Question

An investor is considering the purchase of Gryphon stock, which has returns given in the table below.

Scenario	Probability	Rate of Return
Recession	0.27	2%
Normal	0.58	9%
Boom	0.15	14%

Calculate the expected return and standard deviation of Gryphon. Round your answers to 2 decimal places.

Enter your answers below.

E(r) =    
Correct response: 7.86 %

Std. Dev. =   
Correct response: 3.96±0.01 %

The investor decides to diversify by investing $8,000 in Gryphon stock and $7,000 in Royal stock which has an expected return of 8.5% and a standard deviation of 9.5%. The correlation coefficient for the two stocks' returns is 0.2. Calculate the expected return and standard deviation of the portfolio. Round your answers to 2 decimal places. Use the correct answers from the previous question.

Enter your answers below.

E(r_p) =  %

Std. Dev =  %

Answer 1

1-a). Expected Return = $\sum_{i=1}^{n}$ [Probability(i) * Return(i)]

= [0.27 * 2%] + [0.58 * 9%] + [0.15 * 14%] = 0.54% + 5.22% + 2.10% = 7.86%

1-b). Standard Deviation = [$\sum_{i=1}^{n}${Probability(i) * (Expected Return - Return(i))²}]^1/2

= [{0.27 * (7.86% - 2%)²} + {0.58 * (7.86% - 9%)²} + {0.15 * (7.86% - 14%)²}]^1/2

= [9.27%² + 0.75%² + 5.65%²]^1/2

= [15.68%²]^1/2 = 3.96%

2-a). Expected Return = $\sum_{i=1}^{n}$ [Probability(i) * Return(i)]

= [(8,000/15,000) * 7.86%] + [(7,000/15,000) * 8.5%] = 4.19% + 3.97% = 8.16%

2-b). Standard Deviation = [{w(G)² * S.D.(G)²} + {w(R)² * S.D.(R)²} + {2 * w(G) * w(R) * S.D.(G) * S.D.(R) * Correlation(G,R)}]^1/2

= [{(8,000/15,000)² * (3.96%)²} + {(7,000/15,000)² * (9.5%)²} + {2 * (8,000/15,000) * (7,000/15,000) * 3.96% * 9.5% * 0.2}]^1/2

= [4.46%² + 19.65%² + 3.75%²]^1/2

= [27.86%²]^1/2 = 5.28%