It represents the additional amount of return that an investor receives per unit of increase in risk.
The t-statistic will equal the Sharpe Ratio times the square root of T (the number of returns used for the calculation).
The Sharpe ratio seeks to characterize how well the return of an asset compensates the investor for the risk taken.
When comparing two assets, the one with a higher Sharpe ratio appears to provide better return for the same risk, which is usually attractive to investors.
[3] However, financial assets are often not normally distributed, so that standard deviation does not capture all aspects of risk.
Ponzi schemes, for example, will have a high empirical Sharpe ratio until they fail.
In both cases, the empirical standard deviation before failure gives no real indication of the size of the risk being run.
For example, data must be taken over decades if the algorithm sells an insurance that involves a high liability payout once every 5–10 years, and a high-frequency trading algorithm may only require a week of data if each trade occurs every 50 milliseconds, with care taken toward risk from unexpected but rare results that such testing did not capture (see flash crash).
Additionally, when examining the investment performance of assets with smoothing of returns (such as with-profits funds), the Sharpe ratio should be derived from the performance of the underlying assets rather than the fund returns (Such a model would invalidate the aforementioned Ponzi scheme, as desired).
Berkshire Hathaway had a Sharpe ratio of 0.79 for the period 1976 to 2017, higher than any other stock or mutual fund with a history of more than 30 years.
These include those proposed by Jobson & Korkie[6] and Gibbons, Ross & Shanken.
The definition was: Sharpe's 1994 revision acknowledged that the basis of comparison should be an applicable benchmark, which changes with time.
[9] Example 1 Suppose the asset has an expected return of 15% in excess of the risk free rate.
A negative Sharpe ratio means the portfolio has underperformed its benchmark.
Thus, for negative values the Sharpe ratio does not correspond well to typical investor utility functions.
The Sharpe ratio is convenient because it can be calculated purely from any observed series of returns without need for additional information surrounding the source of profitability.
However, this makes it vulnerable to manipulation if opportunities exist for smoothing or discretionary pricing of illiquid assets.
Statistics such as the bias ratio and first order autocorrelation are sometimes used to indicate the potential presence of these problems.
Abnormalities like kurtosis, fatter tails and higher peaks, or skewness on the distribution can be problematic for the ratio, as standard deviation doesn't have the same effectiveness when these problems exist.
In some settings, the Kelly criterion can be used to convert the Sharpe ratio into a rate of return.
[12] Bailey and López de Prado (2012)[13] show that Sharpe ratios tend to be overstated in the case of hedge funds with short track records.
These authors propose a probabilistic version of the Sharpe ratio that takes into account the asymmetry and fat-tails of the returns' distribution.
With regards to the selection of portfolio managers on the basis of their Sharpe ratios, these authors have proposed a Sharpe ratio indifference curve[14] This curve illustrates the fact that it is efficient to hire portfolio managers with low and even negative Sharpe ratios, as long as their correlation to the other portfolio managers is sufficiently low.
Goetzmann, Ingersoll, Spiegel, and Welch (2002) determined that the best strategy to maximize a portfolio's Sharpe ratio, when both securities and options contracts on these securities are available for investment, is a portfolio of selling one out-of-the-money call and selling one out-of-the-money put.
While it is unclear where this rubric originated online, it makes little sense since the magnitude of the Sharpe ratio is sensitive to the time period over which the underlying returns are measured.