Question

Given the following recorded historical performance of Investments, which would be your choice in terms of expected returns to be generated?

Period	A	B	C	D
1	8%	(2%)	(5%)	2%
2	12%	5%	15%	3%
3	5%	7%	18%	1%
4	6%	5%	12%	2%
5	(3%)	7%	(2%)	3%

Problem 2:

The Investor had the following data on returns of the 3 investments he had undertaken as follows:

Condition	Probability	A	B	C
Boom	40	14%	5%	(2%)
Normal	35	5%	3%	6%
Depression	25	(4%)	2%	10%

Required: Compute the following values for each Investment

2.1   Expected Return

2.2   Standard Deviation

2.3 Coefficient of Variation

Problem 3:

Given the following information below on stocks as Investments, supply the missing data to rearrange them in accordance to the required rate of return.

	Risk Free Rate	Market Return	Beta	CAPM
A	2%	???	1.50	10%
B	3%	15%	???	12%
C	5%	12%	.75	???
D	???	14%	.80	8%
E	2%	10%	(-1.10)	???

Problem 4:

Portfolio	Amount	Return	Beta
A	250,000	5%	1.5
B	500,000	10%	1.0
C	800,000	12%	(.5)
D	1,250,000	(2%)	.5

1. Portfolio Return
2. Portfolio Beta

Answer 1

Problem 1: Period D 1 2 3 A 8.00% 12.00% 5.00% 6.00% -3.00% 28.00% B -2.00% 5.00% 7.00% 5.00% 7.00% 22.00% C -5.00% 15.00% 18.00% 12.00% -2.00% 38.00% 2.00% 3.00% 1.00% 2.00% 3.00% 11.00% 4 5 Total Expected return (total/no. of periods) = 28%/5 =22%/5 = 38%/5 = 11%/5 = 5.60% = 4.40% = 7.60% = 2.20% (A-A)^2 Problem 2: Expected Return (Mean) = [E(P*X)] Standard Deviation (risk) = V[E(P*(X-X)^2)] Where X is the Return of asset every State of Economy X is the Mean STOCK A: State of Economy Probability Stock (A) PA A-A P) Boom 0.40 0.14 0.056 0.0765 Normal 0.35 0.05 0.018 -0.0135 Depression 0.25 -0.04 -0.010 -0.1035 TOTAL 0.064 Mean A [E(PA)] = 6.40% Standard Deviation(Risk) = V0.0052 = 0.0721 or 7.21% Coefficient of variation (O/A) = 6.40%/7.21% = 88.77% 0.0059 0.0002 0.0107 P*[(A- A)^2] 0.0024 0.0001 0.0027 0.0052 STOCKB: State of Economy Stock (B) p*B B-B (B-B)^2 Probability P) 0.40 0.00020 0.00000 0.00020 0.35 P*[(B- B)^2] 0.00010 0.00000 0.00010 0.00020 Boom Normal Depression TOTAL Mean B [3(P*B)] Standard Deviation(Risk) Coefficient of variation (O/A) 0.25 0.05 0.02000 0.01450 0.03 0.01050 -0.00550 0.02 0.00500 -0.01550 0.03550 = 3.55% = V0.00020 = 0.0141 or 1.41% = 3.55%/1.41% = 251.77% STOCK C: State of Economy Stock (C) pic C-C (C-C)^2 Probability P) 0.40 0.35 0.25 0.0034 0.0005 0.0038 Boom Normal Depression TOTAL Mean [(P*C)] Standard Deviation(Risk) Coefficient of variation (O/A) -0.02 -0.0080 -0.0580 0.06 0.0210 0.0220 0.10 0.0250 0.0620 0.0380 = 3.80% = V0.0026 = 0.0510 or 5.10% = 3.80%/5.10% = 74.51% P*[(C- c)^2] 0.0014 0.0002 0.0010 0.0026

Problem 3: For Stock A, computation of market return using CAPM: E('r) = R(f) +B(Rm - Rf) 10% = 2% +1.50(Rm - 2%) 10% = 2% +1.50Rm - 3% 1.50Rm = 10% +3% -2% 1.50Rm = 11% Rm = 11%/1.50 Rm = 7.33% For Stock B, computation of Beta using CAPM: E('r) = R(f) + B(Rm - Rf) 12% = 3% + B(15%-3%) 12% = 3% +B12% B12% = 12% -3% B12% = 9% B = 9%/12% B = 0.75 For Stock C, computation of CAPM return: E('r) = R(f) +B(Rm - Rf) E('r) = 5% +0.75(12% - 5%) E('r) = 5% +0.75*7% E('') = 10.25% For Stock D, computation of risk free return: E('r) = R(f) +B(Rm - Rf) 8% = Rf +0.80(14%-Rf) 8% = Rf + 11.20% - 0.80Rf 8% = 0.20Rf +11.20% 0.20Rf = 8% - 11.20% 0.20Rf = -3.20% Rf = -16% For Stock E, computation of CAPM return: E('r) = R(f) + B(Rm - Rf) E('r) = 2% + (-1.10) * (10%-2%) E('r) = 2% - 8.80 E('r) = -6.80%

Problem 4: Assets Amount Weights Return Beta A 0.09 1.50 B 0.18 1.00 Weighted Return 0.45% 1.80% 3.48% -0.90% 4.83% 2,50,000.00 5,00,000.00 8,00,000.00 12,50,000.00 28,00,000.00 5.00% 10.00% 12.00% -2.00% Weighted Beta 0.14 0.18 -0.15 0.23 0.40 С 0.29 -0.50 D 0.45 0.50 Portfolio Return Porfolio Beta = 4.83% = 0.40