Consider the following data for stocks A and B: a) If the riskless rate of retur

Question

Consider the following data for stocks A and B:

a) If the riskless rate of return were 5%, what percentage of money invested in risky stocks should an investor place in each stock (assuming A and B are the only risky assets available)?

b) If the security market line describes equilibrium, and stocks A and B are in equilibrium, what is the return on the market portfolio and the riskless rate of interest?

c) If an investor can lend and borrow at the riskless rate determined in part b, but is restricted to holding only one of the two risky stocks in this problem, which stock should be held?

Explanation / Answer

WA=Weight of A in the portfolio WB=Weight of B in the portfolio=(1-WA) RP=Portfolio Return=WA*RA+WB*RB=10WA+19WB Portfolio Variance=(WA^2)*(SA^2)+(WB^2)(SB^2)+2WA*WB*Cov(A,B) SA=Standard Deviation of A=3%, SB=Standard Deviation of B=5% Cov(A,B)=Covariance between return of A and B Covariance(A,B)=PAB*SA*SB=0.1*10*8=8 PAB=Correlation between A and B=0.4 Cov (A,B)=0.4*3*5=6 6 Portfolio Variance=(WA^2)*(3^2)+(WB^2)(5^2)+2WA*WB*6 VP=Portfolio Variance=9*(WA^2)+25*(WB^2)(5^2)+12*WA*WB SP=Portfolio Standard Deviation =Square Root of Portfolio Variance Risk free Return=RF=5% SR=Sharp ratio=(RP-RF)/SP The Portfolio Return , Portfolio Standard Deviation and Sharp ratio for different weights of Risky Stocks are calculated below: WA WB RP VP SP SR Weight of Risky stock A Weight of B Portfolio Portfolio Portfolio Sharp Return Variance Standard Deviation Ratio 0 1 19 25 5 2.8 0.1 0.9 18.1 21.42 4.628174586 2.830489593 0.2 0.8 17.2 18.28 4.275511665 2.853459645 0.3 0.7 16.3 15.58 3.947150871 2.862824444 0.4 0.6 15.4 13.32 3.649657518 2.849582447 0.5 0.5 14.5 11.5 3.391164992 2.801397167 0.6 0.4 13.6 10.12 3.181194744 2.703386838 0.7 0.3 12.7 9.18 3.029851482 2.541378694 0.8 0.2 11.8 8.68 2.946183973 2.308070393 0.9 0.1 10.9 8.62 2.935983651 2.009547975 1 0 10 9 3 1.666666667 SHARP RATIO IS LOWEST AT WA=0.3 , WB=0.7 This is the highest Reward/Risk Ratio possible Hence, Investment in Stock A=0.3=30% 30% Investment in Stock B=0.7=70% 70% b) Return of stock=(Risk Free return)+(Beta of stock)*(Market Return-Risk free Return) Return of stockA=RA=10, Return of Stock B=RB=19 Risk Free return=RF Beta of stockA=0.6, Beta of Stock B=1.4 Market Return=RM RA=10=RF+0.6*(RM-RF) RB=19=RF+1.4*(RM-RF) (RB-RA)=(19-10)=(1.4-0.6)*(RM-RF) 9=0.8*(RM-RF) RM-RF=9/0.8=11.25 11.25 6.75 RF+0.6*(RM-RF)=RA=10 RF+0.6*11.25=10 RF+6.75=10 RF=10-6.75=3.25 RETURN ON MARKET PORTFOLIO=RM=11.25+RF=11.25+3.25=14.50 14.50% RISKLESS RATE OF INTEREST=RF=3.25 3.25% c) Sharp Ratio of stock A=(RA-RF)/SA=(10-3.25)/3= 2.25 Sharp Ratio of stock B=(RB-RF)/SB=(19-3.25)/5= 3.15 Stock B has higher Return/Risk ratio Hence STOCK B SHOULD BE HELD

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