Question

You have observed the following returns over time: Year: Stock X: Market: 2014 18% 14% 2015 6% 8% 2016 23% 12% Assume that the risk-free rate is 6% and the market risk premium is 5%. a) What are the expected rates of return on Stock X and the market? b) What is the standard deviation on Stock X and the market? c) What is the Beta for Stock X given a correlation to the market of 0.8117? Is Stock X more or less risky than the market? d) What is the rate of return on a portfolio with 80% Stock X and 20% of Stock Y (where Stock Y has a Beta of 1.5)?

Answer 1

a) Expected return on Stock X (mean return) = (18% + 6% + 23%) / 3 = 15.67%

Expected return on Market (mean return) = (14% + 8% + 12%) / 3 = 11.33%

b) Standard deviation is computed as follows -

where, Return₁, Return₂,Return₃ being the return in the three respective years and Return_mean being the expected return.

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c)

Beta of market is assumed to be 1. Beta is the measure of movement of the stock in relation to the market. Since, the Beta is less than 1, it is less risky than the market. If the market goes down by 1, the stock will move down by 0.93.

d) We have to compute the Expected return on Y using CAPM -

Expected return of Stock Y = Risk free rate + Beta of stock Y x market risk premium = 6% + 1.5 x 5% = 13.5%

Rate of return on portfolio = weight of stock X x expected return on stock x + weight of stock Y x expected return on stock Y = 0.80 x 15.67% + 0.20 x 13.5% = 15.236%