Economic Theory of Choice Certainty

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V. Simplifying the Portfolio Process
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Simplifying the Portfolio Process   Estimating
correlations Single Index Models Multiple Index
Models Average Models   Finding Efficient
Portfolios
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1956 Markowitz not implemented  
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or
return on the market what expect stock i
to return if Rm 0 sensitivity of stock i
to return on the market   random
element of return
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Sharpe Single Index Models   Basic Equation
By Construction
i 1,2,N
By Definition
i 1,2,N
By Assumption
i 1,2,N
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Expected Value
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Expected Variance Stocks own variance
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Covariance Between Stock
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a b c   a Stocks own variances
due to market   b Covariance risk   c Independent
component of stocks own variance
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Alternative way of getting inputs
Input
Alternative Input
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Re-examine Risk
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Non Diversifiable Diversifiable Market
Risk Residual Risk
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Measuring Tendency of Beta to Regress to 1
1. Blume
2. Vasicek (Bayes)
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Vasicek
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How Well Do They Forecast Future Betas
1.       Vasicek 2.            Blume 3.
Unadjusted 4. All Betas 1.0
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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.
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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
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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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Barra
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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
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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.