Question

You own shares of MO and COMS. MO has a standard deviation of .35 and a correlation with the market of .05. COMS has a standard deviation of .10 and a correlation with the market of .75. Assume the market has a standard deviation of .12 and an expected return of 8%. Further, assume T-Bill rates are 1%.

1. What are the expected returns on MO and COMS?
2. What are the expected returns and standard deviation of a portfolio made up of 40% MO and 60% COMS assuming the correlation between MO and COMS is .2?
3. Would you prefer to hold MO only, COMS only, or the combined portfolio if these are your only holdings? Can you provide a strict preference ranking between these choices?

Answer 1

As per CAPM,

Expected return = risk free rate + ( return on market - risk free rate ) * Beta

Beta = correlation between the stock and market * standard deviation of stock / standard deviation of market

Beta for MO = 0.05 * 35 / 12 = 0.1458

Beta for COMS = 0.75 * 10 / 12 = 0.625

Expected return on MO = 1 + ( 8 - 1) * 0.1458 = 2.02 %

Expecetd return on COMS = 1 + ( 8-1) * 0.625 = 5.375 %

Expected return on the portfolio = sum ow weighted average of retuins where weights is the proportion of portolio in respective stocks

= 0.4 * 2.02 + 0.6 * 5.375 = 4.03%

standard deviation of portfolio = [ weight of MO ^2 * Variance of MO + Weight of COMS^2*Variance of COMS + 2 * Weight of MO * Weight of COMS* Correaltion between the stocks * standard deviation of MO * standard deviation of COMS ] ^ 0.50

= [ 0.4^2 * 35^2 + 0.6^2*10^2 + 2*0.4*0.6*0.2*35*10 ] ^0.50

=[ 196 +36 +33.60 ] ^0.50

= 265.60^0.5

= 16.30%

Let us calculate the Coefficient of variation for MO COMS & Portfolio

COV = Standard deviation / mean

COV for MO = 35 /2.02 = 17.33

COV for COMS = 10 / 5.375 = 1.86

COV for Portfolio = 16.30/ 4.03 = 4.04

strict preference ranking is as below on the basis of COV

COMS - Rank 1

Portfolio - Rank 2

MO - Rank 3