Comm W. Suo Slide 1

Comm W. Suo Slide 2 Diversification  Random selection  The effect of diversification  Markowitz diversification What information are needed? How to simplify the approach?

Comm W. Suo Slide 3 Linear Regression  Review  Properties  R-square  Example spreadsheet

Comm W. Suo Slide 4 Advantages:  Reduces the number of inputs for diversification  Easier for security analysts to specialize Drawback:  the simple dichotomy rules out important risk sources (such as industry events) The Single Index Model

Comm W. Suo Slide 5 ß i = index of a security’s particular return to the factor F= some macro factor; in this case F is unanticipated movement; F is commonly related to security returns Single Factor Model Assumption: a broad market index like the S&P500 is the common factor

Comm W. Suo Slide 6 Single Index Model a i = stock’s expected return if market’s excess return is zero b i (r M -r i ) = the component of return due to market movements e i = the component of return due to unexpected firm- specific events

Comm W. Suo Slide 7 Let: R i = (r i - r f ) R m = (r m - r f ) Risk premium format R i = α i + ß i R m + e i Risk Premium Format

Comm W. Suo Slide 8  Market or systematic risk: risk related to the macro economic factor or market index  Unsystematic or firm specific risk: risk not related to the macro factor or market index  Total risk = Systematic + Unsystematic Components of Risk

Comm W. Suo Slide 9  i 2 = total variance  i 2  m 2 = systematic variance  2 (e i ) = unsystematic variance Measuring Components of Risk

Comm W. Suo Slide 10 Total Risk = Systematic +Unsystematic Examining Percentage of Variance

Comm W. Suo Slide 11 Security Characteristic Line Excess Returns (i) SCL Excess returns on market index R i =  i + ß i R m + e i

Comm W. Suo Slide 12 Index Model  Spreadsheet example

Comm W. Suo Slide 13 Index Model and Diversification No. of Securities St. Deviation Market Risk Unique Risk  2 (e P )= 2 (e) / n P2M2P2M2

Comm W. Suo Slide 14 Industry Prediction of Beta  BMO Nesbitt Burns and Merrill Lynch examples BMO NB uses returns not risk premiums a has a different interpretation: a + r f (1-b) Merill Lynch’s ‘adjusted b’  Forecasting beta as a function of past beta  Forecasting beta as a function of firm size, growth, leverage etc.

Comm W. Suo Slide 15 Tests of the Single Factor Model Tests of the expected return beta relationship  First Pass Regression Estimate beta, average risk premiums and unsystematic risk  Second Pass: Using estimates from the first pass to determine if model is supported by the data  Most tests do not generally support the single factor model

Comm W. Suo Slide 16 Single Factor Test Results Return % Beta Predicted Actual

Comm W. Suo Slide 17 Roll’s Criticism on the Tests  The only testable hypothesis: the mean-variance efficiency of the market portfolio  All other implications are not independently testable  CAPM is not testable unless we use the true market portfolio  The benchmark error

Comm W. Suo Slide 18 Measurement Error in Beta Statistical property:  If beta is measured with error in the first stage,  Second stage results will be biased in the direction the tests have supported  Test results could result from measurement error

Comm W. Suo Slide 19 Conclusions on the Tests’ Results  Tests proved that CAPM seems qualitatively correct Rates of return are linear and increase with beta Returns are not affected by nonsystematic risk  But they do not entirely validate its quantitative predictions The expected return-beta relationship is not fully consistent with empirical observation.

Comm W. Suo Slide 20 Multifactor Models  Use factors in addition to market return Examples include industrial production, expected inflation etc. Estimate a beta for each factor using multiple regression  Chen, Roll and Ross Returns a function of several macroeconomic and bond market variables instead of market returns  Fama and French Returns a function of size and book-to-market value as well as market returns

Comm W. Suo Slide 21 Researchers’ Responses to Fama and French  Utilize better econometric techniques  Improve estimates of beta  Reconsider the theoretical sources and implications of the Fama and French-type results  Return to the single-index model, accounting for non-traded assets and cyclical behavior of betas

Comm W. Suo Slide 22 Jaganathan and Wang Study (1996)  Included factors for cyclical behavior of betas and human capital  When these factors were included the results showed returns were a function of beta  Size is not an important factor when cyclical behavior and human capital are included