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Fundamentals Drive AlphaPresentation to the
NYU Economics Honors Society Discussion SeriesApril 12, 2006
This talk is based on a paper, “Fundamentals Drive Alpha” co-authored by:
Andrew Alford, PhDBob Jones, CFATerence Lim, PhD, CFA, CPABob Litterman, PhD
The paper is available at: http://activealpha.gs.com/structured_equity.html
This material is provided for educational purposes only and should not be construed as investment advice or an offer to sell, or the solicitation of offers to buy, any security. Opinions expressed herein are current as of the date appearing in this material.
2
What motivated the Black-Litterman model?
Optimizers are very powerful,
sometimes very sensitive tools
Investors had, historically, found optimizers didn’t add much value to portfolio construction or asset allocation because the results were badly behaved
In 1989 I posed a question to Fischer Black:
“Our asset allocation optimizer is extremely sensitive to its inputs. What can we do?”
Black responded:
“I’ve just written a paper using a Global CAPM framework to analyze currency hedging.
Perhaps we should embed the optimization in the context of such an equilibrium”
I pondered Black’s suggestion and thought:
“I wonder what that means?”
Fundamentals Drive Alpha
3
The Black-Litterman model
The answer begins almost 30 years earlier with Theil and Goldberger (1961) “On Pure and Mixed Statistical Estimation in Econometrics.” They describe how to combine Prior Information with a Sample.
This well known formula is called “mixed estimation”
Black and Litterman (1992) “Global Portfolio Optimization” use the same formula to combine a prior, “Equilibrium” with an investor’s “Views”
The Global CAPM Equilibrium becomes the center of gravity for expected returns.
Views specified by the investor pull expected returns away from the equilibrium values along curved paths defined by the covariance structure of the underlying asset returns
Not only does the equilibrium make economic sense, but when those expected returns are used to drive the optimizer, the optimizer stops misbehaving
Fundamentals Drive Alpha
4
An advertisement for our book(where, in 626 pages, we provide more details)
Fundamentals Drive Alpha
5
Optimal Trades
Optimization
Risk Model
Client objectives
Transaction cost estimates
Constraints
This diagram shows where Black-Litterman fits into our Quantitative Equity process
Reverse Optimization
Implied stock alphas
Optimal Tilt Portfolio
Fundamentals Drive Alpha
View Portfolios
Risk Allocation
Current Portfolio
Black-Litterman
Quantitative Analysis of Fundamental Factors
6
View portfolios
Views are represented as mathematical statements:
A particular portfolio, p, has a particular expected return q
The investor provides a set of such views (defined by a kxn matrix P containing the weights of the portfolios), a k-vector Q of expected returns for the portfolios, and the Covariance Structure for these “View Portfolios”
We write: P = Q + ~ N( 0, )
Where is the vector of expected returns for individual assets
Each row of P reflects a view: that the portfolio with the given weights has the given expected return
specifies, along the diagonal, the degree of uncertainty about the view. We call its inverse the “confidence” in the view. (We can also use the off-diagonal elements of to specify views for which the degrees of confidence should be related)
Fundamentals Drive Alpha
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The Black-Litterman formula
Using the Theil-Goldberger formula, Black-Litterman combines the Views with a prior reflecting the global CAPM Equilibrium: e
is the n-vector of equilibrium risk premia from Fischer’s “Universal Hedging” global CAPM.
e reflects the degree of uncertainty in the prior that expected returns have equilibrium values
We assume the uncertainty about the means has a covariance structure, proportional to the covariance matrix of asset returns
The result is a vector of expected returns:
* P’PP’Q
which can be used as input to an optimizer.
Fundamentals Drive Alpha
8
Traditional asset allocation optimization
We illustrate the traditional approach to asset allocation in a world with 4 equity markets.
The equity markets: ( US, Japan, UK, Germany)
1) Make assumptions about expected returns
Attempt to express a bullish view on the US market
Expected Returns Above the Risk Free Rate
US = 4%; Japan = 3%; UK = 3%; Germany = 3%;
2) Estimate Volatilities and Correlations:
Vols: US = 15%; Japan = 17%; UK = 16%; Germany = 15%;
Corrs: US/Japan = .45; US/UK = .3; US/Germany = .25
Japan/UK = .4; Japan/Germany = .45; UK/Germany = .3
Optimal Portfolio Weights
-10.0%
0.0%10.0%
20.0%
30.0%40.0%
50.0%60.0%
US Japan UK Germany
Fundamentals Drive Alpha
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Black-Litterman and asset allocation
We illustrate two views in a world with 4 equity markets.
The equity markets: ( US, Japan, UK, Germany)
1) Bullish US equities (1 percent above equilibrium )
(1, 0, 0, 0) *
2) Japan equities to outperform UK equities by 1 percent
(0, 1, -1, 0) *
Equilibrium Expected Returns vsThe Black-Litterman Expected Return Vector: *
0.0%
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US Japan UK Germany
Equilibrium
Black-Litterman
Fundamentals Drive Alpha
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The Optimal Tilt Portfolio
The mean-variance optimal portfolio in an unconstrained context based on the Black-Litterman expected returns is a tilt away from a scaled Market portfolio toward a linear combination of the View Portfolios.
