Question

Rachel is a financial investor who actively buys and sells in the securities market. Now she has a portfolio of all blue chips, including: $13,500 of Share A, $7,600 of Share B, $14,700 of Share C, and $5,500 of Share D.

Required:
a) Compute the weights of the assets in Rachel’s portfolio? (2 marks)
b) If Rachel’s portfolio has provided her with returns of 9.7%, 12.4%, -5.5% and 17.2% over the past four years, respectively, calculate the geometric average return of the portfolio for this period. (2 marks)
c) Assume that expected return of the stock A in Rachel’s portfolio is 13.6% this year. The risk premium on the stocks of the same industry are 4.8%, betas of these stocks is 1.5 and the inflation rate was 2.7%. Calculate the risk-free rate of return using Capital Market Asset Pricing Model (CAPM). (2 marks)
d) Following is forecast for economic situation and Rachel’s portfolio returns next year, calculate the expected return, variance and standard deviation of the portfolio. (4 marks)

Answer 1

a) Weight of Assets:

Stock A = 0.33

Stock B = 0.18

Stock C = 0.35

Stock D = 0.13

b) Geometric Average Return = 8.1%

c) Risk free rate (without inflation rate adjustment) = 6.4%

Risk free rate (with inflation rate adjustment) = 3.4%

d) As, this part is incomplete and missing essential data, so we have skipped this part.

Explanation:

a) Weights of the assets:

Weights of the assets in Rachel's portfolio can be calculated as follows:

Weight = Amount in stock/sum of amounts of all stocks

Sum of amount of all stocks = Stock A + Stock B + Stock C + Stock D

= $13500 + $7600 + $14700 + $5,500

Sum = $41,300

Weight of Stock A = .Amount of Stock A/ Sum

= 13600/41300

Weight of Stock A = 0.329 ≈ 0.33

Weight of Stock B = 7600/41300

= 0.18

Weight of Stock C = 14700/41300

= 0.35

Weight of Stock D = 5500/41300

= 0.13

b) Geometric Average Return:

The formula to calculate geometric average return is as follows:

Geometric average return = ((1+r1)x(1+r2)x(1+r3)....x(1+rn))^(1/n) - 1

Don't be confuse! This is a very simple formula, it only looks complex. Just plug in the values of returns given for this portfolio to get the geometric average return.

Here we go:

Geometric Avg. Return = ((1+0.097)*(1+0.124)*(1-0.055)*(1+0.172))^(1/4) - 1

Geometric Avg. Return = 0.081 = 8.1%

c) Risk Free Rate using CAPM:

CAPM = Capital Asset Pricing Model

CAPM gives the formula to calculate risk free rate:

Expected Return = Risk Free rate + (Beta of the stock x Premium Risk)

: As this is without the adjustment of inflation rates.

13.6 = Risk Free Rate + (1.5 x 4.8)

Risk Free Rate = 13.6 - 7.2

Risk Free Rate (without inflation adjustment) = 6.4%

With inflation adjustment of Return rate = ((1+r)/(1+IR))-1

Where, r = return, IR = inflation rate

With inflation adjustment of Return rate = ((1+r)/(1+IR))-1

= ((1+0.136)/(1+0.027))-1

Return rate (with inflation rate) = 0.106 = 10.6%

Now, again using CAPM to get risk free rate with inflation rate adjustment.

Expected Return = Risk Free rate + (Beta of the stock x Premium Risk)

10.6% = Risk free rate + (1.5 x 4.8)

Risk Free Rate = 10.6 - 7.2

Risk Free rate = 3.4