Asset ManagementAsset Management

Lecture ThreeLecture Three

Outline for todayOutline for today

Index modelIndex modelSingle-factor index modelSingle-factor index modelAlpha and security analysisAlpha and security analysis

Drawbacks of MarkowitzDrawbacks of Markowitz

The model requires a huge number of The model requires a huge number of estimates estimates E.g. 50 stocksE.g. 50 stocks

50 estimates of E(r)50 estimates of E(r)50 estimates of var(r)50 estimates of var(r)1225 estimates of cov(ri, rj)1225 estimates of cov(ri, rj)

The model does not provide guideline to The model does not provide guideline to the forecasting of E(r)-rfthe forecasting of E(r)-rf

Assumption: a broad market index like the Assumption: a broad market index like the S&P 500 is the common factor.S&P 500 is the common factor.

ßßii = index of a securities’ particular return = index of a securities’ particular return

to the factorto the factor m m = Unanticipated movement in common = Unanticipated movement in common

factor that drives security returnsfactor that drives security returns eeii = firm-specific surprise = firm-specific surprise

Single Factor ModelSingle Factor Model

( )i i i ir E r m e

Single-Index ModelSingle-Index Model

Regression Equation:Regression Equation:

Expected return-beta relationship:Expected return-beta relationship:

( ) ( ) ( )t i t M iR t R t e t

( ) ( )i i i ME R E R Systematic risk Systematic risk

premiumpremiumNon-market Non-market

premiumpremium

Single-Index Model ContinuedSingle-Index Model ContinuedRisk and covariance:Risk and covariance:

Total risk = Systematic risk + Firm-specific Total risk = Systematic risk + Firm-specific risk:risk:

Covariance = product of betas x market index Covariance = product of betas x market index risk:risk:

Correlation = product of correlations with the Correlation = product of correlations with the market indexmarket index

2 2 2 2 ( )i i M ie

2( , )i j i j MCov r r

2 2 2

( , ) ( , ) ( , )i j M i M j Mi j i M j M

i j i M j M

Corr r r Corr r r xCorr r r

Index Model and DiversificationIndex Model and Diversification Portfolio’s variance:Portfolio’s variance:

Variance of the equally weighted portfolio of Variance of the equally weighted portfolio of firm-specific components:firm-specific components:

When When nn gets large, becomes gets large, becomes negligible negligible

222 2

1

1 1( ) ( ) ( )

n

P ii

e e en n

2 2 2 2 ( )P P M Pe

2 ( )Pe

Figure 8.1 The Variance of an Equally Figure 8.1 The Variance of an Equally Weighted Portfolio with Risk Coefficient Weighted Portfolio with Risk Coefficient

ββpp in the Single-Factor Economy in the Single-Factor Economy

Example: HP and the S&P 500Example: HP and the S&P 500

Example: HP and the S&P 500Example: HP and the S&P 500

Table 8.1 Excel Output: Regression Table 8.1 Excel Output: Regression Statistics for the SCL of Hewlett-PackardStatistics for the SCL of Hewlett-Packard

2500&

2PSHP

3817.01211.0

11.0

012.059/7162.059/2

SDannualized

SDmonthly

SSTotalmonthly HP

Figure 8.4 Excess Returns on Portfolio Figure 8.4 Excess Returns on Portfolio AssetsAssets

Alpha and Security AnalysisAlpha and Security Analysis

Macroeconomic analysis is used to estimate Macroeconomic analysis is used to estimate the risk premium and risk of the market indexthe risk premium and risk of the market index

Statistical analysis is used to estimate the Statistical analysis is used to estimate the beta coefficients of all securities and their beta coefficients of all securities and their residual variances, residual variances, σσ2 2 ( ( e i )e i )

Developed from security analysisDeveloped from security analysis

Alpha and Security AnalysisAlpha and Security Analysis The market-driven expected return is The market-driven expected return is

conditional on information common to all conditional on information common to all securitiessecurities

Security-specific expected return forecasts Security-specific expected return forecasts are derived from various security-valuation are derived from various security-valuation models models The alpha value distills the incremental risk The alpha value distills the incremental risk

premium attributable to private informationpremium attributable to private information Helps determine whether security is a good Helps determine whether security is a good

or bad buyor bad buy