- UID
- 223351
- 帖子
- 237
- 主题
- 49
- 注册时间
- 2011-7-11
- 最后登录
- 2013-10-21
|
5#
发表于 2011-10-5 12:38
| 只看该作者
Omega's okay. It's like the ratio of the positive CVaR at x% divided by the negative CvaR at x%. Not directly comparable to Sharpe, but better in many ways. I would prefer excess return over Mixed Conditional Deviation at Risk (I am going to name this ratio). Mixed CDaR is basically a weighted average of CDaR ( basically if you have CVaR(X), CDaR=CVaR(X-E(X)) ). It's more comparable to standard deviation and has the good property that it can't ever change signs.
If you're dealing with a distribution that's N(10%,10%) the CVaR at 95% is negative, but then if N(10%,1%) it has to be positive since you are unlikely to experience a decline. It's difficult to deal with a ratio when the denominator can turn negative or positive. Similarly, if you're optimizing omega or projecting it out, then it is possible that the bottom part of the ratio can switch from negative to positive, making the ratio go to infinity. The bottom part of the ratio needs to be a deviation measure and not a risk measure, otherwise you have problems. |
|