en>Staszek Lem: /* Relationship with other classes of functions */ well, if it is topical, then don't make topical confusion

2014-01-15T17:31:20Z

Relationship with other classes of functions: well, if it is topical, then don't make topical confusion

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In investing, '''downside beta''' is the element of [[beta (finance)|beta]] that investors associate with [[risk]]. It is defined to be the scaled amount by which an asset moves compared to a benchmark, calculated only on days when the benchmark’s return is negative.<ref name="digest">{{cite web|last=Trent|first=William A.|title=Traditional Beta, Downside Risk Beta, and Market Risk Premiums|url=http://www.cfapubs.org/doi/full/10.2469/dig.v35.n2.1669|work=CFA Digest|publisher=CFA Institute|accessdate=7 January 2014|pages=44–45|doi=10.2469/dig.v35.n2.1669|date=1 May 2005}}</ref>

==Formula==
Downside beta measures [[downside risk]]. The [[CAPM]] can be modified to use semi-variance instead of [[standard deviation]] to measure risk.<ref name="equilcapm">{{cite journal|last=Hogan|first=W.W.|coauthors=Warren, J.M.|title=Toward the development of an equilibrium capital-market model based on semi-variance|journal=Journal of Financial and Quantitative Analysis|year=1977|volume=9|issue=1|pages=1–11}}</ref>

Where <math>r_i</math> and <math>r_m</math> are the excess returns to security <math>i</math> and market <math>m</math>, and <math>u_m</math> is the average market excess return, the CAPM can be modified to incorporate downside (or upside) beta as follows,<ref name="capm">{{cite journal|last=Bawa|first=V.|coauthors=Lindenberg, E.|title=Capital market equilibrium in a mean-lower partial moment framework|journal=Journal of Financial Economics|year=1977|volume=5|pages=189–200}}</ref>

:<math>\beta^-=\frac{cov(r_i,r_m |r_m<u_m)}{var(r_m |r_m<u_m)}</math>

Therefore, <math>\beta^-</math> and <math>\beta^+</math> can be estimated with a regression of excess return of security <math>i</math> on excess return of the market, conditional on excess market return being below the mean for downside beta (or above the mean for [[upside beta]]).<ref name="digest" /> Downside beta is calculated from data points of the asset or portfolio return using only those days when the benchmark return is negative. Downside beta and upside beta are also differentiated in the [[dual-beta]] model.

==Downside Beta vs. Beta==
Downside beta is an effective measure of the risk-return relationship in both developed and growing markets. When companies are grouped according to their two-digit [[United Kingdom Standard Industrial Classification of Economic Activities|SIC]] codes, average downside beta is different from standard [[beta (finance)|beta]] even at the industry average level. Downside market risk can also explain the systematic relative differences in value stocks versus growth stocks, which the CAPM has failed to do, especially in international markets.<ref name=vox>{{cite web|last=Galsband|first=Victoria|title=Downside risk and the value anomaly|url=http://www.voxeu.org/article/downside-risk-and-value-anomaly|work=VoxEU.org|publisher=VOX|accessdate=7 January 2014|date=16 October 2012}}</ref>

Downside beta has greater explanatory power than standard [[beta (finance)|beta]] in bearish markets.<ref name="digest" /><ref name="Mean-semivariance behavior">{{cite journal|last=Estrada|title=Mean-semivariance behavior: Downside risk and capital asset pricing|journal=International Review of Economics and Finance|year=2007|volume=16|page=169}} Estrada computed standard betas and downside betas for stocks across 23 developed markets and 27 emerging markets. This research showed that downside beta did a better job of explaining variations of cross-section returns in both types of market than did standard beta. In emerging markets, downside beta explained 55% of variations in mean returns.</ref> Portfolios that are constructed by minimizing downside beta may be able to maintain more of their value during times of market decline.

==See also==
*[[Beta (finance)|Beta]]
*[[Capital asset pricing model]]
*[[Downside risk]]
*[[Dual-beta]]
*[[Financial risk]]
*[[Upside beta]]

==References==
{{Reflist}}

==External links==
*[http://www.raymondjames.com/branches/c2c/34n/vip/wealth.htm Raymond James - Financial Planning Introduction]
*[http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2241416 An Investigation of Beta and Downside Beta Based CAPM - Case Study of Karachi Stock Exchange], SSRN. M. Tahir, Q. Abbas, S.M. Sargana, U. Ayub and S.K. Saeed; February 2013

{{DEFAULTSORT:Downside beta}}
[[Category:Jargon]]
[[Category:Finance|Terminology, Financial]]

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en>Staszek Lem: /* Relationship with other classes of functions */ well, if it is topical, then don't make topical confusion