Here are returns and standard deviations for four investments. Return Standard D

Question

Here are returns and standard deviations for four investments. Return Standard Deviation Treasury bills 5.5% 0% Stock P 8.0 14 Stock Q 15.0 37 Stock R 23.0 22 Calculate the standard deviations of the following portfolios. a. 50% in Treasury bills, 50% in stock P. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Standard deviation % b. 50% each in Q and R, assuming the shares have: (Do not round intermediate calculations. Round your answers to 1 decimal place.) Standard Deviation Perfect positive correlation % Perfect negative correlation % No correlation %

Explanation / Answer

a) Standard deviation of portfolio is weighted average standard deviation of all the investments in the portfolio.

Standard deviation of portfolio consisting of 50% in Treasury bills, 50% in stock P.

= 0.50 * 0 + 0.50 * 14 = 7 % [0.07]

b) Standard deviation of portfolio consisting of 50% in Q and 50% in R investment

i) Perfect positive correlation:- = (0.5) 2 * (37)2 + (0.5)2 * (22)2 + 2 (0.5)2 * 1 * 37 * 22

   = 342.25 + 121 + 407

   = 870.25

Standard deviation of portfolio in case of perfect positive correlation =Under root of 870.25 = 29.5 % [0.295]

ii) Perfect negative correlation:- = (0.5) 2 * (37)2 + (0.5)2 * (22)2 + 2 (0.5)2 * (-1) * 37 * 22

   = 342.25 + 121 - 407

   = 56.25

Standard deviation of portfolio in case of perfect negative correlation = Under root of 56.25 = 7.5 % [0.075]

iii) No correlation

   = (0.5)2 * (37)2 + (0.5)2 + (22)2

= 342.25 + 121

= 463.25

Standard deviation of portfolio in case of no correlation = Under root of 463.25 = 21.52 % [0.2152]

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