Semi-Deviation
Semi-deviation is a method of measuring the below-mean fluctuations in the returns on investment. The formula for semi-deviation is: Semi-deviation \= 1 n × ∑ r t < Average n ( Average − r t ) 2 where: n \= the total number of observations below the mean r t \= the observed value \\begin{aligned}&\\text{Semi-deviation}\\ =\\ \\sqrt{\\frac{1}{n}\\ \\times\\ \\sum^n\_{r\_t\\ <\\ \\text{Average}}(\\text{Average}\\ -\\ r\_t)^2}\\\\&\\textbf{where:}\\\\&n\\ =\\ \\text{the total number of observations below the mean}\\\\&r\_t\\ =\\ \\text{the observed value}\\\\&\\text{average}\\ =\\text{the mean or target value of a data set}\\end{aligned} Semi-deviation \= n1 × rt < Average∑n(Average − rt)2where:n \= the total number of observations below the meanrt \= the observed value An investor's entire portfolio could be evaluated according to the semi-deviation in the performance of its assets. Harry Markowitz demonstrated how to exploit the averages, variances, and covariances of the return distributions of assets of a portfolio in order to compute an efficient frontier on which every portfolio achieves the expected return for a given variance or minimizes the variance for a given expected return. Semi-deviation is an alternative to the standard deviation for measuring an asset's degree of risk. In investing, semi-deviation is used to measure the dispersion of an asset's price from an observed mean or target value.
What Is Semi-Deviation?
Semi-deviation is a method of measuring the below-mean fluctuations in the returns on investment.
Semi-deviation will reveal the worst-case performance to be expected from a risky investment.
Semi-deviation is an alternative measurement to standard deviation or variance. However, unlike those measures, semi-deviation looks only at negative price fluctuations. Thus, semi-deviation is most often used to evaluate the downside risk of an investment.
Understanding Semi-Deviation
In investing, semi-deviation is used to measure the dispersion of an asset's price from an observed mean or target value. In this sense, dispersion means the extent of variation from the mean price.
The point of the exercise is to determine the severity of the downside risk of an investment. The asset's semi-deviation number can then be compared to a benchmark number, such as an index, to see if it is more or less risky than other potential investments.
The formula for semi-deviation is:
Semi-deviation = 1 n × ∑ r t < Average n ( Average − r t ) 2 where: n = the total number of observations below the mean r t = the observed value \begin{aligned}&\text{Semi-deviation}\ =\ \sqrt{\frac{1}{n}\ \times\ \sum^n_{r_t\ <\ \text{Average}}(\text{Average}\ -\ r_t)^2}\\&\textbf{where:}\\&n\ =\ \text{the total number of observations below the mean}\\&r_t\ =\ \text{the observed value}\\&\text{average}\ =\text{the mean or target value of a data set}\end{aligned} Semi-deviation = n1 × rt < Average∑n(Average − rt)2where:n = the total number of observations below the meanrt = the observed value
An investor's entire portfolio could be evaluated according to the semi-deviation in the performance of its assets. Put bluntly, this will show the worst-case performance that can be expected from a portfolio, compared to the losses in an index or whatever comparable is selected.
History of Semi-Deviation in Portfolio Theory
Semi-deviation was introduced in the 1950s specifically to help investors manage risky portfolios. Its development is credited to two leaders in modern portfolio theory.
Related terms:
Average Price
Average price is the mean price of an asset or security observed over some period of time. read more
Capital Market Line (CML)
The capital market line (CML) represents portfolios that optimally combine risk and return. read more
Covariance
Covariance is an evaluation of the directional relationship between the returns of two assets. read more
Dispersion
Dispersion is a statistical measure of the expected volatility of a security based on historical returns. read more
Downside Risk
Downside risk is an estimation of a security's potential loss in value if market conditions precipitate a decline in that security's price. read more
Expected Return
The expected return is the amount of profit or loss an investor can anticipate receiving on an investment over time. read more
Incremental Value at Risk
Incremental value at risk is the amount of uncertainty added or subtracted from a portfolio by purchasing a new investment or selling an existing one. read more
Modern Portfolio Theory (MPT)
The modern portfolio theory (MPT) looks at how risk-averse investors can build portfolios to maximize expected return based on a given level of risk. read more
Return on Investment (ROI)
Return on investment (ROI) is a performance measure used to evaluate the efficiency of an investment or compare the efficiency of several investments. read more
Semivariance
Semivariance is a measurement of data that can be used to estimate the potential downside risk of an investment portfolio. Semivariance is calculated by measuring the dispersion of all observations that fall below the mean or target value of a set of data. read more