Calculate the following questions. Show all work and assumptions

State of Economy	Probability of state	Returns if state occurs (%)
		BA	BB	BC
Recession	0.10	-5	-5	-7.5
Normal	0.70	+15	+12	+15
Boom	0.20	+40	+28	+26

Required:

(a)

(i)

Calculate the expected return for each of the three stocks.

(ii)

A portfolio is constructed with 30% invested in BA, 25% in BB and 45% in BC. What is the expected return of this portfolio? What is the standard deviation of this portfolio?

(iii)

Based on the expected return of the portfolio in (ii), what is the risk-free interest rate, if the expected market return is 14% and the portfolio beta is 1.2.

(b)

	Standard Deviation (%)	Beta	Expected return (%)
Security A	28	1.2	14
Security B	12	1.6	10
Security C	8	1.1	8
Risk-free	0.0	0.0	2

Correlation	Security A	Security B	Security C
A	+1.0	-0.8	-1.0
B	-0.8	+1.0	+0.5
C	-1.0	+0.5	+1.0

Required:

(i)

Which security has greater total risk? Which has greater systematic risk? Which has greater unsystematic risk? Which security will have a higher risk premium?

(ii)

Construct a two-asset equally weighted portfolio is minimising the overall risk. What is the portfolios Beta? What is the standard deviation of the portfolio?

(iii)

Calculate the Sharpe ratios for the three securities and the equally weighted portfolio in part ii. Is it possible to build a two-asset equally weighted portfolio with a higher Sharpe ratio than the one in part ii?