Question

You have gathered information about the expected returns and standard deviations of two stocks, which is given in the table below:

	Expected return	Standard deviation
Stock A	15.0%	30.0%
Stock B	10.0%	40.0%

a. Discuss which stock is more attractive and why?

You are going to form a portfolio, which includes these two stocks. The value of your total portfolio is 500 000 and investment into stock B is 30% of the total portfolio.

b. It is estimated that the correlation between the stock returns is 0.22. Explain, what does this result mean?

c. Calculate the portfolio risk and expected return, and explain the benefits of diversification.

Answer 1

Answer a)

Stock A has the expected return of 15% and std dev of 30% and stcok B has expected return of 10% and std dev of 40% it means stock a is providing more expected returns than stock b with lesser volatility i.e std dev hence stock A is more attractive than stock B

Answer b) Correlation 0.22?

Correlation is an indicator which describe the relationship between two different variables. correlaion between stock can be positive or negative and can be in the range of -1 to +1. Greater than zero value indicates a positive relationship, less than zero value indicates negative relationship and zero indicates no relationship.
Here, correlation 0.22 is a positive correlation hence stock returns does move together however 0.22 correlation is a weak correlation and value greater than 0.5 can be considered as strong positive correlation.

Answer c)

weight	return	sd
0.3	10%	30%
0.7	15%	40%

Portfolio Return = w1*R1 + w2*R2 = (0.3*10%) + (0.7*15%) = 13.50%

Portfolio Risk =SD(p) = sqrt ( w1^2*R1^2 + w2^2*R2^2 + 2*w1*w2*Corr*sd1*sd2

= sqrt (0.3^2 * 0.1^2 + 0.7^2 * 0.15^2 + 2*0.3*0.7*0.22 * 0.3*0.4)

Portfolio Risk =SD(p) = 10.53%

We can see from the return and risk of the portfolio as 10.53% and 13.50% respectively which denotes than small small change is expected return we manage to reduce the risk significantly hence building a portfolio helps to reduce the risk with slight change in returns.