324:
179:
358:
163:
96:
69:
378:
136:
116:
319:{\displaystyle \beta ^{-}={\frac {\operatorname {Cov} (r_{i},r_{m}\mid r_{m}<u_{m})}{\operatorname {Var} (r_{m}\mid r_{m}<u_{m})}},}
577:
Hogan, W.W.; Warren, J.M. (1977). "Toward the development of an equilibrium capital-market model based on semi-variance".
626:
404:(CAPM) can be modified to work with dual betas. Other researchers have attempted to use semi-variance instead of
29:
401:
550:
Bawa, V.; Lindenberg, E. (1977). "Capital market equilibrium in a mean-lower partial moment framework".
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512:
336:
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in bearish markets. As such, it would have been a better measure of risk than ordinary beta.
141:
74:
47:
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on the excess return of the market, conditional on (excess) market return being negative.
8:
473:
166:
28:) only on days when the market’s return is negative. Downside beta was first proposed by
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is given by this expression with the direction of the inequalities reversed. Therefore,
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Downside beta was once hypothesized to have greater explanatory power than standard
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33:
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426:
513:"Conditional risk premia in currency markets and other asset classes"
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442:
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can be estimated with a regression of the excess return of security
170:
24:
that measures a stock's association with the overall stock market (
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Lettau, Martin; Maggiori, Matteo; Weber, Michael (2014-11-01).
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as the average market excess return, and Cov and Var as the
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Ang, Andrew; Chen, Joseph; Xing, Yuhang (2006-12-01).
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77:
50:
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618:
579:Journal of Financial and Quantitative Analysis
32:and then popularized in an investment book by
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427:"Safety First and the Holding of Assets"
396:Use in Equilibrium Models of Risk-Reward
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13:
98:as the excess returns to security
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478:The Review of Financial Studies
552:Journal of Financial Economics
517:Journal of Financial Economics
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205:
1:
529:10.1016/j.jfineco.2014.07.001
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564:10.1016/0304-405x(77)90017-4
173:operators, Downside beta is
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402:Capital asset pricing model
10:
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353:{\displaystyle \beta ^{-}}
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44:It is common to measure
627:Financial risk modeling
384:Downside beta vs. beta
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159:
132:
112:
92:
65:
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321:
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158:{\displaystyle u_{m}}
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91:{\displaystyle r_{m}}
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64:{\displaystyle r_{i}}
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425:Roy, A. D. (1952).
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408:to measure risk.
406:standard deviation
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88:
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373:{\displaystyle i}
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131:{\displaystyle m}
111:{\displaystyle i}
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632:Finance theories
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484:(4): 1191–1239.
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34:Markowitz (1959)
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591:10.2307/2329964
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474:"Downside Risk"
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443:10.2307/1907413
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118:and the market
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558:(2): 189–200.
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523:(2): 197–225.
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437:(3): 431–449.
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16:In investing,
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18:downside beta
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431:Econometrica
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43:
17:
15:
585:(1): 1–11.
331:upside beta
621:Categories
412:References
167:covariance
607:153337865
537:0304-405X
498:0893-9454
451:0012-9682
346:−
342:β
282:∣
266:
232:∣
203:
189:−
185:β
171:variance
30:Roy 1952
599:2329964
459:1907413
40:Formula
20:is the
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496:
457:
449:
329:while
603:S2CID
595:JSTOR
455:JSTOR
533:ISSN
494:ISSN
447:ISSN
400:The
390:beta
295:<
245:<
169:and
71:and
26:risk
22:beta
587:doi
560:doi
525:doi
521:114
486:doi
439:doi
263:Var
200:Cov
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601:.
593:.
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519:.
515:.
492:.
482:19
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476:.
453:.
445:.
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609:.
589::
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562::
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539:.
527::
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441::
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269:(
258:)
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219:,
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210:r
206:(
194:=
151:m
147:u
126:m
106:i
84:m
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53:r
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