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 return 15% 20% Correlation of coefficient (p) 0.4

No Financial Calculator, Excel Calculations and No Excel files are accepted. You are allowed only one attempt to submit your assignment.

Answer 1

Part (a) The geometric average return is calculated using the following formula:

This implies that, the GAR for the five years returns will be computed as :

GAR = [( 1+ 0.097) * (1-0.062) * (1+ 0.121) * (1+ 0.115) * (1+ 0.133)] ^ 1/5 - 1

= [(1.097) * (0.938) * (1.121) * (1.115) * (1.133)] ^1/5 - 1

=( 1.4572^ 0.2) -1

= 1.0782 - 1

= 0.0782 or 7.82%

Part (b) The CAPM formula is given by :

(It is assumed that the risk free rate is the nominal rate and thus we don't use inflation in the CAPM Model, unless otherwise stated)

where,

Re= Expected return on stock

Rf = Risk free rate

B= Beta of stock

Therefore Beta of the stock is computed as:

0.146 = 0.059 + BETA (0.058)

0.087 = BETA(0.058)

BETA = 1.5

Part ( c) Capital gain is the excess of current value of stock over the purchase price of the stock.

Given:

Purchase price of stock = 1200/200 = $6

Current price of the stock = $75

Capital gain per stock= $75-$6 =$69

Therefore Capital gain = 69*200 = $13800

(Note that Dividends are not used while computing the capital gain, they are used when Total gains are to be computed)

Part(d) The expected return on portfolio is computed as :

where,

Rp= expected portfolio return

Wa = Weight of security A

Wb = Weight of security B

Ra = Return on security A

Rb = Return on security B

THEREFORE, Rp = 0.45* 0.125 + 0.55* 0.185

= 0.05625+ 0.10175

= 0.158 or 15.8%

Portfolio standard deviation is the risk of the portfolio and is computed as:

where,

= Standard deviation of portfolio

= Standard deviation of A returns

= Standard deviation of B returns

= Correlation of A and B

Therefore,

=( 0.2025*0.0225 + 0.3025* 0.04 + 0.00297)^ 1/2

= (0.0045 + 0.0121 + 0.00297)^1/2

= (0.01957)^1/2

= 0.1398 or 13.98%

Variance = 0.01957