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Here are returns and standard deviations for four investments. Standard Return (%) Deviation(%) Treasury bills Slock P Stock Q Stock R 4.0 9.5 13.5 21.5 12 25 24 Calculate the standard deviations of the following portfolios a. 50% in Treasury bills, 50% in stock P (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Standard deviation b 50% each in and R, assuming the shares have: (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places) Standard Deviation Perfect positive correlation Perfect negative correlation No correlation
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Answer #1

Formula for standard deviation of portfolio:

Portfolio Standard Deviation Formula

Here,

  • wA, wB are weights of Stock A and B respectively in the portfolio
  • kA, s kBare Standard Deviation of Stock A, and B respectively in the portfolio
  • R(kA, kB) is the correlation between Stock A and Stock B.

a)

Stock TB P
Standard Deviation 0 12
Investment Proportion 0.5 0.5

It is considered that there is a perfect negative correlation between treasury bill and stock P.

Using above mentioned formula, Standard deviation of Portfolio = 12.02%

b)

Stock Q R
Standard Deviation 25 24
Investment Proportion 0.5 0.5

In case of perfect positive correlation:

Standard deviation = 36.76%   

In case of perfect positive correlation:

Standard deviation = 32.47%

In case of no correlation:

Standard deviation = 34.66%

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