Question

a) Michael has a portfolio comprising 2 assets: Stock X and Stock Y. Probability distribution of returns on Stock X and Stock Y are as follows

	Bear market	Normal market	Bull market
Probability	0.2	0.5	0.3
Stock X	-20%	18%	50%
Stock Y	-15%	20%	10%

i)            What are the expected rates of return for Stocks X and Y?
ii)           What are the standard deviations of returns on Stocks X and Y? (

b) You are a fund manager responsible for a portfolio that currently consists of 10 stocks. Your current portfolio has a beta of 1.2, an expected excess return of 0.096 and a standard deviation of 0.12. You are looking to add an additional share to your portfolio and have narrowed the field to three potential contenders.

The table below reports the expected excess return of each stock (E(R) - Rf), the standard deviation for each stock (σi), the beta for each stock (βi) and the correlation between each stock and the existing portfolio (ρi,P). The returns of all three shares are normally distributed. The current risk-free rate of interest is 0.02 and the expected market return is 0.10.

Share	E(Ri) – Rf	σi	βi	ρi,P
A	0.110	0.14	1.375	0.2
B	0.066	0.09	0.825	0.4
C	0.088	0.14	1.100	-0.3

i)            Calculate the Sharpe Ratio (excess return/standard deviation) for these three stocks. Explain which of these three stocks has historically performed best based on these Sharpe Ratios.  
ii)           Suppose you construct a new portfolio so that you invest 90% of your capital in your existing portfolio of 10 shares and the remaining 10% in the Share C. Calculate the expected return and standard deviation of this new portfolio.

Answer 1

a)