Performance Evaluation
Professor Alexander Barinov
School of Business Administration
University of California Riverside
MGT 295F Empirical Methods
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Outline
1Performance Measures
2Performance Evaluation
3Alpha and Expense Ratio
4Example
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Performance Measures
Appraisal Ratio
If you found a security with positive alpha, you
have to choose between outperformance and
diversification
An analogue of the Sharpe ratio, called
appraisal ratio, may help you in finding the right
trade-off
Suppose you have estimated the market
model/CAPM and have the alpha and the
volatility of the residuals
RFund −RF =αFund +βFund (RM−RF ) +
Appraisal ratio (the more the better) is α
σ
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Performance Measures
How to Calculate Appraisal Ratio
We need to run the market model and take from there the
alpha and the “standard error” for the model
Consider Fidelity Freedom 2030 (alpha 5 bp per month,
standard deviation of the CAPM residuals 67 bp per month)
Consider also T. Rowe Price New Asia (alpha 1.17% per
month, standard deviation of the CAPM residuals 4.98% per
month)
Appraisal ratio is 0.05%
0.67%=0.075 for Freedom, 1.17%
4.98%=0.24
for New Asia
If you accept 1% extra idiosyncratic volatility, with Freedom
you will get extra 7.5 bp per month, with New Asia you will get
extra 24 bp per month – New Asia is better
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Performance Measures
Zero-Investment Portfolios
Why we run RF−RF =α+β·(RM−RF )for a
fund, but HML =α+β·(RM−RF )(without −RF
on the left-hand side for the value minus growth
strategy?
We actually run H−RF =α+β·(E(RM)−RF )for
value and L−RF =α+β·(E(RM)−RF )for
growth and then subtract one from the other
αand βfrom HML =α+β·(RM−RF )are the
difference in αand βbetween value and growth
Same thing with other performance measures if
applied to zero-investment strategies: do not
subtract the risk-free rate or assume it is zero
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Performance Measures
Example 1: Sharpe Ratio of HML
Sample: August 1963 – December 2006
Market portfolio has average excess return
0.49% per month, standard deviation 4.38%
HML portfolio has average return 0.46% per
month, standard deviation 2.9%
SMKT =RMKT −RF
σMKT
=0.49
4.38 =0.11
SHML =RHML
σHML
=0.46
2.9=0.16
HML beats the market on the reward-to-risk
ratio by 42% – HML is a better investment
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Performance Measures
Example 1: Sharpe Ratio of HML
Put it in words: “With MKT, you get extra 11 bp per
month if you increase the standard deviation of your
position by 1% per month; with HML you will get extra
16 bp per month for the same thing”
You do not need to subtract RF from HML, because
