Question

Stock A has an annual expected return of 8%, a beta of .9, and a firm-specific volatility of 50% Stock B has an annual expected return of 9%, a beta of 1.3, and a firm-specific volatility of 40% The market has a standard deviation of 20%, and the risk-free rate is is 2%.

What is the volatility of stock A? (in %, round to 1 decimal place)

Answer 1

standard deviation of market = σ_M = 20%

Expected return on stock A = E[R_A] = 8%

Beta of stock A = β_A = 0.9

Firm specific volatility of stock A = σ_A = 50%

Firm-specific variance for stock A = σ_A² = (50%)² = 0.25

Variance due to market is given by:

Market specific variance for stock A = β_A²*σ_M² = (0.9)²*(20%)² = 0.0324

Total variance for stock A = Firm-specific variance + Market-specific variance = 0.25+0.0324 = 0.2824

Volatility is square-root of variance

Standard deviation or Volatility of stock A = σ_A = (0.2824)^1/2 = 0.53141321 = 53.141321%

Answer -> Volatility of stock A = 53.1%