Standard Deviation of a Portfolio of Risky Securities
What is the standard deviation of a portfolio of risky securities?
a. the square root of the sum of the securities' variances
b. the square root of the sum of the securities' covariances
c. the square root of the weighted sum of the securities' variances and covariances, using multiple/squared weights
d. is the weighted sum of the securities' covariances
e. the square root of the weighted sum of the securities' variances
Answer:
The standard deviation of a portfolio of risky securities is the square root of the weighted sum of the securities' variances and covariances, using multiple/squared weights.
In finance, the standard deviation of a portfolio of risky securities is a crucial measure used to evaluate the volatility or risk associated with the entire portfolio. Unlike calculating the standard deviation for single securities, the standard deviation of a portfolio considers both the individual risk levels of the securities (variances) and the interrelationships between their returns (covariances).
When calculating the standard deviation of a portfolio, it is important to use the formula denoted by option 'c': the square root of the weighted sum of the securities' variances and covariances, using multiple/squared weights. This formula accounts for the fact that securities in a portfolio may not fluctuate independently, but rather their fluctuations may be interrelated.