# Analytics

#### Alpha:

A measure of the difference between a fund’s actual returns and its expected performance, given its level of risk as measured by beta. A positive alpha figure indicates the fund has performed better than its beta would predict. In contrast, a negative alpha indicates the fund’s underperformance, given the expectations established by the fund’s beta. All MPT statistics (alpha, beta, and R-squared) are based on a least-squares regression of the fund’s return over Treasury bills (called excess return) and the excess returns of the fund’s benchmark index. Alpha can be used to directly measure the value added or subtracted by a fund’s manager. Alpha depends on two factors: 1) the assumption that market risk, as measured by beta, is the only risk measure necessary 2) the strength of the linear relationship between the fund and the index, as it has been measured by R-squared. In addition, a negative alpha can sometimes result from the expenses that are present in a fund’s returns, but not in the returns of the comparison index. Example: A fund has an alpha of 0.86, a beta of 0.96 and an R-squared of 97. The high R-squared lends further credibility to the accuracy of the fund’s alpha and beta. The alpha of 0.86 indicates that the fund produced a return 0.86% higher than its beta would predict.

#### Beta:

A measure of a fund’s sensitivity to market movements. The beta of the market is 1.00 by definition. Morningstar calculates beta by comparing a fund’s excess return over Treasury bills to the market’s excess return over Treasury bills, so a beta of 1.10 shows that the fund has performed 10% better than its benchmark index in up markets and 10% worse in down markets, assuming all other factors remain constant. Conversely, a beta of 0.85 indicates that the fund’s excess return is expected to perform 15% worse than the market’s excess return during up markets and 15% better during down markets. Beta can be a useful tool when at least some of a fund’s performance history can be explained by the market as a whole. Beta is particularly appropriate when used to measure the risk of a combined portfolio of mutual funds. It is important to note that a low beta for a fund does not necessarily imply that the fund has a low level of volatility. A low beta signifies only that the fund’s market-related risk is low. (Standard deviation is a measure of a fund’s absolute volatility.) A specialty fund that invests primarily in gold, for example, will usually have a low beta, as its performance is tied more closely to the price of gold and gold-mining stocks than to the overall stock market. Thus, the specialty fund might fluctuate wildly because of rapid changes in gold prices, but its beta will remain low. R-squared is a necessary statistic to factor into the equation, because it reflects the percentage of a fund’s movements that are explained by movements in its benchmark index. Example: A fund has an alpha of 0.86, a beta of 0.96, and an R-squared of 97. The high R-squared lends further credibility to the accuracy of the fund’s alpha and beta. The beta of 0.96 indicates the fund’s performance is very close to that of the market, which would be represented by 1.00.

#### Compounded Annual Return:

The compound return is the rate of return, usually expressed as a percentage, that represents the cumulative effect that a series of gains or losses have on an original amount of capital over a period of time. Compound returns are usually expressed in annual terms, meaning that the percentage number that is reported represents the annualized rate at which capital has compounded over time.

#### Correlation Coefficient:

The correlation coefficient is a measure that determines the degree to which two variables’ movements are associated. The range of values for the correlation coefficient is -1.0 to 1.0. If a calculated correlation is greater than 1.0 or less than -1.0, a mistake has been made. A correlation of -1.0 indicates a perfect negative correlation, while a correlation of 1.0 indicates a perfect positive correlation.

#### Cumulative Return:

The aggregate amount that an investment has gained or lost over time, independent of the period of time involved. Presented as a percentage, the cumulative return is the raw mathematical return of the following calculation:

#### Downside Deviation:

Downside deviation is a measure of downside risk that focuses on returns that fall below a minimum threshold or minimum acceptable return (MAR). It is used in the calculation of a risk measure known as the Sortino Ratio.

Standard deviation, the most widely used measure of investment risk, has some limitations, such as the fact that it treats all deviations from the average – whether positive or negative – as the same. However, investors are generally more concerned with negative divergences than positive ones, i.e. downside risk is a bigger concern. Downside deviation resolves this issue by focusing only on downside risk.

Another advantage over standard deviation is that downside deviation can also be tailored to the specific objectives and risk profile of different investors who have various levels of minimum acceptable return.

#### Maximum Drawdown:

A maximum drawdown (MDD) is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown (MDD) is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as “Return over Maximum Drawdown” and Calmar Ratio.

#### R-squared:

R-squared is a statistical measure that represents the percentage of a fund or security’s movements that can be explained by movements in a benchmark index. For fixed-income securities, the benchmark is the T-bill. For equities, the benchmark is the S&P 500.

#### Sharpe Ratio:

The Sharpe Ratio is a measure for calculating risk-adjusted return, and this ratio has become the industry standard for such calculations. It was developed by Nobel laureate William F. Sharpe. The Sharpe ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return, the performance associated with risk-taking activities can be isolated. One intuition of this calculation is that a portfolio engaging in “zero risk” investment, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.

#### Sortino Ratio:

A modification of the Sharpe ratio that differentiates harmful volatility from general volatility by taking into account the standard deviation of negative asset returns, called downside deviation. The Sortino ratio subtracts the risk-free rate of return from the portfolio’s return, and then divides that by the downside deviation. A large Sortino ratio indicates there is a low probability of a large loss.

#### Standard Deviation:

Standard deviation is a measure of the dispersion of a set of data from its mean. The more spread apart the data, the higher the deviation. Standard deviation is calculated as the square root of variance.

In finance, standard deviation is applied to the annual rate of return of an investment to measure the investment’s volatility. Standard deviation is also known as historical volatility and is used by investors as a gauge for the amount of expected volatility.

Standard deviation is a statistical measurement that sheds light on historical volatility. For example, a volatile stock will have a high standard deviation while the deviation of a stable blue chip stock will be lower. A large dispersion tells us how much the return on the fund is deviating from the expected normal returns.

Sources: Morningstar, Investopedia