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)

State of economy Probability Rate of returns Mild Recession 0.35 - 5% Growth 0.45 15% Strong Growth 0.20 30%

Answer 1

(a) 41300 (b) 8.10 % (c) 3.41% (at real rates)

Explanation:

Solution

Given:

(a) The Weights of assets in Rachel's portfolio: = amount in each stock/ sum of amounts invested in all stocks

Share Amount Weights

A 13500 0.33

B 7600 0.18

C 14700 0.36

D 5500 0.13

THE TOTAL: 41300

(b) The Geometric average return of a portfolio = ((1+R1)*(1+R2)*(1+R3)....*(1+Rn))^(1/n) - 1

Now,

R1= return of period 1 Rn= return in nth period

Thus,

The Geometric average return of Rachel's portfolio= ((1+9.7%)*(1+12.4%)*(1-5.5%)*(1+17.2%))^(1/4) - 1

= 8.10 % (approx) per year.

(c) Using nominal rate of return (including inflation):

The CAPM: Required return= Risk free return + (Risk premium * Beta)

13.6 = Rf + (4.8*1.5)

So,

Rf= 6.4% (not inflation adjusted)

The inflation adjusted rate of return: ((1+return)/(1+inflation rate))-1

= ((1+13.6%)/(1+2.7%))-1 = 10.61%

Using CAPM: 10.61= Rf + (4.8*1.5)

Therefore, Rf= 3.41% (at real rates)