There should be 2 different ways. The first one is Treynor ratio because it is useful when the
portfolio in question represents one of many risky investments. And Jensen’s alpha can also be
used because it is useful when the portfolio in question represents one of many risky investments.
TEPLX
PRWCX
JANSX
FMAGX
TWCGX
OARDX
Treynor's Measure
0.002874
0.009544782
0.001521
0.00093
0.002147
0.002601
TEPLX
PRWCX
JANSX
FMAGX
TWCGX
OARDX
Jensen's Alpha
0.000885
0.004290517

0.00043
0.00109
0.000237
0.00056
For Treynor ratio, we should choose
PRWCX
. For, Jensen’s alpha, we should choose
PRWCX
as
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well.
Comparing these two method, Treynor ratio measures excess return per unit of systematic risk and
it measures abnormal return, adjusts for systematic risk.
9. Suppose that you wish to compute a performance measure that takes into account the total
risk of each fund, yet is easy to interpret in terms of differential returns with the market
index. What performance measure is appropriate here? Based on this measure, which fund
would you choose? Would you expect your results to differ from those in (6)? Why or why
not?
M
2
focuses on total volatility as a measure of risk, and its riskadjusted measure is easy in
terms of differential returns with the market index. Thus, we should choose this performance
measure in this situation.
TEPLX
PRWCX
JANSX
FMAGX
TWCGX
OARDX
M^2
0.000618
0.005888944
0.00051
0.00102
0.000103
0.00039
M^2 is higher and better. Thus, choose
PRWCX.
WE expect that the result here should be the
same as the result in (6) because both of Sharpe ratio and M
2
focus on total volatility as a measure
of risk.
10. Suppose that the pension fund wants to invest in all six of these actively managed funds
for its entire risky portfolio. Use solver to find the maximum attainable Sharpe ratio and
report the optimal weight to put in each of the six active funds. What is the expected return
and standard deviation of this portfolio? Do the results surprise you, or are they intuitively
appealing? Most mutual funds forbid the shortselling of shares. Recalculate the optimal
weights assuming no short sales are allowed. Does the result surprise you?
Optimal weight:
TEPLX
0.30044
return
0.012386
PRWCX
2.129546
variance
0.000931
JANSX
0.237371
Std Dev
0.030508
FMAGX
1.29255
Sharpe Ratio
0.334859
TWCG
X
0.706712
OARDX
0.48064
1.00000
expect return: 0.012386
Standard deviation: 0.030508
This result surprises me because the PRWCX has a pretty high weight. It is much higher than
others.
It is intuitively appealing because its expect return is extremely high and Std Dev is pretty low.
Optimal weight no short sales:
TEPLX
0
return
0.007536
PRWCX
1.00000
variance
0.001085
JANSX
0
Std Dev
0.032942
FMAGX
0
Sharpe Ratio
0.162885
TWCG
X
0
OARDX
0
1.00000
This result surprise me because the optimal weight is all of PRWCX and the expected return and
Std Dev are totally the same with PRWCX.
Part III
The worksheet labeled “FamaFrench” contains four series of returns taken from Ken
French’s website. RMRF is the return in excess of the riskfree rate on the universe of all
NYSE, AMEX, and Nasdaq stocks. (This is similar to the S&P500 series based on the VFINX
mutual fund, but is a more comprehensive market return measure.) SMB is the “size factor”
premium. This is the return on the 30% of the smallest stocks in the market minus the return
on the 30% of the biggest stocks. HML is the “value factor” premium. This is the return on
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 Spring '09
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