Question

You are an active investor in the securities market and you have established an investment portfolio of two stock A and B five years ago. Required:

a) If your portfolio has provided you with returns of 9.7%, -6.2%, 12.1%, 11.5% and 13.3% over the past five years, respectively. Calculate the geometric average return of the portfolio for this period? (1 mark)?

b) Assume that expected return of the stock A in your portfolio is 14.6%. The risk premium on the stocks of the same industry are 5.8%, the risk-free rate of return is 5.9% and the inflation rate was 2.7. Calculate beta of this stock using Capital Asset Pricing Model (CAPM) (1 mark)?

c) Assume that you bought 200 stock B in your portfolio for total investment of $1200, now the market price of the stock is $75, the dividend paid for this stock is $2 each year. How much is the capital gain of this stock (1 mark)?

d) Assume that the following data available for the portfolio, calculate the expected return, variance and standard deviation of the portfolio given stock A accounts for 45% and stock B accounts for 55% of your portfolio?

	A	b
Expected return	12.5%	18.5%
Standard deviation of returns	15%	205
Correlation of coefficient (p)	0.4

Answer 1

1} Average return = Return on all securities / no of security

= 9.7%+, -6.2%+, 12.1%,+ 11.5% +13.3% / 5 = 8.08%

2) calculation of Beta: Using CAPM

Risk free return + Beta( Market return - Risk free return) = cost of equity

i.e 14.6 = 5.9 + Beta (5.8)

on solving the above equation

Beta = 1.5 times.

3) Capital Gain = sales consideration - Cost of asset

Sales consideration ( 200*75) = 15000$

Cost of stock B = 1200$

Capital gain = 13800$

Note: dividend is not part of capital gain as it is income of shareholder hence taxed normally or is exempt if conditions are fulfilled

4) Expected return

A = 12.5 *.45+B=18.5*.55=15.8%

Varinace = 12.5 *15*15 +18.5*20*20+2*.4*15*20=102.23

Standard Deviation-Square root of 102.23

i.e 10.11