We call the deviations from market capitalization weights the “Optimal Tilt Portfolio.” As shown in He and Litterman(1999), the OTP is a linear combination of the View Portfolios and the Market Portfolio
Portfolio Deviations Based on View Portfolio 1
-0.06-0.04-0.020.000.020.040.060.080.100.12
US Japan UK Germany
Portfolio Deviations Based on View Portfolio 2
-0.06-0.04-0.020.000.020.040.060.080.100.12
US Japan UK Germany
Optimal Tilt Portfolio
-0.06-0.04-0.020.000.020.040.060.080.100.12
US Japan UK Germany
Fundamentals Drive Alpha
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Black-Litterman and active stock selection
If (1) the View Portfolios are uncorrelated with the Market
and (2) the Optimal Portfolio is constrained to have zero beta,
Then the Optimal Tilt Portfolio is simply a weighted average of the View Portfolios.
In this case, (and assuming there are no other binding constraints) the optimal active weights are proportional to the Optimal Tilt Portfolio.
You might well ask, “Where’s the Juice?”
Equilibrium returns are no longer even part of the equation.
Fundamentals Drive Alpha
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Capturing views in client stock portfolios:The Black-Litterman framework
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Fundamentals drive alpha!
Capital markets are competitive, but not entirely efficient.
However, beating the market is not easy.
We believe the key driver of superior investment performance is superior fundamental research.
Fundamental characteristics should be robust.
— We start with characteristics that are Economically Intuitive, then we conduct empirical tests
— To be considered an alpha driver, characteristics should demonstrate that they identify stocks with superior returns over time in different regions, economic environments, and market segments.
Superior returns are captured through careful portfolio construction and trading
— We use the Black-Litterman framework and customized quantitative tools to enhance portfolio efficiency and minimize trading costs
Fundamentals Drive Alpha
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Lots of fundamental stock characteristics help determine value
P/E to Growth
XYZ’sValue
Fundamentals Drive Alpha
Return on Equity
Price to Cash Flow
Debt / Equity Dividend Yield
Price / Book
Dividend Discount Model
Earnings Surprise
Price/EarningsBeta
Earnings Momentum
Size
Price Momentum
Payout Ratio
Long Term Growth
Accruals
Interest Coverage
Expected Growth
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A few stock characteristics also help to forecast returnsThis is a surprise: It should not happen in efficient markets
XYZ’sAlpha
Fundamentals Drive Alpha
Price / Book
Earnings Momentum
Price MomentumAccruals
Price to Cash Flow
Return on Equity
P/E to GrowthPrice/Earnings
Dividend Discount Model
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Most stock characteristics don’t forecast returnsThe information they contain is, on average, fully reflected in current prices
XYZ’sValue
Fundamentals Drive Alpha
Debt / Equity
Long Term Growth
Dividend Yield
Beta
Size
Payout Ratio
Interest Coverage
Expected Growth
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We express our investment insights as “views”
We have views about fundamental characteristics, not individual stocks.
We believe portfolios of stocks with positive alpha drivers will outperform portfolios of stocks with negative alpha drivers.
Translating views into portfolios is not easy.
The alpha drivers have different expected returns and risks.
Individual stocks have unequal, and sometimes offsetting, fundamental characteristics.
Many investors use a simplistic approach that ignores risk:
The stronger a stock’s fundamentals
The larger the view
The bigger the stock’s position
Our process combines fundamental characteristics to maximize portfolios’ information ratio.
Fundamentals Drive Alpha
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View portfolios capture the information in the alpha drivers
Our process over-weights stocks with good fundamentals and under-weights stocks with poor fundamentals
• We form multiple view portfolios, one for each alpha driver
• The view portfolios are long (short) stocks with positive (negative) values for the corresponding alpha drivers
• Each view portfolio has a given exposure to the corresponding alpha driver and minimizes exposure to other sources of risk
• View portfolios have superior returns because they have attractive fundamentals and limited risk
Fundamentals Drive Alpha
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What does a stock selection “view portfolio” look like?
It’s really up to the investor.
We think View Portfolios should represent fundamental characteristics that forecast returns, for example, “operating efficiency”
If you believe this characteristic forecasts higher future returns, then you can imbed this belief in a “View Portfolio.”
