quants - positive skewnwss

Hi

while I was going through summaries and EOC questions. I noticed that :

In summaries (p-411)it says, " Positive skewness has frequesnt small losses and few extreme gains".

In EOC Q no. 16,(p- 433)solution says, “positive skew indiacting higher freq of very large positive returns”

I am confused with the frequency party, ie in positive skewness are thr freq losses or gains??

freq losses - this is just a edumucated guess but if you look at the curve, the fast bulk of it would be over to the left side…

per p.411, “positive skewness has frequent small losses and few extreme gains”-- that is accurate. this is a comparison between the frequenccy of large gains and small losses WITHIN A SINGLE PORTFOLIO. the “higher freq of very large positive returns” on p.433 compares the large gains of portfolio B to those of portfolio A (i.e comparison of the large gains BETWEEN TWO PORTFOLIOS). consider portfolio A: it has neg skew, which implies freq small gains and few large losses (within port A only). now consider port B: it has positive skew, which implies small freq losses and few large gains (within port B only). Therefore port B has higher freq of large gains than port A does. let me know if you get it.

also - not sure if this is ‘technically’ correct but if you interpret it this way, the mean is essentially what you’re after, everything else you get is a deviation, whether its a positive or negative deviation, it doesn’t matter. So if you look at the positive skewed graph --> you’ll find that the mean is at the front, the median in the middle and the mode bringing up the rear which means you’ll have alot of losses when compared to the mean.

bbcman - you should not use only the mean because the standard deviation matters a lot. even more so in this case cuz the means are equal. that is the whole idea of risk-adjusted returns. for example if portfolio A has 10% returns and std dev of 30%, it will probably not be chosen by most managers over portfolio B, which has returns of 9% and std dev of 5%. this is because the extra 1% return of port A is way too risky.

Wow i got it!! after reading 4 times…;), Thanks ebowsaah and bbcman.

thanks - i didn’t actually read the question but rather was just going off what he was asking. I suppose its just a matter of the sharpe ratio/CV of returns then.

welcome, and goodluck on your studies/exams.