1 V. Simplifying the Portfolio Process

2 Simplifying the Portfolio Process Estimating correlations Single Index Models Multiple Index Models Average Models Finding Efficient Portfolios

Markowitz – not implemented

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5 or = return on the market = what expect stock i to return if R m = 0 = sensitivity of stock i to return on the market = random element of return

6 Sharpe Single Index Models Basic Equation By Construction i = 1,2,…N By Definition i = 1,2,…N By Assumption i = 1,2,…N

7 Expected Value

8 Expected Variance Stocks own variance

9 Covariance Between Stock

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11 ab c aStocks own variances due to market bCovariance risk cIndependent component of stocks own variance

12 # of rec.N N N N Sharpe Single Index 3N General Model 2N+N(N-1) 2 (11,475)(31,625)

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14 Alternative way of getting inputs N Securities Input Alternative Input N N N 1 1 3N + 2

15 Re-examine Risk

16 Non DiversifiableDiversifiable Market RiskResidual Risk

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22 Measuring Tendency of Beta to Regress to 1 1. Blume 2. Vasicek (Bayes)

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24 Vasicek

25 How Well Do They Forecast Future Betas 1. Vasicek 2. Blume 3. Unadjusted 4. All Betas = 1.0

26 How Well Do They Forecast Future Correlation Offsetting Influences 1. Plain Vanilla Beta - a) understates for assumes only reason stocks move together is due to market Blume - b) overstates - product of shrunk numbers is larger (.8) (1.2) =.96 (.9) (1.1) =.99 c) over or understates because of trend 2. Vasicek no c d) understates for larger Betas have larger standard errors therefore, moves larger betas more toward 1 than it moves smaller betas toward 1. 3.

27 Which of these biases are more important - empirical matter - ranking when adjust for mean 1. Vasicek 2. Blume 3. Plain Vanilla Beta 4. Beta = 1 5. Historical

28 Can we do better - Round 1- Fundamental Betas Why look at Fundamental Variables 1. Betas are risk measures - they should be related to fundamental variables 2. Betas are typically based on 60 months of data what happens is something changes 10 months after.

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30 Barra 1. Market Variability- 14 eg., Beta, trading volume, price range 2. Earnings Variability- 7 eg., earnings beta, unpred. of earnings 3. Unsuccess & Low Valuation - 8 eg., book/market, relative strength 4. Immaturity & Smallness - 9 eg., total assets, market share, age 5. Growth Orientation- 9 eg., div. yield, E/P, part growth 6. Financial Risk- 9 eg., leverage, interest coverage 7. Firm Characteristics- 6 eg., where stock trades, type of business 8. Industry Dummies

31 Forecast Fundamental Can we do better - Round 2 - Multi Index Models Assume E Indexes uncorrelated Mathematically we can always take a set of correlated indexes and convert them to a set of uncorrelated indexes (Appendix A) Then if E

32 Average Correlation Models If the single index model works better than the historic correlation matrix will other types of smoothing work better. Overall mean outperformed Single Index Models. Differences were statistically significant and economically significant 2 to 5 percent per year. Industry and pseudo industry mean models performed almost as well. International evidence.