**Provides A Totally Free Variation Of Its Own Business Intelligence Software Application.** – The Sharpe ratio compares the return of an investment to its risk. It is a mathematical expression of the insight that excess returns over a period of time may indicate greater volatility and risk rather than investment skill.

Economist William F. Sharpe proposed the Sharpe ratio in 1966 as an enhancement of his work on the capital asset pricing model (CAPM), calling it the reward-to-variability ratio. Sharpe won the Nobel Prize in Economics in 1990 for his work on the CAPM.

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The numerator of the Sharpe ratio is the difference between the actual, or expected, return and the risk-free rate of return or the performance of a particular investment category, such as a benchmark. Its denominator is the standard deviation of returns over the same period of time, a measure of volatility and risk.

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Sharpe Ratio = R P − R F σ P Where: R P = Return of the portfolio R F = Risk-free rate of return σ P = Standard deviation Excess return of the portfolio begin &textit = frac\ &textbf\ &R_ =text\ &R_ = text\ &sigma_p = text\ end SharpeRatio = σ p R p – R f Where: R p = Returnofportfolio R f = Risk-free rate σ p = Standard deviation of portfolio additional return of

The standard deviation is derived from the variability of returns for a series of time intervals by adding them to the total performance sample under consideration.

It is calculated as the average of the return differences over each incremental time period, making up the total. For example, the numerator of the 10-year Sharpe ratio might be an average of the 120 monthly return difference for a fund versus an industry benchmark.

The Sharpe ratio is one of the most widely used methods for measuring risk-adjusted relative return. It compares the historical or projected returns of a fund to the historical or expected variability of such returns relative to an investment benchmark.

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The risk-free rate was initially used in the formula to denote an investor’s notional minimum borrowing cost. More generally, it represents the risk premium of an investment versus a safer asset such as Treasury bills or bonds.

When benchmarked against the returns of an industry sector or investment strategy, the Sharpe ratio provides a measure of risk-adjusted performance that is not accounted for by such affiliations.

The ratio is useful in determining the extent to which excess historical returns were accompanied by excess volatility. While excess return is measured in comparison to an investment benchmark, the standard deviation formula measures volatility based on the variation of returns from their mean.

The usefulness of the ratio rests on the assumption that the historical record of relative risk-adjusted returns has at least some predictive value.

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The Sharpe ratio can be used to evaluate the risk-adjusted performance of a portfolio. Alternatively, an investor can use the fund’s return objective to estimate its expected Sharpe ratio ex-ante.

The Sharpe ratio can help explain whether a portfolio’s excess returns are due to smart investment decisions or simply luck and risk.

For example, low-quality, highly speculative stocks may outperform blue chip stocks for considerable periods of time, as during the dot-com bubble or, more recently, the meme stock craze. If a YouTuber happens to beat Warren Buffett on the market a few times, the Sharpe ratio will provide a quick reality check by adjusting each manager’s performance for the volatility of their portfolios.

The higher the Sharpe ratio of a portfolio, the better its risk-adjusted performance. A negative Sharpe ratio means that the risk-free or benchmark rate of return is greater than the portfolio’s historical or projected return, otherwise the portfolio’s return is expected to be negative.

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The Sharpe ratio can be manipulated by portfolio managers to boost their apparent risk-adjusted return history. This can be done by lengthening the return measurement interval, resulting in an underestimation of volatility. For example, the standard deviation (volatility) of annual returns is generally lower than that of monthly returns, which are less volatile than daily returns. Financial analysts typically consider the volatility of monthly returns when using the Sharpe ratio.

Calculating the Sharpe ratio for the most favorable stretch of performance instead of an objectively chosen look-back period is another way of selecting data that will distort risk-adjusted returns.

The Sharpe ratio also has some inherent limitations. The standard deviation calculation in the denominator of the ratio, which serves as its proxy for portfolio risk, calculates volatility based on a normal distribution and is most useful in evaluating symmetric probability distribution curves. In contrast, financial markets subject to herdsman behavior can move to extremes much more often than a normal distribution is possible. As a result, the standard deviation used to calculate the Sharpe ratio can underestimate tail risk.

Market returns are also subject to serial correlation. The simplest example is that returns in adjacent time intervals can be correlated because they were influenced by the same market trend. But mean reversion also depends on serial correlation like market momentum. The result is that serial correlation leads to lower volatility, and as a result investment strategies relying on serial correlation factors may exhibit deceptively high Sharpe ratios as a result.

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One way to visualize these criticisms is to consider the investment strategy of taking a nickel in front of a steamroller, which moves slowly and predictably almost all the time except for a few rare occasions when it accelerates suddenly and fatally. Is. Because such unfortunate events are extremely uncommon, nickel picks tend to produce positive returns with minimal volatility most of the time, earning high Sharpe ratios as a result. And if the fund taking the proverbial nickel in front of a steamroller goes flat on one of those extremely rare and unfortunate occasions, its long-term sharps can still look good: just one bad month, after all. Unfortunately, this will bring little comfort to the fund’s investors.

The standard deviation in the Sharpe ratio formula assumes that price movements in either direction are equally risky. In fact, the risk of abnormally low returns is very different from the potential for abnormally high returns to most investors and analysts.

A variation of Sharpe, called the Sortino ratio, ignores above-average returns to focus solely on downside divergence as a better proxy for a portfolio’s fund risk.

The standard deviation in the denominator of a Sortino ratio measures the variance of negative returns at or below a chosen benchmark relative to the average of such returns.

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Another variation of the Sharpe is the Treynor ratio, which divides the excess return over the risk-free rate or benchmark by the beta of a security, fund or portfolio as a measure of its systematic risk exposure. Beta measures the degree to which a stock or fund’s volatility is relative to the market as a whole. The goal of the Trainer Ratio is to determine whether an investor is being compensated for the additional risk introduced by the market.

The Sharpe ratio is sometimes used to assess how adding investments may affect a portfolio’s risk-adjusted return.

For example, an investor is considering adding a hedge fund allocation to a portfolio that has returned 18% over the past year. The current risk-free rate is 3%, and the annualized standard deviation of the portfolio’s monthly returns was 12%, giving it a one-year Sharpe ratio of 1.25, or (18 – 3)/12.

The investor believes that adding the hedge fund to the portfolio will reduce the expected return for the coming year by 15%, but also expects the volatility of the portfolio to drop by 8% as a result. The risk free rate is expected to remain the same in the coming year.

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Using the same formula with the estimated future numbers, the investor finds that the portfolio will have an estimated Sharpe ratio of 1.5, or (15% – 3%) divided by 8%.

In this case, while the hedge fund investment is expected to reduce the absolute return of the portfolio, it will improve the portfolio’s performance on a risk-adjusted basis based on its perceived low volatility. If new investment lowers the Sharpe ratio, it would be considered detrimental to the risk-adjusted return based on forecasts. This example assumes that the Sharpe ratio can be compared based on the historical performance of portfolios using the investor’s return and volatility assumptions.

Sharpe ratios above 1 are generally considered “good”, offering excess returns relative to volatility. However, investors often compare the Sharpe ratio of a portfolio or fund to its peers or market sector. So there can be a portfolio with a Sharpe ratio of 1. For example, if most competitors have a ratio above 1.2, a shortage can be found.

To calculate the Sharpe ratio, investors first use the U.S. dollar as a proxy for the risk-free rate of return. Using Treasury bond yields, subtract the risk-free rate from the portfolio’s rate of return. Then, they divide the result by the standard deviation of the portfolio’s excess return.

## What Is Variance In Statistics? Definition, Formula, And Example

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