There should be 2 different ways The first one is Treynor ratio because it is

There should be 2 different ways the first one is

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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 risk-adjusted 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 short-selling of shares. Re-calculate 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
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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 “Fama-French” contains four series of returns taken from Ken French’s website. RMRF is the return in excess of the risk-free 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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