Market portfolio has an expected return of 11% and volatility of 20%. Risk-free

Question

Market portfolio has an expected return of 11% and volatility of 20%. Risk-free rate is 3%. Security X and Y have betas of 1.4 and 0.9 respectively.(pls write details with the formulas not just the answer)

a)(10 points) According to CAPM, what are the expected return of X and Y?

b)(10 points) What should be X worth today, if X pays a dividend of $1.2 one year from today and is priced at 30 one year from today? The required rate of return is the expected return using CAPM from part a).

c)(10 points) If security X has expected return of 15%, is it underprice/overprice/fairly priced according to CAPM? What is its alpha?

d)(15 points) Plot SML and label X, Y and Market portfolio on the line.

e) (10 points) What is the beta of a portfolio with 50% in X and 50% in Y?

f)(10 points) What is the beta of a portfolio with 55% in Market portfolio and 45% in risk-free asset?

g)(15 points) You are investing in a complete portfolio. The complete portfolio is composed of risk-free asset and a risky portfolio, P, constructed with 20% in X and 80% in Y. It turns out that your complete portfolio has an expected rate of return of 9.4%. What is the beta of your complete portfolio? (hint: you may or may not use all information to solve this problem)

Explanation / Answer

CAPM = RF + BETA(RM-RF)

2. TO FIND THE WORTH OF X WE NEED TO USE PV FORMULA
PV= DIVIDEND/(1+R)^1 + FV/(1+R)^N
=(1.2 + 30)/1.142
=27.3205

3 .CAPM LOWER THAN EXPECTED RETURN THAT MEANS SECURITY IS OVERVALUED
CAPM = 14.2%
EXPECTED RETURN =15%
ALPHA = EXPECTED RETURN - CAPM RETURN
=15-14.2
=0.8%

4. PORTFOLIO BETA = BETA1*W1 + BETA2 * W2...........

5. BETA OF RISK FREE RETUEN =0,
HEENCE BETA OF PORTFOLIO = BETA OF MARKET PORTFOLIO * WEIGHTS

BETA OF MARKET PORTFOLIO =1

HENCE TOTAL PORTFOLIO BETA = 1*O.55 = 0.55

X Y CAPM = RF +BETA(RM-RF) RM= MARKET RETURN 11% 11% RF= RISK FREE RETURN 3% 3% BETA 1.4 0.9 CAPM= 14.200% 10.200%

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