The Sharpe ratio compares the return of an investment with its risk. It's a mathematical expression of the insight that excess returns over a period of time may signify more volatility and risk, rather than investing skill. 1
Economist William F. Sharpe proposed the Sharpe ratio in 1966 as an outgrowth of his work on the capital asset pricing model (CAPM), calling it the reward-to-variability ratio.
Sharpe won the Nobel Prize in economics for his work on CAPM in 1990.
The Sharpe ratio's numerator is the difference over time between realized, or expected, returns and a benchmark such as the risk-free rate of return or the performance of a particular investment category. Its denominator is the standard deviation of returns over the same period of time, a measure of volatility and risk.
The expense ratio measures how much of a fund's assets are used for administrative and other operating expenses. For investors, the expense ratio is deducted from the fund's gross return and paid to the fund manager.
An expense ratio is determined by dividing a fund's operating expenses by the average dollar value of its assets under management (AUM). Operating expenses reduce the fund's assets, thereby reducing the return to investors.
Operating expenses vary according to the fund or stock; however, the expenses within the fund remain relatively stable. For example, a fund with low expenses will generally continue to have low expenses. The largest component of operating expenses is the fee paid to a fund's investment manager or advisor.
Other costs include recordkeeping, custodial services, taxes, legal expenses, and accounting and auditing fees. Expenses that are charged by the fund are reflected in the fund's daily net asset value (NAV) and do not appear as a distinct charge to shareholders.
The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative portfolio returns—downside deviation—instead of the total standard deviation of portfolio returns. The Sortino ratio takes an asset or portfolio's return and subtracts the risk-free rate, and then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.
The Sortino ratio is a useful way for investors, analysts, and portfolio managers to evaluate an investment's return for a given level of bad risk. Since this ratio uses only the downside deviation as its risk measure, it addresses the problem of using total risk, or standard deviation, which is important because upside volatility is beneficial to investors and isn't a factor most investors worry about.
Alpha (α) is a term used in investing to describe an investment strategy's ability to beat the market, or its "edge." Alpha is thus also often referred to as “excess return” or “abnormal rate of return,” which refers to the idea that markets are efficient, and so there is no way to systematically earn returns that exceed the broad market as a whole. Alpha is often used in conjunction with beta (the Greek letter β), which measures the broad market's overall volatility or risk, known as systematic market risk.
Alpha is used in finance as a measure of performance, indicating when a strategy, trader, or portfolio manager has managed to beat the market return over some period. Alpha, often considered the active return on an investment, gauges the performance of an investment against a market index or benchmark that is considered to represent the market’s movement as a whole.
The excess return of an investment relative to the return of a benchmark index is the investment’s alpha. Alpha may be positive or negative and is the result of active investing. Beta, on the other hand, can be earned through passive index investing.
A stock that swings more than the market over time has a beta greater than 1.0. If a stock moves less than the market, the stock's beta is less than 1.0. High-beta stocks tend to be riskier but provide the potential for higher returns. Low-beta stocks pose less risk but typically yield lower returns.
As a result, beta is often used as a risk-reward measure, meaning it helps investors determine how much risk they are willing to take to achieve the return for taking on that risk. A stock's price variability is important to consider when assessing risk. If you think of risk as the possibility of a stock losing its value, beta is useful as a proxy for risk.
Covariance measures how two stocks move together. A positive covariance means the stocks tend to move together when their prices go up or down. A negative covariance means the stocks move opposite of each other.
Variance, on the other hand, refers to how far a stock moves relative to its mean. For example, variance is used in measuring the volatility of an individual stock's price over time. Covariance is used to measure the correlation in price moves of two different stocks.
The formula for calculating beta is the covariance of the return of an asset with the return of the benchmark, divided by the variance of the return of the benchmark over a certain period.
Standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance. The standard deviation is calculated as the square root of variance by determining each data point's deviation relative to the mean.
If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation. Standard deviation is a statistical measurement in finance that, when applied to the annual rate of return of an investment, sheds light on that investment's historical volatility.
The greater the standard deviation of securities, the greater the variance between each price and the mean, which shows a larger price range. For example, a volatile stock has a high standard deviation, while the deviation of a stable blue-chip stock is usually rather low.
R-squared (R2) is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. Whereas correlation explains the strength of the relationship between an independent and dependent variable, R-squared explains to what extent the variance of one variable explains the variance of the second variable. So, if the R2 of a model is 0.50, then approximately half of the observed variation can be explained by the model's inputs.
The actual calculation of R-squared requires several steps. This includes taking the data points (observations) of dependent and independent variables and finding the line of best fit, often from a regression model. From there you would calculate predicted values, subtract actual values and square the results. This yields a list of errors squared, which is then summed and equals the unexplained variance.
To calculate the total variance, you would subtract the average actual value from each of the actual values, square the results and sum them. From there, divide the first sum of errors (unexplained variance) by the second sum (total variance), subtract the result from one, and you have the R-squared.
In investing, R-squared is generally interpreted as the percentage of a fund or security's movements that can be explained by movements in a benchmark index. For example, an R-squared for a fixed-income security versus a bond index identifies the security's proportion of price movement that is predictable based on a price movement of the index.