Asset Management

Lecture 5

1st case study

Dimensional Fund Advisors, 2002The question set is available onlineThe case is due on Feb 27.

Outline for today

Tracking portfolioBeta

Adjustmentsestimation

CAPM vs. single-factor index modelStructural multifactor model

Tracking Portfolio

A Tracking Portfolio (T) is designed to match the systematic component of a portfolio (P)’s return, and has as little nonsystematic risk as possible.

This procedure is called Beta Capture. Example:

R(P) = 0.04 + 1.4R(S&P500) + e(P) R(T) = 1.4R(S&P500)

A long position in P + a short position in T R(C) = R(P) – R(T) = 0.04 + 1.4R(S&P500) + e(P) -1.4R(S&P500) = 0.04 + e(P) Long-Short Strategy to achieve a Market Neutral position Alpha Transport

Beta

Adjustment Beta coefficients seem to move to 1 over time Example by Merrill Lynch

Adjusted beta=2/3 sample beta + 1/3 (1) Prediction

Simple approach Current beta = a + b (Past beta) Forecast beta= a + b (current beta)

An expanded version Current beta = a + b1 (Past beta) + b2 (Size) + b3 (debt

ratio) Variance of earnings, growth in earnings, dividend yield

etc.

CAPM vs. the Single-Factor Index Model

For the index model

For the CAPM model

What is different?

),cov(),cov( MiMiiMi ReRaRR 2),cov(),cov(),cov( MiMiMMiMi ReRRRR

2

),cov(

M

Mii

RR

2

),cov(

M

Mii

rr

CAPM vs. the Single-Factor Index Model

CAPM Single-Factor Index Model

Returns Expected Realized

Equilibrium Yes No

Residual returns Not uncorrelated

Uncorrelated

Expression fMifi rrErrE )()( iMiii eRaR

The CAPM and Reality

Is the condition of zero alphas for all stocks as implied by the CAPM metNot perfect but one of the best available

Figure 9.4 Estimates of Individual Mutual Fund Alphas, 1972-1991

The CAPM and Reality

Is the condition of zero alphas for all stocks as implied by the CAPM metNot perfect but one of the best available

Is the CAPM testableProxies must be used for the market

portfolio CAPM is still considered the best available

description of security pricing and is widely accepted

Structural Multifactor Models

)()()( , tetbXtr ikk

kii )(tri

)(, tX ki

Excess return of stock i from time t to t+1

Exposure (factor loading) of stock i to factor k, estimated at time t.

For industry: 0/1

For other factors: standardized with mean=0 and SD=1)(tbk Factor return to factor k from time t to t+1

)(tei Stock i’s idiosyncratic return from time t to t+1

Return structure:

Structural Multifactor Models

jikjkk

k

kkkiji XFXV ,2,2,1

12,11,,

jiV ,

1,kiX

Covariance of stock i with stock j

Exposure (factor loading) of stock i to factor k1, estimated at time t.

2,1 kkF Covariance of factor k1 with factor k2

ji , idiosyncratic covariance of stock i with stock j

Risk structure:

Structural Multifactor Models

The choice of factors A priori factors Three categories

Response to external influences (macro factors) inflation oil price Exchange rates GDP Problems:

Estimation error (error in variable) Nonstationary response coefficients Poor data quality

Structural Multifactor Models

The choice of factors A priori factors Three categories

Response to external influences (macro factors) Cross-sectional comparisons of asset attributes

Compare attributes of the stocks Fundamental

Ratios (dividend yield etc) analysts forecasts

Market Volatility, return, share turnover, etc.

Problem: Error in variable Nonstationary coefficient

Structural Multifactor Models

The choice of factors A priori factors Three categories

Response to external influences (macro factors) Cross-sectional comparisons of asset attributes Internal or statistical factors

Factors produced by statistical methods: Principal component analysis Maximum likelihood analysis Expectations maximization analysis

Problems: Very difficult to interpret Spurious correlations Cannot capture changes over time

Structural Multifactor Models

The choice of factors A priori factors Three categories

Response to external influences (macro factors) Cross-sectional comparisons of asset attributes Internal or statistical factors

Criteria: Incisive: distinguish returns Intuitive: interpretable and recognizable

Recognizable investment themes: industry, size, value, growth etc.

Interesting: help to explain alpha or beta or volatility

Structural Multifactor Models

Typical factors Industry factors : 0/1 factors Risk indices

Volatility Momentum Size Liquidity Growth Value Earnings volatility Financial leverage

Example: The Relationship Between Illiquidity and Average Returns

Another Example:Fama-French Three-Factor Model

The factors chosen are variables that on past evidence seem to predict average returns well and may capture the risk premiums

Where: SMB = Small Minus Big, i.e., the return of a portfolio of small stocks

in excess of the return on a portfolio of large stocks HML = High Minus Low, i.e., the return of a portfolio of stocks with a

high book to-market ratio in excess of the return on a portfolio of stocks with a low book-to-market ratio

it i iM Mt iSMB t iHML t itr R SMB HML e