1. Under what condition will the population standard deviation of the return to a 2-asset portfolio be the weighted average of the two assets' standard deviations of returns?(Hint: Consider the formula for the standard deviation of the return to a 2-asset portfolio given in lectures, and recall from high school that

2. The possible rates of return you might expect by investing in shares C and D are as follows (assuming there are only three types of economic conditions):

Economic Conditions	Probability of State of Economic Conditions	Return on C	Return on D
Poor	0.2	-5%	-3%
Average	0.5	8%	5%
Good	0.3	14%	10%

(a) Calculate the expected returns and standard deviations for both shares C and D.Express your answers as percentages rounded to 2 decimal places if required.

(b) Calculate the standard deviation of returns on a portfolio with asset weights of 70% and 30% for assets C and D, respectively. Again express your answer as a percentage rounded to 2 decimal places if required. (Hint: Start by working out the return on the portfolio in each type of economic conditions)

3. The following table shows the returns (in percent) on ordinary shares A and B in three possible states of nature, together with the probabilities of these states of nature occurring.

State of Nature	Probability	Return on A (%)	Return on B (%)
Recession Normal Boom	0.2 0.4 0.4	4 6 8	12 5 2

With reference to the above table:

(a) Calculate the expected return and standard deviation of returns for A shares and for B shares (separately).

(b) If a risk averse investor had to choose between holding A shares and holding B shares, which would he/she choose. Give a reason for your answer.

(c) If an investor were to form a portfolio consisting of A and B shares, would it be possible for the portfolio to offer a lower standard deviation of returns than both A and B shares, and an expected return that is not lower than the expected returns of both shares? Give a reason for your answer (Hint: you should be able to give a reason for your answer without having to perform any further calculations)

4. If the return on asset A for 2010 to 2014 are as follows:

Year	Return (%)
2009	0.52
2010	5.21
2011	6.23
2012	1.20
2013	3.22
2014	5.96

Calculate the mean and standard deviation (sample) of the return for asset A.

5. Calculate the portfolio standard deviation for stock A and stock B from the following given data:

Year	Return A (%) Weight=65%	Return B (%) Weight=35%
2009	0.52	1.65
2010	5.21	2.15
2011	7.23	0.25
2012	1.22	5.32
2013	3.22	3.12
2014	5.96	4.26