# Sharpe ratio

**risk-adjusted returnrisk adjusted returnSharpe diagonal (or index) modelSharpe type ratio**

In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) measures the performance of an investment (e.g., a security or portfolio) compared to a risk-free asset, after adjusting for its risk.wikipedia

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### William F. Sharpe

**William SharpeBill SharpeSharpe, William Forsyth**

It was named after William F. Sharpe, who developed it in 1966.

He created the Sharpe ratio for risk-adjusted investment performance analysis, and he contributed to the development of the binomial method for the valuation of options, the gradient method for asset allocation optimization, and returns-based style analysis for evaluating the style and performance of investment funds.

### Information ratio

The information ratio is similar to the Sharpe ratio, the main difference being that the Sharpe ratio uses a risk-free return as benchmark whereas the information ratio uses a risky index as benchmark (such as the S&P500).

The information ratio is similar to the Sharpe ratio, the main difference being that the Sharpe ratio uses a risk-free return as benchmark (such as a U.S. Treasury security) whereas the information ratio uses a risky index as benchmark (such as the S&P500).

### Treynor ratio

**Treynor measure**

Sharpe ratios, along with Treynor ratios and Jensen's alphas, are often used to rank the performance of portfolio or mutual fund managers.

Like the Sharpe ratio, the Treynor ratio (T) does not quantify the value added, if any, of active portfolio management.

### Risk-free interest rate

**risk-free raterisk free raterisk-free asset**

In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) measures the performance of an investment (e.g., a security or portfolio) compared to a risk-free asset, after adjusting for its risk. It is defined as the difference between the returns of the investment and the risk-free return, divided by the standard deviation of the investment (i.e., its volatility). where R_a is the asset return, R_b is the risk-free return (such as a U.S. Treasury security).

The risk-free rate is also a required input in financial calculations, such as the Black–Scholes formula for pricing stock options and the Sharpe ratio.

### Bias ratio

**Bias ratio (finance)**

Other ratios such as the bias ratio have recently been introduced into the literature to handle cases where the observed volatility may be an especially poor proxy for the risk inherent in a time-series of observed returns.

Your peer group consists of funds with similar mandates, and all have track records with high Sharpe ratios, very few down months, and investor demand from the "[one per cent per month]" crowd.

### Sortino ratio

Roy's ratio is also related to the Sortino ratio, which also uses MAR in the numerator, but uses a different standard deviation (semi/downside deviation) in the denominator.

It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally.

### Alpha (finance)

**alphaexcess returnoutperform market averages**

We typically do not know if the asset will have this return; suppose we assess the risk of the asset, defined as standard deviation of the asset's excess return, as 10%.

Alpha, along with beta, is one of two key coefficients in the capital asset pricing model used in modern portfolio theory and is closely related to other important quantities such as standard deviation, R-squared and the Sharpe ratio.

### Modigliani risk-adjusted performance

This weakness was well addressed by the development of the Modigliani risk-adjusted performance measure, which is in units of percent return – universally understandable by virtually all investors.

It is derived from the widely used Sharpe ratio, but it has the significant advantage of being in units of percent return (as opposed to the Sharpe ratio – an abstract, dimensionless ratio of limited utility to most investors), which makes it dramatically more intuitive to interpret.

### Jensen's alpha

**alphaJensen**

Sharpe ratios, along with Treynor ratios and Jensen's alphas, are often used to rank the performance of portfolio or mutual fund managers.

Nevertheless, Alpha is still widely used to evaluate mutual fund and portfolio manager performance, often in conjunction with the Sharpe ratio and the Treynor ratio.

### Omega ratio

The ratio is an alternative for the widely used Sharpe ratio and is based on information the Sharpe ratio discards.

### Modern portfolio theory

**portfolio theoryportfolio analysismean-variance**

It is tangent to the hyperbola at the pure risky portfolio with the highest Sharpe ratio.

### V2 ratio

The goal of the V2 ratio is to improve on existing and popular measures of risk-adjusted return, such as the Sharpe ratio, information ratio or Sterling ratio by taking into account the psychological impact of investment performances.

### Calmar ratio

Later versions of the Calmar ratio introduce the risk free rate into the numerator to create a Sharpe type ratio.

### Hansen–Jagannathan bound

**Hansen-Jagannathan boundHansen-Jagannathan bounds**

Hansen–Jagannathan bound is a theorem in financial economics that says that the ratio of the standard deviation of a stochastic discount factor to its mean exceeds the Sharpe ratio attained by any portfolio.

### Sterling ratio

This version of the Sterling ratio may be adjusted to something more like a Sharpe ratio as follows:

### Roy's safety-first criterion

The Sharpe ratio is defined as excess return per unit of risk, or in other words:

### Risk-adjusted return on capital

**RAROCRisk adjusted return on capitalrisk-adjusted return**

### Finance

**financialfinancesfiscal**

In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) measures the performance of an investment (e.g., a security or portfolio) compared to a risk-free asset, after adjusting for its risk.

### Risk

**risksdangerrisk-taking**

In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) measures the performance of an investment (e.g., a security or portfolio) compared to a risk-free asset, after adjusting for its risk.

### Standard deviation

**standard deviationssample standard deviationSD**

It is defined as the difference between the returns of the investment and the risk-free return, divided by the standard deviation of the investment (i.e., its volatility).

### 1966

**other events of 1966the year in which it was founded**

It was named after William F. Sharpe, who developed it in 1966.

### Ex-ante

**ex antebefore the eventexante**

Since its revision by the original author, William Sharpe, in 1994, the ex-ante Sharpe ratio is defined as:

### United States Treasury security

**Treasury billsTreasury securitiesTreasury bond**

where R_a is the asset return, R_b is the risk-free return (such as a U.S. Treasury security).