# High values of skewness and kurtosis of realized protfolio returns

I am investigating some asset allocation strategies and I am wondering about the results I obtain. I am working on monthly and weekly data of the same stock indices (SP500, FTSE 100 etc). And when I compute the summary statistics of the realized returns I observe that for the very same strategy those statistics vary greatly between weekly and monthly data. For the monthly f.e. I obtain skewness = 0.4 and kurtosis = 5, while for the weekly frequency skewness = 1.5 and kurtosis = 25.

Are the results for the weekly data plausible? And is it possible that the difference in the frequency of data results in such differences in the summary statistics? All computations are identical, the only difference is the data frequency.

I hope the question is not too general and it is possible to give some insight based on my description.

• Hard to say what is plausible without knowing your strategies but skewness and kurtosis tend to their normal values under temporal aggregation. – Bob Jansen Dec 2 '15 at 21:52
• hum....that's sounds a bit dodgyfor vanilla indexes although some differences are expected but not that huge (focusing on the kurtosis side). Please make me a favor by re-checking your weekly return series to see if there are no outliers, errors there. Alternatively specify your time horizon... As a matter of fact got 6.559... (weekly) for spx from jan-99 til nov-15 vs 10.63..(weekly) for ukx from jan-98 til nov-15. hope you understand more about my reluctance here. Please quickly use Excel kurt() on your data and keep me posted as I am curious.   – owner Dec 2 '15 at 22:03
• @owner I am solving the asset allocation problem on excess returns and the values of kurtosis for spx is 6.66 and for ftse 7.72. The values for non-excess returns are very similar. And I think there are no mistakes in the data, I have not omitted any outliers, as research on which I base mine didn't omit any either. The most intriguing thing is the difference between monthly and weekly data, as the computation process is the same in both cases, only the data changes. – Masher Dec 2 '15 at 22:30
• @Masher: fair enough... I had seen such a big gap in the past on an academic paper focusing on intra-day calculations vs other frequencies on fx markets, and am fine to discover something unexpected a priori from your asset allocation problem. – owner Dec 2 '15 at 22:46
• @owner do you remember the paper which you have mentioned? It would be great to show that such a case did not only happen in my research but in other works too. I am still wondering how is it possible, since there are no indications in the data or the calculations that the results would be so extreme in case of the weekly data. – Masher Dec 2 '15 at 22:54