Question

Question 1
Richard must decide how to allocate the capital in his portfolio.
Richard has		$37,000	available to invest. He finds the rates of
return for four stocks for the past 12 years and the results are given
below. Richard plans to invest 25% of his funds in each stock.
a) How much will he invest in each stock?					$
(1 Mark)
b) The expected value of Richard's porfolio is:								%
(Round your answer to one one-hundreth of a percent)
c) The standard deviation of Richard's portfolio is:						Enter Answer		%
(1 Mark)(Round your answer to one one-hundredth of a percent)
						↑
Year	Stock A (%)	Stock B (%)	Stock C (%)	Stock D (%)		Enter your Final Answer Here
1	-6.470	-1.700	2.440	-10.730
2	18.110	4.445	-3.705	26.140
3	26.790	6.615	-5.875	39.160
4	24.790	6.115	-5.375	36.160
5	-16.470	-4.200	4.940	-25.730
6	32.630	8.075	-7.335	47.920
7	74.130	18.450	-17.710	110.170
8	27.050	6.680	-5.940	39.550
9	14.330	3.500	-2.760	20.470
10	20.110	4.945	-4.205	29.140
11	-10.330	-2.665	3.405	-16.520
12	-0.470	-0.200	0.940	-1.730

Question 2
Anna is a Vice President at the J Corporation. The company is considering
investing in a new factory and Anna must decide whether it is a feasible
project. In order to assess the viability of the project, Anna must first calculate
the rate of return that equity holders expect from the company stock. The
annual returns for J Corp. and for a market index are given below. Currently,
the risk-free rate of return is				1.9%	and the market risk-premium is				6.1%	.
a) What is the beta of J Corp.'s stock?										0.70
(1 Mark)(Round your answer to two decimal places)
b) Using the CAPM model, what is the expected rate of return on J Corp. stock for the coming year?										5.64		%
(2 Mark)(Round your answer to one one-hundreth of a percent)										↑
Year	J Corp. Return (%)	Market Return (%)								Enter your Final Answer Here
1	-2.63	-3.70
2	6.59	8.59
3	9.85	12.93
4	9.10	11.93
5	-6.38	-8.70
6	12.04	15.85
7	27.60	36.60
8	9.95	13.06
9	5.18	6.70
10	7.34	9.59
11	-4.07	-5.63
12	-0.37	-0.70

Question 5							0.00
Refer to Questions 1 and 2. Richard has just received an unexpected
bonus at work worth			$9,250	and, given the J. Corp.'s reputation
for excellent investment decision making, he will invest all of the bonus
in J Corp. stock. Given the rates of return for stocks A, B, C, and D
presented in Question 1 and the rates of return for J Corp. stock and
the market presented in Question 2, as well as the cash amounts he
is investing in stocks A, B, C, and D as you determined in Question 1,
a) What is the beta of Richard's portfolio?							Enter Answer
(round to two decimal points)
b) Richard's portfolio is…					Aggressive			}
					Defensive				Check only one box
					Neither
							↑
							Enter your Final Answer Here

Answer 1

1. a. He will invest 25% in each of the stocks.

Total investment is 37000. So he will invest 25% * 37000 = $ 9250 in each stock (A, B, C and D).

b. Expected value of richard's portfolio = Weighted average of average returns of each stock.

Let the average return for stock A, B, C and D be rA, rB, rC and rD respectively.

So the expected value of the portfolio = 9250 * (1+rA) + 9250 * (1+rB) + 9250 * (1+rC) + 9250 * (1+rD)

Average returns of the stock is arithemetic average of the stock over all the years.

Year	Stock A (%)	Stock B (%)	Stock C (%)	Stock D (%)
1	-6.47	-1.7	2.44	-10.73
2	18.11	4.445	-3.705	26.14
3	26.79	6.615	-5.875	39.16
4	24.79	6.115	-5.375	36.16
5	-16.47	-4.2	4.94	-25.73
6	32.63	8.075	-7.335	47.92
7	74.13	18.45	-17.71	110.17
8	27.05	6.68	-5.94	39.55
9	14.33	3.5	-2.76	20.47
10	20.11	4.945	-4.205	29.14
11	-10.33	-2.665	3.405	-16.52
12	-0.47	-0.2	0.94	-1.73
Average	17.01666667	4.171666667	-3.431666667	24.5

Thus,

rA = 17.02%

rB = 4.17%

rC = -3.43%

rD = 24.5%

Expected value of the portfolio = 9250 * (1+17.02%) + 9250 * (1+4.17%) + 9250 * (1-3.43%) + 9250 * (1+24.5%)

= 10824.04 + 9635.88 + 8932.57 + 11516.25 = $ 40908.74

Variance of the portfolio = Wa^2*Var(rA)+Wb^2*Var(rB)+Wc^2*Var(rc)+Wd^2*Var(rd)+2*Wa*Wb*Cov(A,B)+2*Wa*Wc*Cov(A,C)+2*Wa*Wd*Cov(A,D)+2*Wb*Wc*Cov(B,C)+2*Wb*Wd*Cov(B,D)+2*Wc*Wd*Cov(C,D)

W = weights of respective stocks

Wa=Wb=Wc=Wd=0.25

Year	Stock A (%)	Stock B (%)	Stock C (%)	Stock D (%)		Enter your Final Answer Here
1	-6.47%	-1.70%	2.44%	-10.73%
2	18.11%	4.45%	-3.71%	26.14%
3	26.79%	6.62%	-5.88%	39.16%
4	24.79%	6.12%	-5.38%	36.16%
5	-16.47%	-4.20%	4.94%	-25.73%
6	32.63%	8.08%	-7.34%	47.92%
7	74.13%	18.45%	-17.71%	110.17%
8	27.05%	6.68%	-5.94%	39.55%
9	14.33%	3.50%	-2.76%	20.47%
10	20.11%	4.95%	-4.21%	29.14%
11	-10.33%	-2.67%	3.41%	-16.52%
12	-0.47%	-0.20%	0.94%	-1.73%
	Covariance
	A,B	0.0136
	A,C	-0.0034
	A,D	-0.0203
	B,C	-0.0034
	B,D	0.0203
	C,D	-0.0203
	Standard Deviation
	A	0.2432
	B	0.0608
	C	0.0608
	D	0.3648

Variance = Standard Deviation ^2

Using above formula, Variance of the portfolio = 0.01078

Standard Deviation of the portfolio = Sqrt (Variance) = 0.1038 = 10.38%