R² as the split between market risk and stock-specific risk

Question

You regress a stock's daily returns on the market's returns (a single-factor model) and get $R^2 = 0.64$ . The stock's total volatility is $30\%$ per year.

What does the $R^2$ tell you about the stock's risk, and what is its idiosyncratic (stock-specific) volatility?

Accepted Answer

Variance splits, volatility does not. In a one-factor regression, total return variance decomposes into a systematic part (driven by the market) plus an idiosyncratic part (everything else), and these add: \sigma{	ext{total}}^2 = \sigma{	ext{systematic}}^2 + \sigma{	ext{idiosyncratic}}^2. R^2 is exactly the systematic fraction of variance: R^2 = \sigma{	ext{sys}}^2 / \sigma{	ext{total}}^2 = 0.64. So 64\% of the stock's variance comes from market moves, and the remaining 1 - 0.64 = 0.36 is idiosyncratic. Get the idiosyncratic volatility. Apply the fractions to the total variance, then tak…

R² as the split between market risk and stock-specific risk

Your answer

More Statistics questions