Hello,I'm doing a research on assymetric beta (downside beta and upside beta). I wanted to know what are your opinion on this? Do you beleive it is interesting to implement in a portfolio strategy?Thanks for sharing your opinion/ideas!Best regards.

Hi RolandograndiI have done some work on this and there are a couple of issues / problems. Firstly in principle one might want to maximise your portfolio's upside beta, minimise your downside beta and have close to a zero correlation to some benchmark. The main problem here is that because of the asymmetry of the individual up and down beta's there is no one common location point or global mode = global mean as in the case of a multi-variate normal distribution. Rather there is an unknown joint distribution coupling your individual marginal densities together. You therefore either have to fit or assume some joint density or set the global mean to an arbitrary value like 0 that may not be the point of best fit in terms of maximising the rsquareds for the up and down regression lines and betas. There are also sign change issues relating to your benchmark. Two approaches that seem to work are 1) Making your benchmark relative to which your are optimising the above parameters = the portfolio pnl 2) similar to 1) working with just excess returns relative to your benchmark. Obviously this all works for the in-sample period only and out-of-sample next period performance will vary. In essence very similar to a 2 regime state Markov Model or mixture of normals approach. In practice I have found that trying to minimise your downside whilst maximising your upside tends to lead to some shrinkage and diminution of overall performance - I believe you are better off finding those co-skewnesses that amplify your 'good' / upside volatility.Kind regards,Peter U