Question

If the covariance between the excess return of stock A and the market excess return is 0.03, the standard deviation of the market excess return is 0.15, and the standard deviation of the excess return of stock A is 0.25, what is the idiosyncratic volatility? What fraction of the total risk (variance) comes from the systematic risk (variance)? Please show work.

Answer 1

SUGGESTED ANSWER

• The Idiosyncratic Volatility is 0.04 or 4 percent.
• The fraction of total risk (variance) which comes from the systematic risk (variance) is 1.3333.

IMPORTANT KEY TERMS PERTINENT TO THE GIVEN QUESTION

1. The variance and standard deviation of a return are statistical measures that are used in measuring the risk in investment
2. Covariance (a statistical measure) between 2 securities or 2 portfolios or a security and a portfolio that indicates how the rates of return  for the two concerned entities behave relative to each other
3. Covariance can be expressed as a correlation between the security and the market and the standard deviations of the security and market
4. Total Variance or the portfolio risk is the square of the standard deviation of the security if the portfolio consists of only one security.
5. Market Variance is the square of the standard deviation of the market
6. Idiosyncratic Volatility can be calculated as the difference between the Total Variance and Market Variance
7. Systematic Risk is the variability in security returns caused by changes in the economy or the market and all securities are affected by such changes to some extent. A higher variability would indicate higher systematic risk and vice versa
8. The systematic risk of a security is measured by a statistical measure which is called Beta. There are 2 statistical methods that can be used for the calculation of Beta which is the Correlation Method and Regression Method. In the present question, the Correlation method is used to calculate the value of Beta ie the systematic risk of the total risk
9. A positive Beta indicates that security return is dependent on the market return and moves in the direction in which the market moves. Further, as Beta measures the volatility of a security's return relative to the market, the larger the Beta, the more volatile the security.

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