Question

1. Two securities – PohKeong Gold and Mama Care are currently being considered by Jason. He is considering either to invest 100% in PohKeong Gold or building a portfolio that consist of both security – 60% in PohKeong Gold and 40% in Mama Care. The probability distribution of expected returns of these assets are shown in the following table.

State      of Economy	Probability	Return             on PohKeong Gold	Return           on Mama Care
Bear	0.30	3%	2%
Bull	0.70	18%	10%

1. Calculate the expected return for each of the two alternatives. 4m
2. Calculate the standard deviation of returns of the two alternatives. 6m
3. Evaluate the investors decisions, based on the above calculations. 4m (200 words)

Answer 1

Part i)
Expected return on alternative 1 = (3%*0.3)+(18%*0.7) = 0.9%+12.6% = 13.5%
Expected return on alternative 2 = 0.6*[(3%*0.3)+(18%*0.7)]+0.4*[(2%*0.3)+(10%*0.7)] = 0.6*[0.9%+12.6%]+0.4*[0.6%+7%] = (0.6*13.5%)+(0.4*7.6%) = 8.1%+3.04% = 11.14%

Part ii)
PohKeong gold is considered as "x", Mama Care is considered as "y"
Mean on x (x') = (3%*0.3)+(18%*0.7) = 0.9%+12.6% = 13.5%
Mean on y (y') = (2%*0.3)+(10%*0.7) = 0.6%+7% = 7.6%

State	Probability (p)	x	y	(x-x')	(y-y')	(x-x')^2	(y-y')^2	P*(x-x')^2	P*(y-y')^2	(x-x')(y-y')
Bear	0.3	3%	2%	-10.50%	-5.60%	0.011025	0.003136	0.0033075	0.0009408	0.00588
Bull	0.7	18%	10%	4.50%	2.40%	0.002025	0.000576	0.0014175	0.0004032	0.00108
		21%	12%			0.013050	0.003712	0.0047250	0.0013440	0.00696

Standard deviation of x (SD x) = square root of {Σ P*(x-x')^2} = square root of {0.004725} = 6.87%
Standard deviation of y (SD y) = square root of {Σ P*(y-y')^2} = square root of {0.001344} = 3.67%
Correlation of x & y (r):

r=0.00696/square root of {0.01305*0.003712} = 0.00696/0.00696 = 1

Standard deviation of alternative 1 = SD x = 6.87% (Because 100% invested in x)
Standard deviation of alternative 2 = Square root of {[(weight on x^2)*(SD x^2)]+[(weight on y^2)*(SD y^2)]+[weight on x*SD x*weight on y*SD y*r]} = Square root of {[(0.6^2)*(0.0687^2)]+[(0.4^2)*(0.0367^2)]+[0.6*0.0687*0.4* 0.0367*1]} = Square root of {[0.36*0.004725]+[0.16*0.001344]+0.0006048} = Square root of {0.001701+ 0.00021504+0.0006048} = Square root of {0.00252084} = 5.02%

Part iii)

Portfolio	Return	Risk
100% in PohKeong Gold	13.50%	6.87%
60% in PohKeong Gold and 40% in Mama Care	11.14%	5.02%

Since the correlation between two stock is exactly 1, so whatever proportion invested on the securities, all are equally good. In 1st alternative higher return as well as high risk & in 2nd alternative low return low risk.