Explanation
Security A 'dominates' security B, ie it offers the most return per unit of volatility. However, because it is less volatile, its returns are likely to be more concentrated around its mean compared to Security B which will have
'fatter tails' compared to Security A. Therefore Security B will offer a much better chance of making the desired 25% return. Of course, this also means that Security B is much more likely to lose a lot more money than Security A. However, if the portfolio manager is only interested in maximizing his chances of making a
25% or greater return, he should select Security B. The answer can be verified using Excel's Normdist formula, and probability of exceeding 25% will be given by [=1-NORMDIST(0.25,0.1,0.1,TRUE)] for Security A and =1-NORMDIST(0.25,0.1,0.2,TRUE)] for Security B. A combined portfolio of the two will have a return of 10% and variance less than that of Security B (or at the most equal to the weighted average of the two variances, even if their correlation is 1), which means a combined portfolio will also have a lower probability of exceeding a 25% return.
This question reflects how portfolio managers may be tempted to make sub-optimum decisions for their investors by swinging for the fences by taking large bets, for example, when they have had a big drawdown and have to make it up to the high water mark levels before they earn performance fees.