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Asset Management Lecture 5 1st case study Dimensional Fund Advisors, 2002 The question set is available online The case is due on Feb 27. Outline for today Tracking portfolio Beta Adjustments estimation CAPM vs. single-factor index model Structural 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 cov( Ri , RM ) cov( ai i RM ei , RM ) cov( Ri , RM ) i cov( RM , RM ) cov( ei , RM ) i M2 i M2 For the CAPM model i cov( Ri , RM ) cov( ri , rM ) M2 What is different? CAPM vs. the Single-Factor Index Model CAPM Single-Factor Index Model Returns Expected Realized Equilibrium Yes No Residual returns Not uncorrelated Expression E (ri ) rf i E (rM ) rf Uncorrelated Ri ai i RM ei The CAPM and Reality Is the condition of zero alphas for all stocks as implied by the CAPM met Not 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 met Not perfect but one of the best available Is the CAPM testable Proxies 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 Return structure: ri (t ) X i ,k bk (t ) ei (t ) k ri (t ) X i , k (t ) 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 bk (t ) For other factors: standardized with mean=0 and SD=1 Factor return to factor k from time t to t+1 ei (t ) Stock i’s idiosyncratic return from time t to t+1 Structural Multifactor Models Risk structure: Vi , j k X k 1, k 2 1 i ,k1 Fk1,k 2 X j ,k 2 i , j Vi , j Covariance of stock i with stock j X i ,k 1 Exposure (factor loading) of stock i to factor k1, estimated at time t. Fk 1,k 2 i, j Covariance of factor k1 with factor k2 idiosyncratic covariance of stock i with stock j 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 rit i iM RMt iSMB SMBt iHML HMLt eit 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