Question

1. Given the information below about a portfolio comprised of 3 stocks, answer the following: (show all the details of your calculations):

1. The expected return on each stock;

2. The expected return on the portfolio using the individual securities’ expected returns obtained in question (a) above.

3. Assume that the correlation between stock A and B is -0.25. Calculate the standard deviation of a portfolio containing 50% of stock A and 50% of stock B.

Stock	Initial investment value	Expected end-of-period investment value	Proportion of portfolio initial market value	Standard Deviation
A	£400.00	£300.00	30%	0.13
B	£250.00	£350.00	40%	0.3
C	£800.00	£850.00	30%	0.25

2. Next year a security will yield £98 with a probability of 0.65 and £112 with a probability of 0.35. An investor is willing to pay £90 for this asset today. The risk-free interest rate is 10%. Answer the following questions (show all the details of your calculations):

1. Is this investor risk seeking or risk averse? Explain.

2. What is the risk premium?

3. Assume that the investor is ready to pay £88 for this asset, is this investor risk seeking or risk averse? Explain.

4. Considering the result in question (iii) above, what is the risk premium?

Answer 1

a. Question from Portfolio Management
(i)
Stock	Initial Investment	Expected Value	Increase/(Decrease) in value	Expected return
A	400	300	-100	-25.00%
B	250	350	100	40.00%
C	800	850	50	6.25%
(ii)
	Expected return of portfolio = Wa*Ra + Wb*Rb + Wc * Rc
	= 0.3 * -25% + 0.4 * 40% + 0.3 * 6.25
	= 10.375%
(iii)
	S.D of Portfolio (A,B) = underroot of [(Wa)2 (S.D.a)2 + (Wb)2 (S.D.b)2 + 2 (correlation) * (Wa) (S.D.a) * (Wb)(S.D.b) ]
	= underroot of [(0.5)2 (0.13)2 + (0.5)2 (0.3)2 + 2 (-0.25) * (0.5) (0.13) * (0.5)(0.3) ]
		= 0.1478 or 14.78%

a. (i)	Expected price = [(98*0.65)+(112*0.35)]/1.10 = 93.54/-
	And willing to pay 90, so investor is risk averse
(ii)	Expected return = (93.54-90)/90 = 3.93%
	Risk Premium = 10% - 3.93% = 6.07%
(iii)	If ready to pay 88, investor is risk averse.
(iv)	Expected return = (93.54-88)/88 = 6.30%
	Risk Premium = 10% - 6.30% = 3.70%