T9 - UNIVERSITY OF TORONTO Joseph L. Rotman School of...

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UNIVERSITY OF TORONTO Joseph L. Rotman School of Management RSM332 Tutorial #9 Problem Set Nov.16/Nov.17 2011 1. In your research of two mutual funds, Thrifty Fund and Ponzi Fund, you estimate their respective expected returns over the next year as 3 percent for Thrifty and 21.4 percent for Ponzi. Thrifty Fund invests only in short-term T-bills and is risk-free. Its return for the following year is known in advance. Ponzi invests in risky securities. The estimated standard deviation of its returns is 64 percent. To better gauge Ponzi’s risk you ran the usual CAPM regression in Excel, R Ponzi - R f = α + β ( R m - R f ) + ±. The regression generated the following output (Δ is an unknown you will need to compute below): Regression Statistics R Square 0.262 Observations 120 Coefficients t Stat. Intercept Δ 0.875 R m - R f 2.050 4.235 The market expected return is 11% and market standard deviation is 16 percent. (a) You would like to create the minimum-variance portfolio using Thrifty and Ponzi. Compute the weights of the two funds in the MVP. (5 points) (b) Given the estimated coefficients, what is the correlation between returns on Ponzi and returns on the market? (5 points) (c) Given the estimated coefficients, does Ponzi fund lie above, on, or below the Security Market Line? Estimate how much more or less return Ponzi fund earns relative to the expected return the CAPM predicts for a portfolio of Ponzi’s risk? (5 points) (d) Does your answer to (c) imply that the CAPM holds or that is it violated? How confident are you making this statement? (Please, maximum three sentences here. Anything longer than three sentences will not be graded.) (5 points) Solution: (a) Thrifty fund is risk-free, so the variance of its returns is 0. No other portfolio can have a lower variance, so the Minimum Variance Portfolio will assign the weight of 100% to Thrifty and 0% to Ponzi. (You could get the same answer by using the 1
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formula derived in class. In that case you will also need to notice that the covariance between Thrifty and Ponzi is zero.) (b) β Ponzi = cov ( R Ponzi ,R market ) σ 2 market cov ( R Ponzi ,R market ) = 2 . 05 × 0 . 16 2 = 0 . 05248 , corr ( R Ponzi ,R market ) = cov ( R Ponzi ,R market ) σ market σ Ponzi = 0 . 5125 . (c)Ponzi fund’s alpha is α Ponzi = E [ R Ponzi ] - R f - β Ponzi ( E [ R market ] - R f ) = 0 . 02 The alpha is positive and indicates that Ponzi earns 2% more per year than what the CAPM predicts for a portfolio of its risk. Thus, Ponzi fund lies above the SML, which may mean that its manager, Mr. Charles Ponzi, is able to identify underpriced companies. (d) As we showed in (c), Ponzi fund lies above the SML, which seems to contradict the
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This note was uploaded on 12/20/2011 for the course RSM 332 taught by Professor Raymondkan during the Fall '08 term at University of Toronto- Toronto.

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T9 - UNIVERSITY OF TORONTO Joseph L. Rotman School of...

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