Question

You are a financial investor who actively buys and sells in the securities market. Now you have a portfolio, including four shares: $5,500 of Share A, $4,600 of Share B, $5,700 of Share C, and $2,500 of Share D . Required: a) Compute the weights of the assets in your portfolio. b) If your portfolio has provided you with returns of 5.7%, 10.5%, 8.7% and 13.2% 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 your portfolio is 13.2%. The risk premium on the stocks of the same industry are 6.8%, betas of these stocks is 1.2. Calculate the risk-free rate of return using Capital market pricing model (CAPM). d) You have another portfolio that comprises of two shares only: $500 blue chip shares and $700 junk shares. Below is the data of your portfolio: Blue Chips Junk Expected return 13% 20% Standard Deviation of return 20% 45% Correlation of coefficient (p) 0.4 Compute the expected return of your portfolio. e) Compute the expected risk (standard deviation) of the portfolio.

Answer 1

(a)

Stocks	Number of shares (X)	Weights (X/Y)
A	5500	0.3005
B	4600	0.2514
C	5700	0.3115
D	2500	0.1366
Total (Y)	18300	1

(b)

Goemetric Mean = {[(1+R1)*(1+R2)*(1+R3)*(1+R4)]^(1/n)} - 1

Given R1 = 5.7%, R2 = 10.5%, R3 = 8.7%, R4 = 13.2%

n= 4 years

Goemetric Mean = {[(1+0.057)*(1+0.105)*(1+0.087)*(1+0.132)]^(1/4)} - 1

= 1.094910 - 1

= 9.4910%

Geometric average return of the portfolio = 9.4910%

(c)

Given Expected return on portfolio A = 13.2%

Risk premium (Rm-Rf) = 6.8%

Beta of portfolio A = 1.2

Risk Free rate (Rf) = ?

Expected return = Rf + (Rm-Rf)*Beta

13.2% = Rf + (6.8%)*(1.2)

Rf = 13.2% - 8.16%

Rf = 5.04%

Risk Free rate (Rf) = 5.04%

(d)

Stocks	Number of shares (X)	Weights (X/Y)
A	500	0.4167
B	700	0.5833
Total (Y)	1200	1.0000

Expected Return of Portfolio = Expected reurn of A * Weight of A + Expected reurn of B* Weight of B

Weight of Stock of A = 0.4167 , Weight of Stock B = 0.5833, Expected retrun of A = 13%,

Expected Return of B = 20%

Expected Return of Portfolio = 0.4167*(13%) + 0.5833*(20%) = 5.4167 + 11.6667 = 17.0833%

Standard Deviation of a portfolio is calculated as below

= (WASA)^2 + (WBSB)^2 + 2WAWBSASBp(A,B)

WA = Weight of Stock A = 0.4167

SA = Standard Deviation of Stock A = 0.20

WB = Weight of Stock B = 0.5833

SB = Standard Deviation of Stock B = 0.45

p(A,B) = Corelation coeffecient between A and B = 0.4

= (0.4167* 0.20)^2 + (0.5833*0.45)^2 + 2*0.4167*0.20*0.5833*0.45*0.4

= 0.006946 + 0.06890 + 0.017500

= 0.09335

Standard deviation of portfolio = 9.335%