QUANTATIVE

                                           INVESTMENT ANALYSIS

                                                 تحليل الاستثمار  الكمى 

                                                         The Sharpe Ratio

Although CV was designed as a measure of relative ,n, its inverse reveals something about return per unit of risk because the standard deviation of returns is commonly used a measure of investment risk. For example, a portfolio with a mean monthly return of 1.19 percent and a standard deviation of 4.42 percent has an inverse CV of 1.19%/4.42% = 0.27. This result indicates that each unit of standard deviation represents a 0.27 percent return.

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A more precise return-risk measure recognizes the existence of a risk-free return, a return for virtually zero standard deviation. \With a risk-free asset, an investor can choose a risky portfolio, p and then combine that portfolio with the risk-free asset to achieve any desired level of absolute risk as measured by standard deviation of return, sp. Consider a graph with mean return on the vertical axis and standard deviation of return on the horizontal axis. Any combination of portfolio p and the risk-free asset lies on a ray (line) with slope equal to the quantity (Mean return - Risk-free return) divided by s,. The ray giving investors choices offering the most reward (return in excess of the risk-free rate) per unit of risk is the one with the highest slope. The ratio of excess return to standard deviation of return for a portfolio p-the slope of the ray passing through p-is a single-number measure of a portfolio's performance known as the Sharpe ratio, after its developer, William F. Sharpe.