Question

The following information is available on the percentage rates of return on various assets for the last three years. You determine that this is a sample which is representative of the data population for these securities.

Security Year 1

Security	Year 1	Year 2	Year 3
Stock A	6%	18%	60%
Stock B	32%	22%	32%
Market	50%	12%	20%
Government Bonds	10%	10%	10%

(a) Consider only shares A and B for this part. Compute the portfolio weights that yield the portfolio of A and B which has the lowest possible standard deviation. Then compute that portfolio’s expected return and standard deviation. Hint: Write down the formula for this, then compute all the ingredients you require.

Answer 1

Answer )

Security	Year 1	Year 2	Year 3	Average return	Std dev	(Std dev)^2
Stock A	6%	18%	60%	28%	0.283549	0.0804
Stock B	32%	22%	32%	29%	0.057735	0.003333
Market	50%	12%	20%	27%	0.200333
Government Bonds	10%	10%	10%	10%

Correlation Matrix
	Stock A	Stock B	Market
Stock A	1
Stock B	0.305424	1
Market	-0.51053	0.662849	1

For portfolio
R_p = W_AR_A + W_BR_B , W_A =W_B = weight of stock A/B and R_A =R_B = return of stock A/B.

_p2 ₌  W_A²_A2 + W_B²_B2 + 2 W_{A *} W_B *_A *_B * r_AB , where , _A =_B + standard deviation of A/B , and r_AB = correlation between A/B.

W_A = 1- W_B.

Below table indicate the standard deviation of portfolio at different level (value of ) W_A and W_B

Situation	WA	WB	p2	p	RP
1	0.01	0.99	0.003374	0.058086	28.66%
2	0.02	0.98	0.003429	0.058562	28.65%
3	0.05	0.95	0.003684	0.060699	28.63%
4	0.25	0.75	0.008775	0.093675	28.50%
5	0.5	0.5	0.023433	0.15308	28.33%
6	0.75	0.25	0.047308	0.217505	28.17%
7	0.8	0.2	0.053189	0.230628	28.13%
8	0.9	0.1	0.066057	0.257016	28.07%

From the above table , situation 1 has the minimum value of risk ( _p) . and return at calculated .