Question

In her new career in a portfolio management firm, a portfolio manager is learning the way to select securities for including in a portfolio. She has gathered recent data about the market and observed that the govt bond rate is 5.0 per cent and the risk premium for the market is 8.6 per cent. She has identified one security, TSR, with a beta value of 3.0 and an expected return of 22.2 per cent. She becomes confused after finding another security, ZXN, with a beta value of -1.1 and an expected return of 6.3 per cent. For further analysis, she calculated standard deviations for TSR and ZXN as 30.8 per cent and 9.4 per cent respectively. In addition, a correlation coefficient of 0.31 is calculated between returns of these two securities. The portfolio manager is asking for details about the following requirements:

Requirement-a. Draw the Security Market Line (SML) with clear labels and plot these two securities on the graph.

Requirement-b. Are these securities properly priced? If not, explain what we might expect to happen to the prices of these securities in the market.

Requirement-c. Briefly explain with necessary calculation and using your own words to the query of the manager: "Why isn't the total risk of a portfolio simply equal to the weighted average of the risks of the securities in the portfolio?". You can make a portfolio by investing 70 per cent in TSR and the remaining (to make it 100 per cent) in ZXN.  

Answer 1

a. SECURITY MARKET LINE:

E(Ri)=Rf+BETA(i)*(Rm-Rf)

E(Ri)=Expeced Return of the stock

Rf=Risk Free Rate=5.6%

BETA(i)=Beta of the stock

Rm=Expected market return=5+8.6=13.6%

E(Ri)=5.6+BETA(i)*8.6

	BETA	E(Ri)
	-2.0	-11.6	%
ZXN	-1.1	-3.86	%
	-0.5	1.3	%
	0.5	9.9	%
	1.0	14.2	%
	2.0	22.8	%
TSR	3.0	31.4	%
	4.0	40	%

b.

Actual Expected Return of TSR	22.20%
Actual Expected Return of ZXN	6.30%

TSR is Overpriced. Hence its return is lower than expected

ZXN is Under priced. Hence its return is higher than expected

Price of TSR is likely to come down

Price of ZXN is likely to go up

Risk of a portfolio is expressed as Standard deviation of return

PORTFOLIO STANDARD DEVIATION =Sp=SQUARE ROOT of PORTFOLIO VARIANCE =Vp

PORTFOLIO VARIANCE(Vp)=(w1^2)*(S1^2)+(w2^2)*(S2^2)+2*w1*w2*Cov(1,2)

w1=Weight of Stock1(TSR) in the portfolio=0.7

w1=Weight of Stock2(ZXN) in the portfolio=0.3

S1=Standard Deviation of TSR=30.8%

S2=Standard Deviation of ZXN=9.4%

Cov(1,2)=Covariance of TSR and ZXN=Correlation*S1*S2=0.31*30.8*9.4=89.7512%%

Portfolio Variance=Sp=(0.7^2)*(30.8^2)+(0.3^2)*(9.4^2)+2*0.7*0.3*89.7512=510.4815

Portfolio Standard Deviation=Sp=Square Root(510.4815)=22.59%

PORTFOLIO TOTAL RISK

22.59%