Quantitative Investing

Kernel of error

In our last post, we looked at a rolling average of pairwise correlations for the constituents of XLI, an ETF that tracks the industrials sector of the S&P 500. We found that spikes in the three-month average coincided with declines in the underlying index. There was some graphical evidence of a correlation between the three-month average and forward three-month returns. However, a linear model didn’t do a great job of explaining the relationship given its relatively high error rate and unstable variability.


We recently read two blog posts from Robot Wealth and FOSS Trading on calculating rolling pairwise correlations for the constituents of an S&P 500 sector index. Both posts were very interesting and offered informative ways to solve the problem using different packages in R: tidyverse or xts. We’ll use those posts as a launchpad to explore the rolling correlation concept with respect to forecasting returns. But we’ll be using Python to do a lot of the heavy lifting.

Writing conundrums

We’re taking a break from our portfolio series and million sample simulations to return to a subject that we haven’t discussed of late despite its featured spot in this blog’s name—options. In this post, we’ll look at the buy-write (BXM) and put-write (PUT) indices on the S&P 500, as conceived, calculated, and published by the CBOE. Note: we’ve discussed the buy-write strategy in the past here and here. In those posts, we analyzed the performance of the buy-write relative to its underlying index, the S&P 500.


In our last post, we discussed using the historical average return as one method for setting capital market expectations prior to constructing a satisfactory portfolio. We glossed over setting expectations for future volatility, mainly because it is such a thorny issue. However, we read an excellent tutorial on GARCH models that inspired us at least to take a stab at it. The tutorial hails from the work of Marcelo S.

Skew who?

In our last post on the SKEW index we looked at how good the index was in pricing two standard deviation (2SD) down moves. The answer: not very. But, we conjectured that this poor performance may be due to the fact that it is more accurate at pricing larger moves, which occur with greater frequency relative to the normal distribution in the S&P. In fact, we showed that on a monthly basis, two standard deviation moves in the S&P 500 (the index underlying the SKEW) occur with approximately the same frequency as would be expected in a normal distribution.

Null hypothesis

In our previous post we ran two investing strategies based on Apple’s last twelve months price-to-earnings multiple (LTM P/E). One strategy bought Apple’s stock when its multiple dropped below 10x and sold when it rose above 20x. The other bought the stock when the 22-day moving average of the multiple crossed above the current multiple and sold when the moving average crossed below. In both cases, annualized returns weren’t much different than the benchmark buy-and-hold, but volatility was, resulting in significantly better risk-adjusted returns.

Valuation hypothesis

In our last post on valuation, we looked at whether Apple’s historical mutiples could help predict future returns. The notion was that since historic price multiples (e.g., price-to-earnings) reflect the market’s value of the company, when the multiple is low, Apple’s stock is cheap, so buying it then should produce attractive returns. However, even though the relationship between multiples and returns was significant over different time horizons, its explanatory power was pretty low.

Price is what you pay

Stock analysts are usually separated into two philosophical camps: fundamental or technical. The fundamental analyst uses financial statements, economic forecasts, industry knowledge, and valuation to guide his or her investment process. The technical analyst uses prices, charts, and a whole host of “indicators”. In reality, few stock analysts are purely fundamental or technical, usually blending a combination of the tools based on temperament, experience, and past success. Nonetheless, at the end of the day, the fundamental analyst remains most concerned with valuation, while the technical focuses on price action.

Playing with averages

In a previous post we compared the results from employing a 200-day moving average tactical allocation strategy to a simple buy-and-hold investment in the S&P500. Over the total period, the 200-day produced a higher cumulative return as well as better risk-adjusted returns. However, those metrics did erode over time until performance was essentially in line or worse since 1990. While there’s still some more work to do on understanding the drivers of performance for the 200-day strategy.

My strategy beats yours!

Don’t hold your breath. We’re taking a break from our deep dive into diversification. We know how you couldn’t wait for the next installment. But we thought we should revisit our previous post on investing strategies to mix things up a bit. Recall we investigated whether employing a 200-day moving average tactical allocation would improve our risk-return proflie vs. simply holding a large cap index like the S&P500. What we learned when we calculated rolling twenty-year cumulative returns was that the moving average strategy outperformed the S&P 500 76% of the time.