Market dips are good for stats

I’m sure you’ve heard the argument about buying market dips? You know, buying stocks at a discount because the market went down short term, while you’re expecting things to continue up long term.

But there’s another thing that dips are good for: Your strategy stats.

The reasoning is fairly straight forward. If you only measure performance in one type of market environment, like only bear or only bull, you can’t know what impact a change in this state will have on your stats.

Of course you want to measure your performance across various types of market conditions. Therefore, dips are good, because it gives you this opportunity. It might not be good for your actual performance, but then at least you know. Like Warren Buffett said, “only when the tide goes out do you discover who has been swimming naked”.

So what are we measuring here on our portfolio? Primarily the relative performance, specifically measured as alpha. There are many methods of measuring portfolio performance. Most of them use linear regression, and they compare one asset or portfolio to another asset or portfolio.

On our alpha/beta measurement we’re solving for the below formula:

Simple regression model

If the return of the active, which is a function of alpha and the relationship between beta and the benchmark returns, is such that our alpha is positive (and significant by some standard), it means we’re beating the market. Doesn’t matter if the returns are positive or negative overall (state of market), because we’re still doing better when our alpha is positive.

Beta on the other hand highlights our general exposure to the benchmark. You can say it’s related to correlation, but correlation is technically measured slightly differently.

So what then if we measure only in a bull market? Well, you might find that you have a nice positive alpha and a beta close to 1 or less. All seems good. But then suddenly the market changes into a bear market. Something happened in the world and things went south. Looking at your stats again, you now see that in fact, your alpha was practically zero, and your beta was higher than 1. So you didn’t add any extra value, you just took on more risk.

Looking at it visually

Doing math and stats and calculating these measures should be done. It’s important. But it’s also important to be able to visually look at something and spot the obvious. You might have seen the Anscombe’s quartet illustration before showing us statistics being equal for all of these, but clearly the actual data tells a more intricate story.

Anscombe's quartet

This is why we include the relative difference on our portfolio page. Looking at the past year I’ve annotated a few sections of the timeline I think illustrate what we want to measure rather well.

AgoraOpus relative portfolio performance

As you can see there are three regions highlighted, A, B, and C. The bottom red line shows the relative difference in value between the active portfolio and our benchmark portfolio.

In short, we can see that during period A, the market overall was showing a fairly flat development, and our active portfolio was under-performing but still remaining fairly flat as well.

Then we had a sharp decline during period B. As both the active and benchmark portfolio represent long only positions, both naturally followed the same path down, but, looking at the relative performance we see this now going up. So while both head down, our active portfolio is going down less and therefore performing better.

Then the market turns again, during period C. Initially we slightly underperform, but overall during period C we continue to outperform the benchmark, somewhat less than during period B.

All these periods represent what I’d call different states of the market. Period A is during a fairly flat period, with not much excitement. Period B is clearly a bear market, followed by a bull market in period C. In 2 of these 3 periods we’re outperforming our benchmark. The overall alpha for the full period (A, B, and C) is shown to be 15.37%, with a beta close to 1.

This blog post was written by Christian, the main portfolio curator here at AgoraOpus. With a background from FinTech, he holds a MSc in Quantitative Finance and a BSc in Computer Science and Industrial Automation.

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