Thank you Paul for your contribution to this discussion. This example you have drawn is very valuable - to be honest until now I have been using discrete rates in all my calculations, which now seems to me as very tricky. Since - as far as I am concerned - AB calculates all performance metrics basing on arithmetic values, it would be advisable to prepere my own measures through CBT.
--- In [email protected], "paultsho" <paul.t...@...> wrote: > > > > There is also an article on your reference site on MaxDd > http://www.intelligenthedgefundinvesting.com/ch06.html. In fact, there were > other performance measures for you to consider. while I'll need sometime to > look at the AIRAP more closely. I think it is important to point out that it > is just as important to understand how different ways of applying your data > to generate statistical fitness can affect your final answer just as much as > choosing different fitness functions. For example, consider the follwoing > Rate of return calculation: > Period : Discrete Rate Continuously compounded > 1 100% 0.693 =log(1+1) > 2 -50% -0.693 =log(1-0.5) > Avg 0.25 0 > As we can see the arithmetic average, or the mean of the discrete rates of > return, is plus 25% per period. Yet the investment has simply doubled and > then halved to return to its original value at time 0. > > --- In [email protected], "tf28373" <tomfid@> wrote: > > > > > > Hello everyone > > > > I have been working on the choose of fitness function following the > > Howard Bundy's advices in his "Quantitative Trading Systems" and come > > across M. Sharma's Alternative Investments Risk Adjusted Performance > > (AIRAP). > > > > The equation of it is as following: > > > > AIRAP = [ E pi*(1+TRi)(1-c) ] 1/(1-c) - 1, > > > > where TRi - ith period total fund return (in my opinon it can also be > > ith trade net return), c - risk aversion parameter (author suggests to > > set its value to c=4), i=1,...,N - number of periods (as for me it can > > be number of trades), pi - the probability of the ith period's total > > return (according to the author it can be replaced with 1/N). (For > > futher information please check this working paper: > > http://www.intelligenthedgefundinvesting.com/pubs/rb-ms01.pdf > > <http://www.intelligenthedgefundinvesting.com/pubs/rb-ms01.pdf> .) > > > > M. Sharma argues that this measure captures all higher moments, > > penalizes for higher volatility and leverage (downside risk is penalized > > more) and has all merits of Sharp ratio, though without its limitations > > and disadvantages. I have carried out some simulations on the artificial > > returns of different distributions and indeed it makes some difference. > > Nevertheless what I am suspicious about is the fact that it was the very > > first time I found this objective function even though it was created by > > Sharma about 5 years ago. As for me it can mean that AIRAP is in fact > > far from being effective or/and practical fitness measure at least for > > trader like us and nobody use it (maybe I am wrong...). Another issue > > that concerns me a bit is omission of MaxDrawDown in the equation, which > > - at least for me - is a very important risk measure. According to many > > experienced wise people writing on this forum (like ex Mr Bundy), an > > effective fitness function shouls take Max DD or some comparable risk > > measure into consideration in order to be really useful. > > > > What do you think about AIRAP? Should I proceed with utilizing this > > function? > > > > I am looking forward to your response. Thank you in advance. > > > > Tomasz > > >
