Your excel is better I must have highlighted a different region for the second result. The first is easily explainable as I didn't use excel and the program unlike excel adds +3 to the kurtosis taking the normal distribution to have kurt = 3.
One major reason for the difference in Kurtosis between weekly and daily: In October 1987, the worst week for the S&P was -12.1%. But the worst day was about -22%. So even though daily vol is lower than weekly, the daily black swan is larger. But I still find it hard to believe a kurtosis of 39.3. Using the daily data posted, I find a kurtosis of 27.7. Using the daily data from 1950 on, I see a kurtosis of 37.7. Why is daily kurtosis so much higher than weekly? Or why is Dow kurtosis so much higher than the S&P's?
Well I got the same value of 39.3 (Pearson) and 36.3 (Fischer) as did GBOS. Donât know how you arrive at 27.7. Donât take this as an insult, but are you measuring the kurtosis of the daily logarithmic prices changes ? Just thought Iâd ask. It shouldnât be. If you took the DOW weekly price (rather than daily price) the Kurtosis would be (more or less) the same. I think perhaps that what you may be doing is looking at particular periods of extreme price move, and asking why ?
Using the logarithmic returns, I get a kurtosis of 36.3 as you say. But using S&P weekly data (logarithmic returns), I still see 3.49 (I had 3.31 using nominal returns).
I just don't understand why the DJIA's kurtosis would be so much higher than the S&Ps. Either something is wrong or there is something I don't understand going on.
Out of curiosity i downloaded the s&p500 data from yahoo (^GSPC) symbol (1950 - today) and the calculator gave these statistics