Question

Week 5 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)
i need onlu part d)
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)


Required: step by step explanation with formula please

Answer 1

Answer: The answer is provided below

Explanation:

The weights of assest in Rachel's portfolio: = amount in each stock ÷ sum of the amounts invested in all stocks.

Share Amount Weight

A. 13500. 0.33

B. 7600. 0.18

C. 14700. 0.36

D. 5500. 0.13

Total 41300

Note that weight = amount/total

Geometric average return of a portfolio:

((1+R1)×(1+R2)×(1+R3)....×(1+Rn))^(1/n) - 1

where,

R1= return of period 1

Rn= return in nth period

Hence, the geometric average return of Rachel's portfolio will be:

((1+9.7%)×(1+12.4%)×(1-5.5%)×(1+17.2%))^(1/4) - 1

= 8.10 % (approximately) per year.

Using the nominal rate of return which includes inflation:

CAPM: Required return will be:

= Risk free return + (Risk premium × Beta)

13.6 = Risk free return + (4.8 × 1.5)

13.6 = Risk free return + 7.2

Risk free return = 13.6 - 7.2

= 6.4% which is not inflation adjusted)

The inflation adjusted rate of return will be:

= (1+return)/(1+inflation rate))-1

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

= 10.61%

Using CAPM:

10.61= Risk free return + (4.8 × 1.5)

10.61 = Risk free return + 7.2

Risk free return = 10.61 - 7.2

Risk free return = 3.41% (at real rates)

In practice, the use of inflation adjusted return i.e the real rate of return which is 10.61% is better as it puts forth a long term perspective on how a stock is performing.