Nearly all real-world problems encountered in such diverse areas as finance, engineering, defence, and economics are associated with a certain level of risk. This demands that risk be quantified to aid in decision-making and to also enable stakeholders to come to terms with what they are getting themselves into. Some of the measures developed to quantify risks in portfolio selection include variance and semi-variance. Variance is a measure of risk linked to return on investment based on the mean-variance of return of such an investment. However, this model is limited in that it cannot compute the skewed investment return distribution evident in real-life situations (Estrada 2007). This prompted the development of the semi-variance.
Semi-variance is amongst the most popular measure of downside risk on account of its being clear, relatively simple, and direct in reflecting an investor's premonition about risk (Knight & Satchell 2002). Semi-variance as a tool to compute downward volatility blends in with the assumption that there is a link between risk is linked to the inability to attain a below-target or target outcome. According to Dreman (2008) 'Semi-variance measures the performance of your portfolio only in a down market or in down quarters, to see how it holds up relative to the market' (p. 303).
Semi-variance hinges on the assumption that investors derive joy from beating the market as it rises, but wish to see experience a fall in their portfolio below the average in a bear market. Semi-variance, therefore, assesses the downside risk. It is only concerned with the negative fluctuations in the value of an asset. Semi-variance forecasts the average loss that an investor is likely to incur over a given portfolio. A reduction in semi-variance would thus enable risk-averse investors to minimise the possibility of a large loss.
Dreman, D (2008), Contrarian Investment Strategies: the Next Generation, New York: Simon & Schuster.
Estrada, J.T. (2007),' Mean-semivariance behavior: Downside risk and capital asset pricing', International Review of Economics and Finance, vol. 16, pp. 169-185.
Ibrahim, T (2007),'Can the normality of the semi-variance be improved? Evidence from financial stock indexes with hourly, daily, quarterly and annual data of DJIA and SP500 eldomiaty', Applied Econometrics and International Development, vol. 7, no. 2, pp. 96-120. Knight, J.L., & Satchell, S (2002), Forecasting Volatility in the Financial Markets, Oxford: Butterworth-Heinemann.