Evaluating Sorted Portfolios with Factor Models and Robust Inference
Summary
The document discusses how to evaluate a stock-sorting strategy whose portfolio returns appear to have different Fama–French three-factor alphas. It recommends using Newey–West standard errors to account for autocorrelation and heteroskedasticity, and expanding the benchmark to include profitability and investment factors, with momentum as a possible additional control. A factor omitted from the model can make an apparent alpha reflect exposure to that factor instead of genuine strategy performance.
It also recommends testing the long–short return of the good portfolio minus the bad portfolio, since the spread directly measures whether the sorting variable separates returns. The example reports a significant intercept for one portfolio and a nonsignificant one for the other, but those individual regressions do not establish that the strategy works. The answer further flags return-data quality as a concern. These are diagnostics rather than proof of robustness: the document gives limited details about portfolio construction, trading costs, or out-of-sample performance, and its suggested inference and factor controls should be matched to the study design.
Key ideas
- Use heteroskedasticity- and autocorrelation-robust standard errors when evaluating portfolio alphas.
- Consider profitability and investment factors, and potentially momentum, when assessing returns beyond a three-factor model.
- Test the return spread between the good and bad portfolios to measure the sorting strategy directly.
- A significant alpha in one portfolio alone does not demonstrate that the sorting variable explains return differences.
- Check the underlying return data for cleaning and quality problems.
Tags
Full text
# Answer by dm63 (score 2) # I can’t understand why the premium of two butterflies with same strike but different broadness are approximately the same Consider the following premiums of calls option with different strikes. C90 = 57.35 C95 = 52.55 C100 = 47.3 C105 = 42.9 C110 = 38.25 In this case, the butterfly 90-100-110 cost 1 and the 95-100-105 cost 0.85. I expected them to be very different. By drawing the payoff curve, I expected the payoff to be at least 4 times higher.. Thanks ! ## Answer by dm63 (score 2) https://quant.stackexchange.com/a/73563 The following argument shows that the price of the big fly should be approximately 4* the price of the small fly: Consider the portfolio of large flies B(0,10,20)+B(10,20,30)+……B(80,90,100)+….+all the way to infinity. This portfolio pays exactly 10 at maturity. Hence each fly represents 1/10 of the probability of being in the range of the fly, in a sense. This approximation works if we approximate each fly by a digital payoff , for example B(90,100,110) represents 1/10 the probability that the stock finishes in the range (95,105). A similar argument for the small flies shows that B(95,100,105) represents 1/20 of the probability of being in the range (97.5,102.5). Then it’s easy to see that these should be in the approximate ratio 4:1. This was intuitively obvious by looking at the payoff diagrams. As others point out , any large deviation from this in the marketplace is almost certainly due to asynchronous data or transaction costs. ## Answer by AKdemy (score 1) https://quant.stackexchange.com/a/73551 In most realistic scenarios, the price of Apple will end up outside the range of your proposed butterflies and you simply pay or receive the costs. Insofar, your argument with going long the 90-100-110 and shorting the 95-100-110 twice sounds plausible given your numbers. However, bear in mind what @nbbo2 wrote in the first comment: > These problems are often caused by using prices of transactions that did not occur at the same time (non-simultaneity problem). If you look up the option prices on Bloomberg (`OMON`), you see the following picture on October 6th. As you can see, the volume column (Volm) is either not showing any volume, or very low volumes for almost all strikes you consider (you did not specify the expiry date but it should be similar for all expiries). If you now look at `GIT`, you can see when these prices were observed. There is a considerable mismatch in terms of timing, which means you are not using prices that reflect the actual costs of your butterflies if you were to buy them simultaneously. If you price it with `OVME`, you can use the OTC mode to use a VOL surface (called `BVOL` here), that you could also look up on `OVDV`. Doing this gives the following butterfly prices. ``` 56.8076371 | 52.0521078 -94.6852675 | -94.6852675 38.1983043 | 42.7308402 ------------------------ =0.3206740 | =0.0976805 ``` In this case, your argument no longer holds. Regarding your last comment, you do not have 99.5 and 100.5 but 95 and 105. In any case, the prices you looked at were almost certainly not from the same time period. How to (best) assess risk neutral probabilities using option prices is a separate question really.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.