The Sharpe Ratio measures a portfolio's returns in terms of the risk taken to achieve them. Try not to get too caught up in the "math" component of this concept. Remember that each step in the formula is communicating an idea. We take the returns the portfolio is showing, but we only give the portfolio manager credit for the returns that are above the returns on risk-free 3-month T-bills. That makes sense, right? If he's putting your money at risk, he only gets credit if he does better than what you could get in a government-guaranteed T-bill. So we take the return and subtract the yield on 3-month T-bills over the period. Why do we then divide by the standard deviation? Because we are taking points off his score for the amount of variance the returns showed. If the portfolio tends to jump up 10 percent one month then drop 20 percent the next, that standard deviation is going to lower his score. So, if the portfolio earns a 9% return when T-bills returned 5%, we take 9 minus 5 to get 4. We then divide 4 by the standard deviation. The higher that number, the lower our Sharpe ratio will be--if the standard deviation is 8, the Sharpe ratio is a puny .5. If the standard deviation were only 4, however, the Sharpe ratio would be 1, which is much better. The higher the Sharpe ratio, the better the risk-adjusted return.
That's basically what you need to know about the Sharpe ratio. Now you can move on to the 9,873 other things that you need to know for your exam.