1. You are a market analyst and have identified 4 different market conditions together with the returns that two shares will earn if each condition occurs as well as the probability that the conditions will eventuate. The table below presents this information:

Market Condition	Probability	Return
APA	NCM
Boom	0.25	8%	11%
Good	0.35	3%	6%
Average	0.10	1%	2%
Poor	0.30	-10%	-9%

1. Calculate the expected return on each of the two shares. (2 marks)
2. Calculate the standard deviation on the return of each share. (4 marks)
3. You work as a financial analyst for Rio Tinto, Ltd. and specialise in constructing share portfolios for investors. You have just been given the following information on two stocks:

Stock	BHP	RIO
Expected Return (%)	12	22
Variance (%2)	28	33

Additionally, you have been told that the correlation between these two stocks is -0.32. Given this information, you are asked to calculate the following figures for a client who is interested in investing in a portfolio comprising only these two stocks:

1. What weights would you need to hold of BHP and RMD shares in order to obtain an expected return of 16% on your portfolio? (2 marks)
2. What is the standard deviation of the portfolio comprising BHP and RMD in the weights calculated above in part i.)? (2 marks)

Part 1

Market Condition Probability Return (APA) Return (NCM) Boom 0.25 8% 11% Good 0.35 3% 6% Average 0.10 1% 2% Poor 0.30 -10% -9%

Expected Return

APA: 0.0015 NCM: 0.0235

Standard Deviation

APA: 0.0702 NCM: 0.0788

Part 2

Weights

BHP: 0.6 RIO: 0.4

Portfolio Standard Deviation: 0.327