Industry Normalized Operating Efficiency
(2.50)(2.00)(1.50)(1.00)(0.50)0.000.501.001.50
EX
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The data above is for illustrative purposes only and is not a recommendation of any security. Fundamentals Drive Alpha
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There are different approaches to setting the weights in view portfolios
Weights Based on Factor Ranks
-1.500-1.000-0.5000.0000.5001.0001.500
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Minimum Risk Exposure to Factor
-2.5-2
-1.5-1
-0.50
0.51
1.5
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Weights Based on Factor Values
(2.50)(2.00)(1.50)(1.00)
(0.50)0.000.501.001.50
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The data above is for illustrative purposes only and is not a recommendation of any security. Fundamentals Drive Alpha
21
Historical effectiveness of each alpha driver
Fundamentals Drive Alpha
The performance results stated above are backtested based on a methodology that is derived from an analysis of past market data with the benefit of hindsight. These results do not reflect the performance of a GSAM managed account or composite and are being shown for informational purposes only. If GSAM had managed your account during the period shown above it is highly improbable that your account would have been managed in a similar fashion due to differences in economic and market conditions. The performance results disclosed herein do not represent the results of actual trading using client assets. The backtested performance results depicted above reflect the reinvestment of dividends and other earnings, but do not reflect the deduction of advisory fees, brokerage or other commissions or exchange fees or any other expenses a client would have to pay. Source: Goldman Sachs.
-10%
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Cum
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Simulated excess returns to CORE themes (June 1977 to September 2004)
MomentumEarnings Quality
Management Impact
Valuation
Analyst SentimentProfitability
22
Combining view portfolios
The Black-Litterman framework delivers a robust combination of view portfolios
The weights in the Optimal Tilt Portfolio (OTP) are driven by a number of considerations. We allocate more risk to view portfolios (alpha drivers) with:
• Better historical results
• More consistent results
• Stronger confidence (lower uncertainty)
• Greater diversification benefits
• Longer signal persistence
• Lower required turnover
Fundamentals Drive Alpha
23
Limitations of the optimal tilt portfolio
In an ideal world, a client’s portfolio would be the benchmark plus the OTP
Portfolio weight = Benchmark weight + OTP weight
= +
Unfortunately, the OTP is not appropriate for most clients:
• The OTP is a zero-investment, long-short portfolio
• The OTP does not reflect client-specific guidelines and restrictions
• The OTP ignores transaction costs
Fundamentals Drive Alpha
24
Consistency with the risk model
The Black-Litterman framework produces individual stock alphas, based on the OTP, that are consistent with the risk model. They are, in effect, a reverse-optimization of the OTP based on the same risk model.
We believe that risk models play a central part throughout the investment process
They should be applied consistently when creating the OTP and stock alphas, as well as in the final portfolio optimization step with client objectives, constraints, and transactions costs
They should be robust: We estimate our risk models using a parsimonious factor structure, we use daily data, and we use shrinkage estimators
Our risk models are customized and proprietary: they measure the unique risks in our view portfolios. How else could one expect to accurately allocate risk across those factors?
Comparing two managers who have the same fundamental views, the one who captures those views most efficiently, through better risk modeling and portfolio construction, will be more successful
Fundamentals Drive Alpha
25
Optimal Trades
Optimization
Risk Model
Client objectives
Transaction cost estimates
Constraints
This diagram shows where Black-Litterman fits into our Quantitative Equity process
Reverse Optimization
Implied stock alphas
Optimal Tilt Portfolio
Fundamentals Drive Alpha
View Portfolios
Risk Allocation
Current Portfolio
Black-Litterman
Quantitative Analysis of Fundamental Factors
P
*
26
References
Black, F., and Litterman, R. 1992. “Global Portfolio Optimization.” Financial Analysts Journal 48 (September/October): 28-43
He, G., and Litterman, R. 1999. “The Intuition behind Black-Litterman Model Portfolios.” Goldman Sachs Investment Management Series.
Theil, H., Goldberger, A.S., 1961. On pure and mixed estimation in econometrics. International Economic Review 2, 65–78.
References
27
Additional information
Additional Information
GeneralOpinions expressed are current opinions as of the date appearing in this material only. No part of this material may, without Goldman Sachs Asset Management’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.
In the event any of the assumptions used in this presentation do not prove to be true, results are likely to vary substantially from the examples shown herein. These examples are for illustrative purposes only and do not purport to show actual results.
This material is provided for educational purposes only and should not be construed as investment advice or an offer to sell, or the solicitation of offers to buy, any security. Opinions expressed herein are current as of the date appearing in this material.
Expected returns are statistical estimates of hypothetical average returns of economic asset classes, derived from statistical models. Actual returns are likely to vary from expected returns. Expected return models apply statistical methods and a series of fixed assumptions to derive estimates of hypothetical average asset class performance. Reasonable people may disagree about the appropriate statistical model and fixed assumptions. These models have limitations, as the assumptions may not be consensus views, or the model may not be updated to reflect current economic or market conditions. Accordingly, these models should not be relied upon to make predictions of actual future account performance. Goldman Sachs has no obligation to provide recipients hereof with updates or changes to such data.
Copyright 2004 Goldman, Sachs & Co. All Rights Reserved
Review #04-3856
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