Can we use Stock Return Distributions to help us?

[candreouTrade 59]

@Kim, @Yowster

I was wondering if there would be any value in calculating the statistics (Kurtosis, Skew, Variance, Mean) for the return distribution of stocks,etfs and using them in our options trading as an edge?

 

For example could we filter stocks with Low Skew, Low Kurtosis and high Variance and then use them in some type of Butterfly trade?

 

We could then look for other statistics that would be suited to different option trade structures.

 

Any thoughts?

[Djtux 542]

Do you compute the moments from the historical stock return or from the option prices ?

If from the historical stock return, there is a possibility with page 6 of http://public.econ.duke.edu/~ap172/ACJV_26Dec2011.pdf

If from the option prices, either get that from a volatility smile calibrated on the implied vol of the options, or some model-free approximation calibrated on the option prices (a bit like VIX) page 5 of http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.217.4447&rep=rep1&type=pdf

 

The difference between the 2 approach is that one is backward looking (think historical volatility) and the other one is forward looking (implied vol, and contains in the option price the expectation of the market participants for the distribution of the stock return).

I think it might be challenging to compute higher order moments like skewness/kurtosis from something like daily stock prices because there is just not enough history. And increasing the frequency (intraday) not only cost more to get the data but you might be calibrating on noise.

In english : skewness should be thought as the asymmetry of the distribution of return, whereas the kurtosis is the tail fatness. All compared to a normal distribution.

And the tails are lower probability so you don't observe them that often which makes it challenging to calibrate on the past.

And you think about left tail, but there is also right tail risk, say if the inflation gets out of control.

 

In the end, it was fun to take a look at that though experiment and don't really know what to think about it. Sorry!

 

[candreouTrade 59]

I was more thinking of historical stock returns.

 

I would think that returns going back maybe 6-9 months would be most relevant and enough to calculate the moments. The reason is that when you look at our TLT trade, we are playing for the stock to be range bound, and I don't believe we have made this decision on many years of data. i guess we are playing the short term trend and will continue to until it no longer holds.

 

Might be interesting to calculate statistics such as moments and mean-reversion on TLT, and use it as a benchmark.  We could then scan for any stocks/etfs with better or comparable statistics? These could be candidates to use in a option trading back test, on butterfly trades for example.

[Christof+ 272]

44 minutes ago, candreouTrade said:

I was wondering if there would be any value in calculating the statistics (Kurtosis, Skew, Variance, Mean) for the return distribution of stocks,etfs and using them in our options trading as an edge?

@candreouTrade like your way of thinking and would like to join such the discussion further. Unfortunately do not have time right now to wrap my head around it a lot, just some very quick unripe 2 cts. popping up:

- Concerning your thoughts on range boundedness of TLT: looking at the moments of the return distribution might not be of much help in the end since they ultimately will not relate too much to the actual course of the price over a comparably short time relevant to us
- since the trading range is what counts for us it might be more interesting to simply look at some rolling average true range of, say, a month and see how it develops over time:

   * don't forget it's a long rate. So that range might well react to earlier changes in 'influencing' factors, (say, inflation expectations, standard leading indicators, possibly transportation index, fx etc., possibly in a weekly frame). When you see strong movement in those factors reason to be a bit more broad/conservative with next month's range expectation. Of course is an empirical issue in the end.

   * naturally, good times to sell a fly will be low range with high IV. To get a feel for TLT wanted to plot both over time since long as a simple exercise. So far never did  

- with moments you could also play the 'old' game of implied vol vs. realized moments. There is tons of literature on ti (might be more interesting for option writers though)

[candreouTrade 59]

ATR might be good, but i don't think it would help us identify if the stock had a drift. I imagine something like TLT would have a very low drift over time.

 

What could also be good is running a OLS regression on the stocks (again over a 90 day or so period) and seeing which stocks have the lowest coefficient over time. Assuming the R2 was high, stocks with a low coefficient could be good calendar candidates. We could then somehow improve/punish the rating of the stock, based on R2 fit and IV (so low coefficient stocks with high R2 and high IV would be fantastic butterfly candidates in theory)