Risk and Return

(i). You are advising an investor who has $30,000 to invest in two securities: Spot and Dot. After doing an extensive analysis of the economy and the two securities, you came up with the following forecasts:

State of the economy	Probability of Occurrence	Spot Expected Return	Dot Expected Return
Boom	15%	-8%	35%
Normal	60%	14%	20%
Bust	25%	18%	-10%

a) What are the expected returns of Spot and Dot shares? b) What are the standard deviations of the returns on Spot and Dot? c) Estimate the covariance of the returns on Spot and Dot d) What is the correlation coefficient between Spot and Dot returns? e) How much of the money should be invested in Spot and how much in Dot if you wish to have an expected return of 12 percent on the portfolio?

f) Compute the standard deviation of the portfolio in (e)

(ii) Why does diversification reduce risk? Answer the question with reference to why the standard deviation of the portfolio in (f) above is lower than the standard deviation of the two stocks (in b) that make up the portfolio.