Question

1.) Two securities have the following characteristics:

E(Ra)= 0.06​ 0.04

E(Rb)= 0.08​ 0.10

A) Fill in the missing cells in the table.

For each of two correlation cases, corr. = -1 and corr. = 0, calculate the attainable portfolios' mean and standard deviation from combining the two assets together using weights in increments of 25% from 1 to 0. Also, calculate the minimum risk portfolio's weights, mean and standard deviation for each correlation case. Assume that the risk free rate is .04. Hint: in some of the cases, filling in the cells requires no calculations.

		Corr = 0			Corr = -1
Weight in A	Weight in B	E(Rp)		E(Rp)
1.0	0.0	0.06
0.75	0.25		0.03905			0.005
0.50	0.50	0.07	0.05385
0.25	0.75	0.075				0.065
0.0	1.0		0.10			0.10
Minimum risk portfolio for corr=0
		0.06275		NA		NA
Minimum risk portfolio for corr=-1
0.7143	0.2857	NA	NA	0.0657

NA = not applicable

E(Ra)= 0.06​ 0.04

E(Rb)= 0.08​ 0.10

Answer 1

The return of a portfolio is the weighted return of the two stocks

The standard deviation of a portfolio is given by

Where Wi is the weight of the security i,

is the standard deviation of returns of security i.

and is the correlation coefficient between returns of security i and security j

Using these formulas, the completed table is shown below

		Corr = 0	Corr = -1
Weight in A	Weight in B	ER(p)	Standard Deviation	ER(p)	Standard Deviation
1	0	0.060000	0.04	0.06	0.04
0.75	0.25	0.065000	0.039051	0.065	0.005
0.5	0.5	0.070000	0.053852	0.07	0.03000
0.25	0.75	0.075000	0.075664	0.075	0.0650000
0	1	0.080000	0.1	0.08	0.1

The formula for minimum risk weights in a two stock portfolio (Stock S and Stock B ) is

Let S = A

Minimum risk portfolio for corr=0

So, W_A = (0.10^2-0.04*0.10 *0) / ( 0.04^2+0.10^2 -2*0.04*0.10 *0)

= 0.8621 = 86.21%

and W_B = 1-   W_S = 1-0.8621 =0.1379=13.79%

So, portfolio Return = 0.8621*6%+0.1379*8% = 6.28%

Standard deviation = 3.71%

Similarly

Minimum risk portfolio for corr=-1

So, W_A = (0.10^2-0.04*0.10 *(-1)) / ( 0.04^2+0.10^2 -2*0.04*0.10 *(-1))

= 0.7143 = 71.43%

and W_B = 1-   W_S = 1-0.7143 =0.2857=28.57%

So, portfolio Return = 0.7143*6%+0.2857*8% = 6.57%

Standard deviation = 0%

So, the table is given below

	Weight in A	Weight in B	ER(p)	Standard Deviation
Minimum risk portfolio for corr=0	0.8621	0.1379	0.06275	0.0371
Minimum risk portfolio for corr=-1	0.7143	0.2857	0.0657	0