Black-Litterman Model converts the views into a

set of consistent expected excess returns

4.5%

5.0%

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. Strategiclong-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect futureperformance. 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 beno assurance that these returns can be achieved. Actual returns are likely to vary. Please see additional disclosures.For illustrative purposes only.


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One can also specify higher or lower degrees of

confidence in a view

4.5%

5.0%

Equilibrium expected returns above reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategiclong-term assumptions are subject to high levels of uncertainty regarding future economic and market factors that may affect futureperformance. 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 beno assurance that these returns can be achieved. Actual returns are likely to vary. Please see additional disclosures.For illustrative purposes only.


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The Black-Litterman expected excess returns

lead to a well behaved optimal portfolio

70%

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


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In fact, in the simplest context the deviations from

the market cap portfolio are the view portfolio

1400%

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



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More generally, the Black-Litterman model

allocates risk to a combination of view portfolios

In the absence of:

A benchmark

Constraints

Transactions costsThe optimal portfolio is a linear combination of the market and

the view portfolios

PBL

= 0

x M + 1x p

1+

2x p

2+

3x p

3


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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


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In more complicated contexts the optimal portfolio

is not so obvious

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

60%When private equity

is constrained the

allocations to public

equity increase

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


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The Role of Active Management


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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

independen

t return

ExcessReturn (%)

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)


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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.

12%


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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.

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

0 0.1 0.2 0.3 0.4 0.5 0.6

Aggregate Active Risk Information Ratio

OptimalAllocationtoA

ctiveRisk

Allocations 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 resultsdo not reflect actual tradingand have inherent limitations.Please see additionaldisclosures.


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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


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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


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Appendix


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Strategic Long-Term AssumptionsRisk and Return characteristics

All tracking error assumptions reflect GSAM Global Investment Strategies estimates for above-average active managers and are basedon a historical study of the results of active management [see Active Risk Budgeting in Action: Evaluating Historical Characteristics ofTraditional Managers by Yoel Lax, Tarun Tyagi, and Kurt Winkelmann (GSAM Strategic Research, October 2003)], which is availableupon request. Expected returns are estimates of hypothetical average returns of economic asset classes derived from statisticalmodels. There can be no assurance that these returns can be achieved. Actual returns are likely to vary. Please see additionaldisclosures. All numbers reflect GSAM Global Investment Strategies strategic assumptions as of a certain date. Strategic long-termassumptions 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 S i T A i


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

Strategic Long-Term AssumptionsCorrelations

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Appendix

The currency market affords investors a substantial degree of leverage. This leverage presents the potential forsubstantial profits but also entails a high degree of risk including the risk that losses may be similarly substantial. Suchtransactions are considered suitable only for investors who are experienced in transactions of that kind. Currencyfluctuations 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 fixedincome securities.

An investment in real estate securities is subject to greater price volatility and the special risks associated with directownership 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 areprovided for your information only and do not imply that the portfolio will achieve similar results. The index compositionmay not reflect the manner in which a portfolio is constructed. While an adviser seeks to design a portfolio which reflectsappropriate risk and return features, portfolio characteristics may deviate from those of the benchmark.

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Appendix

There may be conflicts of interest relating to the Alternative Investment and its service providers, including Goldman Sachsand its affiliates, who are engaged in businesses and have interests other than that of managing, distributing and otherwiseproviding 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 theAlternative Investment, or in other investment vehicles that may purchase or sell such securities and instruments. Theseare considerations of which investors in the Alternative Investment should be aware. Additional information relating tothese 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 frominvestments 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 portfoliohas a steady investment return, gross of fees, of 0.5% per month and total management fees of 0.05% per month of themarket 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 remainconstant, the difference increases due to the compounding effect over time. Of course, the magnitude of the differencebetween 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

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Appendix

Alternative Investments such as hedge funds are subject to less regulation than other types of pooled investmentvehicles such as mutual funds, may make speculative investments, may be illiquid and can involve a significant useof leverage, making them substantially riskier than the other investments. An Alternative Investment Fund may incurhigh fees and expenses which would offset trading profits. Alternative Investment Funds are not required to provideperiodic pricing or valuation information to investors. The Manager of an Alternative Investment Fund has totalinvestment discretion over the investments of the Fund and the use of a single advisor applying generally similartrading programs could mean a lack of diversification, and consequentially, higher risk. Investors may have limitedrights 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 aninvestor's capital. Fund performance can be volatile. There may be conflicts of interest between the AlternativeInvestment Fund and other service providers, including the investment manager and sponsor of the AlternativeInvestment. Similarly, interests in an Alternative Investment are highly illiquid and generally are not transferablewithout the consent of the sponsor, and applicable securities and tax laws will limit transfers.

Strategic Long Term Assumptions

The data regarding strategic assumptions has been generated by GSAM for informational purposes. As such data isestimated and based on a number of assumptions; it is subject to significant revision and may change materially withchanges 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 futurereturns. They are not representative of how we will manage any portfolios or allocate funds to the asset classes.

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Appendix

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

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

Simulated Performance

Simulated performance is hypothetical and may not take into account material economic and market factors thatwould impact the advisers decision-making. Simulated results are achieved by retroactively applying a model withthe 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 GSAMs 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.

litterman asset allocation

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