Four question about Finance (show all the work)

1. The following information is available on the percentage rates of return on various assets for the last three years. You determine that this is a sample which is representative of the data population for these securities. Security                           Year 1    Year 2    Year 3

Share A                            −6%      −18%      60%

Share B                            32%      −22%      35%

Market                              50%      −10%      20%

Government Bonds       10%        10%      10%

(a) Consider only shares A and B for this part. Compute the portfolio weights that yield the portfolio of A and B which has the lowest possible standard deviation. Then compute that portfolio’s expected return and standard deviation. Hint: Write down the formula for this, then compute all the ingredients you require.

(b) What is the numerical equation for the Capital Markets Line in this situation?

(c) Do shares A and B plot on the Securities Market Line? Hint: you will have to determine Betas in order to figure this out.

2. Determine whether the following statements are true or false and in either case briefly explain why.

(a) Assume the CAPM holds. Two stocks A and B have the same Beta, but stock A has much higher idiosyncratic risk than stock B. This means that stock A must have a higher expected return than B to reward risk-averse investors for holding the additional risk.

(b) Assume that a risk-free asset as well as two risky securities exist in the economy. If the risky securities are perfectly positively correlated with each other, diversifying among the two will not make a greedy risk-averse investor better off. Hint: it may be worth drawing a diagram to clarify your point.

3. Assume that the CAPM holds. Cella, Inc stock is currently trading at $50 per share and the security’s expected return is 15% per year. You expect all of this return to be paid as a cash dividend; no price 1 increase is expected. The risk-free rate is 5% per year and the market’s risk premium is 9%. What will be Cella, Inc’s new equilibrium price if its covariance with the market portfolio doubles, but everything else (including the dollar-value of the cash dividend) remains the same?

4. While Peter Lynch was the manager of Fidelity’s Magellan fund family, these funds outperformed the S&P 500 in 11 out of 13 years, and in those years they outperformed by an average of 10%. Do these facts alone constitute evidence against market efficiency? 

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