Question

Miss Angela is considering two securities, A and B, and the relevant information is given below:

State of Economy

Probability

Return on Security A (%)

Return on Security B (%)

Bear

0.6

3.0%

6.5%

Bull

0.4

15.0%

6.5%

1. Calculate the expected returns of each security

2. Calculate the standard deviation of each security

3. Calculate the Variance of each security

4. Calculate the coefficients of variation of each security.

5. Suppose Miss Angela invested $2,500 in Security A and $3,500 in security B. Calculate the expected return of her portfolio.

6. Calculate the standard deviation of Miss Angela's portfolio

Calculate the Variance of each security

Answer 1

Choose...

Calculate the expected return of her portfolio.

Answer 2

Choose...

Calculate the standard deviation of each security

Answer 3

Choose...

Calculate the standard deviation of Miss Angela's portfolio, assume that correlation coefficient = 0.4

Answer 4

Choose...

Calculate the coefficients of variation of each security

Answer 5

Choose...

Calculate the expected returns of each security

Answer 6

Choose...

Answer 1

1). Expected return (Er) = sum of [probability*return]

Expected return of A (ErA) = (0.6*3%) + (0.4*15%) = 7.80%

Expected return of B (ErB) = (0.6*6.50%) + (0.4*6.50%) = 6.50%

2). Standard deviation (SD) = variance^0.5 where

variance (V) = sum of [probability*(return - Er)^2]

Variance of A (VA) = 0.6*(3%-7.80%)^2 + 0.4*(15%-7.80%)^2 = 0.003456

Variance of B (VB) = 0 since it gives same return for both bear and bull states.

SDA = 0.003456*0.5 = 5.88%

SDB = 0%

3). Variance of A (VA) = 0.003456 (Calculated above)

VB = 0 (since return remains same in both states)

4). Coefficient of variation (CoV) = SD/Er

CoV for A = 5.88%/7.80% = 0.7537

CoV for B = 0/6.50% = 0.0000

5). Portfolio expected return = sum of [weight of asset*expected return of asset]

weight of asset = amount invested in asset/total amount invested

weight of A (wA) = 2,500/(2,500+3,500) = 41.67%

weight of B (wB) = 3,500/(2,500+3,500) = 58.33%

Portfolio expected return = (41.67%*7.80%) + (58.33%*6.50%) = 7.04%

6). Portfolio standard deviation = [(wA*SDA)^2 + (wB*SDB)^2 + (2*wA*wB*SDA*SDB*correlation)]^0.5

= [(41.67%*5.88%)^2 + (58.33%*0%)^2 + (2*41.67%*58.33%*5.88%*0%*0.4)]^0.5 = 2.45%