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Downside risk is the
financial risk Financial risk is any of various types of risk associated with financing, including financial transactions that include company loans in risk of default. Often it is understood to include only downside risk, meaning the potential for financia ...
associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. Risk measures typically quantify the downside risk, whereas the
standard deviation In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, whil ...
(an example of a
deviation risk measure In financial mathematics, a deviation risk measure is a function to quantify financial risk (and not necessarily downside risk) in a different method than a general risk measure. Deviation risk measures generalize the concept of standard deviation. ...
) measures both the upside and downside risk. Specifically, downside risk can be measured either with downside beta or by measuring lower semi-deviation. The statistic ''below-target semi-deviation'' or simply ''target semi-deviation'' (TSV) has become the industry standard.


History

Downside risk was first modeled by Roy (1952), who assumed that an investor's goal was to minimize his/her risk. This mean-semivariance, or downside risk, model is also known as “safety-first” technique, and only looks at the lower standard deviations of expected returns which are the potential losses. This is about the same time
Harry Markowitz Harry Max Markowitz (born August 24, 1927) is an American economist who received the 1989 John von Neumann Theory Prize and the 1990 Nobel Memorial Prize in Economic Sciences. Markowitz is a professor of finance at the Rady School of Management ...
was developing mean-variance theory. Even Markowitz, himself, stated that "semi-variance is the more plausible measure of risk" than his mean-variance theory. Later in 1970, several focus groups were performed where executives from eight industries were asked about their definition of risk resulting in semi-variance being a better indicator than ordinary variance. Then, through a theoretical analysis of capital market values, Hogan and Warren demonstrated that 'the fundamental structure of the "capital-asset pricing model is retained when standard semideviation is substituted for standard deviation to measure portfolio risk."' This shows that the CAPM can be modified by incorporating downside beta, which measures downside risk, in place of regular
beta Beta (, ; uppercase , lowercase , or cursive ; grc, βῆτα, bē̂ta or ell, βήτα, víta) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Modern Greek, it represents the voiced labi ...
to correctly reflect what people perceive as risk. Since the early 1980s, when Dr. Frank Sortino developed formal definition of downside risk as a better measure of investment risk than standard deviation, downside risk has become the industry standard for risk management.


Downside risk vs. capital asset pricing model

It is important to distinguish between downside and upside risk because security distributions are non-normal and non-symmetrical. This is in contrast to what the
capital asset pricing model In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio. The model takes into accou ...
(CAPM) assumes: that security distributions are symmetrical, and thus that downside and upside betas for an asset are the same. Since investment returns tend to have a non-normal distribution, however, there in fact tend to be different probabilities for losses than for gains. The probability of losses is reflected in the downside risk of an investment, or the lower portion of the distribution of returns. The CAPM, however, includes both halves of a
distribution Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations *Probability distribution, the probability of a particular value or value range of a varia ...
in its calculation of risk. Because of this it has been argued that it is crucial to not simply rely upon the CAPM, but rather to distinguish between the downside risk, which is the risk concerning the extent of losses, and upside risk, or risk concerning the extent of gains. Studies indicate that "around two-thirds of the time standard beta would underestimate the downside risk."


Examples

* ''
Value at Risk Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by ...
'' * '' Average value at risk'' * The ''
semivariance In spatial statistics the theoretical variogram 2\gamma(\mathbf_1,\mathbf_2) is a function describing the degree of spatial dependence of a spatial random field or stochastic process Z(\mathbf). The semivariogram \gamma(\mathbf_1,\mathbf_2) is hal ...
'' is defined as the expected squared deviation from the mean, calculated over those points that are no greater than the mean. Its square root is the ''semi-deviation'': : SD(X) = \left(\mathbb X_-_\mathbb[X^2_1_.html" ;"title=".html" ;"title="X - \mathbb[X">X - \mathbb[X^2 1_">.html" ;"title="X - \mathbb[X">X - \mathbb[X^2 1_right)^ : where 1_ is an indicator function, i.e. 1_ = \begin1 & \text X \leq \mathbb[X]\\ 0 & \text\end * ''Below target semi-deviation'' for target t defined by : TSV(X,t) = \left(\mathbb[(X - t)^2 1_]\right)^.


See also

* * *


References


External links


Preparing for the Worst: Incorporating Downside Risk in Stock Market Investments
1st Edition. {{ISBN, 9780471234425 Financial risk modeling