The question: you have a portfolio of risky assets that with a 90% probability (normal state of the world) has an expected annual return of 10% plus a random variable with a standard deviation of 15%. With a 10% probability (crisis state) the annual return would be -30% plus a random variable with a standard deviation of 15%. What is the expected return and volatility of the portfolio?
I know the answer is 6% expected return and 19.21% volatility. I understand the annual return but get 12% when calculating the volatility. What am I doing wrong? Thanks!