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# Mean, standard deviation, covariance & correlation of return

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Securities A & B have the following rates of return & probabilities of occurrence:

Probability ROR on Securities: A B
0.3 -2% 28%
0.3 4% 12%
0.4 20% 3%

a. calculate mean & standard deviation in the return for each asset.
b. calculate the covariance & the correlation coefficient on the returns of the two assets
c. calculate the mean & standard deviation in the return on the following portfolios of the two assets:
(1) 75% in A and 25% in B
(2) 50% in each
(3) 25% in A & 75% in B

ROR: Rate of Return

#### Solution Summary

Calculates mean, standard deviation, covariance, correlation coefficient, for returns on securities and mean & standard deviation of return for portfolios.

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## Calculating the Return, Variance and Standard Deviation

Given the large-cap stock index and the government bond index data in the following table, calculate the expected mean return and standard deviation of return for a portfolio 75 percent invested in the stock index and 25 percent invested in the bond index
Assumed Returns, Variances, and Correlations
Large-Cap Stock Index Government Bond Index

Expected return 15% 5%
Variance 225 100
Standard Deviation 15% 10%
Correlation 0.5

A. Mean and geometric mean of the rate of return
B. Variance and standard deviation of the rate of return
C. Covariance and correlation coefficient of the rate of return.

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