Question

Assume that the only source of systematic risk in the economy is the market risk. Consider a portfolio (P) with the following characteristics (which were measured over a certain timeperiod T): mean or expected annual return (µp) = 100%, standard deviation of annual portfolio returns (σp) = 25% and a beta relative to the market (βp) = −1. During the same time-period T, the market index (M) had the following characteristics: mean or expected annual return (µm) = 33% and the standard deviation of annual market returns (σm) = 20%. Assume that the riskfree asset has an annual return of 2%.

What percentage of the total portfolio risk is systematic risk and what percentage is idiosyncratic risk? Show calculations

Answer 1

Systematic Risk = (βp * σm)²

Systematic Risk = (-1 * 20%)²

Systematic Risk = 0.04

Systematic Risk = 20%

(Total Portfolio Risk)² = (Systematic Risk)² + (Non-Systematic Risk)²

(Non-Systematic Risk)² = (Total Portfolio Risk)² - (Systematic Risk)²

Non-Systematic Risk = (33%)² - (20%)²

Non-Systematic Risk = 0.0689

Non-Systematic Risk = 26.25%

Percentage of Systematic Risk = (Systematic Risk)² /  (Total Portfolio Risk)²

Percentage of Systematic Risk = (20%)² / (33%)²

Percentage of Systematic Risk = 36.73%

Percentage of Non-Systematic Risk = (Non-Systematic Risk)² /  (Total Portfolio Risk)²

Percentage of Non-Systematic Risk = (26.25%)² / (33%)²

Percentage of Non-Systematic Risk = 63.27%