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, $7600 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? 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. 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). 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. State of economy Probability Rate of returns Mild Recession 0.35 - 5% Growth 0.45 15% Strong Growth 0.20 30%

Answer 1

Solution a) Share A = $ 13,500, Share B = $ 7,600, Share C = $ 14,700, Share D = $ 5,500

Total = 13,500+7,600+14,700+5,500 = 41,300

i) Weight of A = Share A / Total = 13500/41300 = 32.69%

ii) Weight of B = Share B / Total = 7600/41300 = 18.40%

iii) Weight of C = Share C / Total = 14700/41300 = 35.59%

iv) Weight of D = Share D / Total = 5500/41300 = 13.32%

Solution b) Geometric mean = [(1+r1)*(1+r2)*.......*(1+n)]^(1/n) - 1

Returns of share A = 9.7%,

Returns of share B = 12.4%,

Returns of share C =- 5.5%

Returns of share D = 17.2%

Geometric Mean = [(1+9.7%)*(1+12.4%)*(1-5.5%)*(1+17.2%)]^(1/4)-1 = 1.08102 - 1 = 8.10%

Solution c) Expected return of the stock A = 13.6%

Beta = 1.5

Risk premium on the stocks = 4.8%

According to CAPM, Expected return = Risk-free Rate(Rf) + Beta*Market risk premium

13.6% = Rf + 1.5*4.8% = Rf + 7.2%

Rf = 13.6% - 7.2% = 6.4%

Solution d) The calculations are done below: