Return Standard Deviation Treasury bills 6.0% 0% Stock P 10.5 13 Stock Q 16.5 31
ID: 2709018 • Letter: R
Question
Return Standard Deviation
Treasury bills 6.0% 0%
Stock P 10.5 13
Stock Q 16.5 31
Stock R 20.5 23
Here are returns and standard deviations for four investments.
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)Since there is no correlation between Stock P and Treasury bills, Standard deviation of portfolio will be weighted average standard deviation of the same:
SD portfolio = SDt x Wt + SDp x Wp
= 0% x 0.50 + 0.105 x0.50
= 5.25%
b) Since there is correlation, we can use following formula to calculate variance:
Perfect positive correlation
Variance = (SDq x Wq)^2 + (SDr x Wr)^2 +2xWqxWrxSDqxSDr x correl
= (16.5 x 0.5)^2 + (20.5x0.5)^2 + 2x 0.5 x0.5 x16.50 x20.5 x1
= 173.125 +169.125
= 342.25
Standard Deviation of portfolio = variance ^0.50
= 342.25^0.50
= 18.50%
Perfect negative correlation
Variance = (SDq x Wq)^2 + (SDr x Wr)^2 +2xWqxWrxSDqxSDr x correl
= (16.5 x 0.5)^2 + (20.5x0.5)^2 + 2x 0.5 x0.5 x16.50 x20.5 x-1
= 173.125 - 169.125
= 4
Standard Deviation of portfolio = variance ^0.50
= 4^0.50
= 2%
no correlation
Variance = (SDq x Wq)^2 + (SDr x Wr)^2 +2xWqxWrxSDqxSDr x correl
= (16.5 x 0.5)^2 + (20.5x0.5)^2 + 2x 0.5 x0.5 x16.50 x20.5 x0
= 173.125 + 0
= 173.125
Standard Deviation of portfolio = variance ^0.50
= 173.125^0.50
= 13.16%
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