A Brief History of Downside Risk Measures

International portfolio diversification: Is there a role for the Middle East and North Africa?

“…The popularity of these risk measures is explained by Nawrocki (1999) who points out that investors are interested in minimizing downside risk, since that is what is relevant to them. Further justification is given in Harvey (2000) and Estrada (2000Estrada ( , 2002 who support the idea that downside risk measures matter for studying emerging market equity indices.…”

The effect of downside risk reduction on UK equity portfolios included with Managed Futures Funds

“…Lower Partial Moment and the relation to Value-at-risk Nawrocki (1999) observed that the research and subsequent development of downside risk measures and Lower Partial Moment (LPM) progressed greatly following the published work of Bawa (1975) and Fishburn (1977). The LPM describes below-target risk in terms of risk tolerance.…”

“…Max indicates that the formula will square the greater of the two values, 0, or (t -R T ). Nawrocki (1999) and Harlow (1991) discussed the development and research of both below target and below means semi-variances and found one of the most enduring and related ideas involves focusing on the tail of the relevant distribution of returns, i.e., the returns below some specific threshold level or target rate. Risk measures of this type are referred to as "Lower Partial Moments" (LPM) because only the left-hand tail (i.e., probability of under-achieving a threshold return) of the return distribution is used in calculating risk.…”

“…According to Nawrocki (1999), Markowitz (1959) provides two suggestions for measuring downside risk: a semi-variance computed from the mean return or below-mean semi variance (SVm) (shown by equation (1) as follows) and a semi variance computed from a target return or below-target semi variance (SVt) (shown by 2 However, due to the complexity and the costs involved in the computation of semi-variance analyses, Markowitz (1959) chose not to pursue this line of inquiry. He rejected the semi-variance as the referred risk measure and concentrated instead on his now famous mean-variance approach to portfolio theory.…”

Investment Characteristics of Natural Monopoly Companies

“…Both measures compute a variance using only the returns below the mean return (SVm) or below a target return (SVt). Markowitz called these measures partial or semi-variances, because only a subset of the return distribution is used (see Nawrocki, 1999).…”