Question

The expected return of Monty is 19.0 percent, and the expected return of Flounder is 24.0 percent. Their standard deviations are 13.0 percent and 21.0 percent, respectively. If a portfolio is composed of 40 percent Monty and the remainder Flounder, calculate the expected return and the standard deviation of the portfolio, given a correlation coefficient between Monty and Flounder of 0.35. (Round intermediate calculations to 4 decimal places, e.g. 31.2125 and final answers to 2 decimal places, e.g. 15.25%.)

The expected return		%
Standard deviation of portfolio		%

Calculate the standard deviation if the correlation coefficient is −0.35. (Do not round intermediate calculations. Round answer to 2 decimal places, e.g. 15.25%.)

Standard deviation of portfolio

%

Answer 1

Question a:

E(r)m = Expected Return on Monty = 19%

E(r)f = Expected Return on Flounder = 24%

Wm = Amount invested in Monty = 40%

Wf = Amount invested in Flounder = 60%

Expected return = [E(r)m * Wm] + [E(r)f * Wf]

= [19% * 40%] + [24% * 60%]

= 7.6% + 14.4%

= 22%

Therefore, The expected Return is 22%

Question b:

σm = Standard Deviation of Monty = 13%

σf = Standard Deviation of Flounder = 21%

Wm = Amount invested in Monty = 40%

Wf = Amount invested in Flounder = 60%

Cor(m,f) = Correlation coefficient = 0.35

Variance of Portfolio = [(Wm)^2 * (σm)^2] + [(Wf)^2 * (σf)^2] + [2*Cor(m,f) * Wm* σm * Wf * σf]

= [(40%)^2 * (13%)^2] + [(60%)^2 * (21%)^2] + [2 * 0.35 * 40% * 13% * 60% * 21%]

= [0.16 * 0.0169] + [0.36 * 0.0441] + 0.0045864

= 0.002704 + 0.015876 + 0.0045864

= 0.0231664

Standard Deviaiton of Portfolio = Square root of Variance

= (0.0231664)^(1/2)

= 0.152205125

= 15.22%

Therefore, Standard deviation of portfolio is 15.22%

Question c:

σm = Standard Deviation of Monty = 13%

σf = Standard Deviation of Flounder = 21%

Wm = Amount invested in Monty = 40%

Wf = Amount invested in Flounder = 60%

Cor(m,f) = Correlation coefficient = -0.35

Variance of Portfolio = [(Wm)^2 * (σm)^2] + [(Wf)^2 * (σf)^2] + [2*Cor(m,f) * Wm* σm * Wf * σf]

= [(40%)^2 * (13%)^2] + [(60%)^2 * (21%)^2] + [2 * -0.35 * 40% * 13% * 60% * 21%]

= [0.16 * 0.0169] + [0.36 * 0.0441] - 0.0045864

= 0.002704 + 0.015876 - 0.0045864

= 0.0139936

Standard Deviaiton of Portfolio = Square root of Variance

= (0.0139936)^(1/2)

= 0.118294548

= 11.83%

Therefore, Standard deviation of portfolio is 11.83%