5F.10
10. You hold one stock (A) with a standard deviation of 20%. You are thinking about buying another stock (B) with a standard deviation of 30%. You will hold these two stocks in a portfolio, with 50% of your money invested in each. Stock B has a correlation coefficient of –0.2 with stock A. Your friend says that adding a stock with higher standard deviation (B) than stock A will result in a riskier portfolio than just holding A alone. Is he right? That is, will your portfolio of A & B be riskier than just stock A? Why or why not? [6]
Your friend's a bozo. You learned that the most important factor in portfolio risk is how the stocks in the portfolio covary—even to very risky stocks can make a safe portfolio if they tend to offset each other. The important point in this question is that the correlation between the two stocks is negative, so the portfolio standard deviation turns out to be less than the standard deviation of even the less risky of the two stocks:
Thus, the fact that the two stocks tend to offset each other makes the portfolio less variable than either stock in isolation. That is, even though either stock in isolation might shoot all over the place, tie it to the other and the net movement is dampened.