Question

The following information is available for four securities:

  

Stock E(r) Std. Dev. p 1 p 2 p 3 p 4   

1 14% 30% 1.0 0.6 0.4 -0.2

2 10% 25% 1.0 .20 0.5

3 15% 34% 1 0.1

4 9% 22% 1

(a) [30 points] Calculate the expected returns and standard deviations of returns of the following two portfolios: P1 : {31%, 5%, 19%, 45%} P2 : {4%, 35%, 2%, 59%}

(b) [10 points] Which portfolio will be preferred by risk averse investors? Why?

Answer 1

(a) Given Information is as follows:

Expected Return of Stock 1 = 14%

Expected Return of Stock 2 = 10%

Expected Return of Stock 3 = 15%

Expected Return of Stock 4 = 9%

Standard Deviation of Stock 1 = 30%

Standard Deviation of Stock 2 = 25%

Standard Deviation of Stock 3 = 34%

Standard Deviation of Stock 4 = 22%

Correlation between stocks 1 and 2 = 0.60

Correlation between stocks 1 and 3 = 0.40

Correlation between stocks 1 and 4 = -0.20

Correlation between stocks 2 and 3 = 0.20

Correlation between stocks 2 and 4 = 0.50

Correlation between stocks 3 and 4 = 0.10

Expected Return of a portfolio =

Expected Return of portfolio 1 = 0.31*0.14 + 0.05*0.10 + 0.19*0.15 + 0.45*0.09 = 0.1174 = 11.74%

Expected Return of portfolio 2 = 0.04*0.14 + 0.35*0.10 + 0.02*0.15+ 0.59*0.09 = 0.967 = 9.67%

Standard Deviation of a portfolio =

Standard Deviation of portfolio 1 =

= 16.77%

Standard Deviation of portfolio 2 = = 19.28%

(b)

A risk averse investor will prefer Portfolio 1 as the standard deviation of that portfolio is lower hence the risk of volatility in returns is lower as compared to Portfolio 2