Rising like a pigeon from the ashes

Older & less faithful in some ways

Here we are, two posts deep on a factor investing. If you managed to muscle through the first post, I'm going to assume I've piqued your inner egg head's interest, which is a good thing. Remember that this site's main objective is to strip finance of (most) jargon so that everyday people can understand what's going on in financial markets. If you're not working in finance and you're coming back for more, then that's a success in my books. If you're back for more and working in the industry, that reassures me that these posts have a little something in them for everyone, which is also one of the site's goals.

But enough about that, today we will do a deep dive into one of the oldest factor models in finance, the Capital Asset Pricing Model (CAPM). I'm sure some of the industry vets will be rolling their eyes at this point, and I don't blame you; the CAPM is long past its prime, and this post is not going to paint this model as a phoenix rising from the ashes. But, with that said, there's a lot to learn from the CAPM, and although the way I use it may be different from its original intent, I think it is a valuable tool to use when looking at markets from the perspective of risk. So in that respect, the CAPM is more of a less sexy, nerdy, and more subtle version of phoenix; call it a pigeon, rising from the ashes. But, before we go any further, I want to note that I've already spilled some digital ink on factor investing in another post titled Welcome to the jungle. I highly recommend folks give that post a read before going through this one to get some context for why I'm prattling about factor investing.

Believe it or not, the CAPM garnered much attention when it made its debut back in the 1960s, enough so that its creator, William Sharpe, won a Nobel prize for his work on it. It's the centerpiece of most introductory finance classes, and often the only asset pricing model taught in those classes (for better or worse). Now look, let's not beat around the bush here; much like my back (sadly), this thing doesn't work as well as it used to, and there are plenty of questions of reliability. So why waste my time? Well, going through the CAPM's mechanics will serve as a template for more complex modeling to come. Moreover, we can still use the ideas behind the CAPM to explain some aspects of modern markets even while the model does a poor job of explaining asset returns.

The CAPM emphasized the notion of more risk, more reward. However, one crucial nuance was that the type of risk mattered greatly for whether investors should take the risk. Here, the CAPM refers to the notion of systematic risk and that the market would only compensate investors for taking on risks that investors could not diversify away. More astute readers will probably catch that the CAPM takes a shot at stock pickers here by saying that no amount of stock picking will give you more return than the risk you took on over the long run. There might be some truth to that, but that's not a statement I'm willing to get behind. The reality we know is probably somewhere in the middle when you consider that not all market participants have the same access to information.

Red pant PTSD.

So what is the CAPM? Well, the theory here is straightforward, you take on more risk, you get more return. So how do you measure risk? Well, the CAPM looks at broader market risk, which, at the heart of it, is just looking at how sensitive a given asset is to changes in the overall market. This sensitivity is known as "Beta" in financial market doublespeak and provides us with an idea of how much of that asset's risk premia gets passed onto the investor's returns. Of course, the theory goes that the more of that risk premia gets passed onto investors, the higher the returns.

All of this sounds cute; how do we calculate the Beta? Before we get further into the weeds, I want to emphasize that we are not doing anything more complicated here than a linear regression. Still, for those of you who weren't forced to sit through a 90-minute class where a Russian guy wearing red pants would spray math equations at you like a firehose, all we're trying to do here is draw a line of best fit through a scatter plot of market returns and another asset's returns. Many brains heavier than mine have devised algorithms to calculate the line of best fit, so fortunately for us, we don't have to do much of the heavy lifting. The slope of this line tells us how sensitive an asset's returns are to the broader market's returns and is the asset's "Beta." For example, the chart below compares three different companies, one with a lower beta (Kellogs), one with a beta of 1 (Southwest Airlines), and a company with a very high beta (Lincoln National Corporation). I have sorted the panels by the company's Beta (lowest to highest from left to right).

The slope of the line gives us an estimate of how sensitive each asset is to the broader market. Any value that is less/greater than one means that the company is less/more sensitive to the broader market, while a Beta of one implies that the company trades 1-for-1 with the market.

The CAPM is no longer a good indicator of future returns. So, as you can probably tell from the chart, companies with higher Beta's tend to have more volatility in their returns because they tend to be more sensitive to the broader risk sentiment in the market. Unfortunately, higher volatility is typically a bad thing for overall wealth through something known as volatility drag. I won't get into too much detail about that here, but the point is that higher volatility typically leads to lower returns, which is precisely the opposite of what we thought should happen! The chart below shows the relationship between Beta and 1-year returns for all the stocks in the S&P500 over 15 years. We can see that there appears to be no relationship between returns and a company's measure of systematic risk.

It will always be about how many biscuits you've got to lose.

The CAPM may not do a great job predicting returns, but it can better predict risk. Now look, returns matter and understanding which direction asset prices will go is important, but frankly, that's tough to do (think about information asymmetry). So the next best thing we can do is rely on volatility, and the CAPM still has some predictive power in that respect despite being a stone's throw away from retirement. The chart below shows the Beta estimate at the beginning of each year compared to the average 1-month volatility for that year. We can see that the basic CAPM does a decent job of explaining volatility across companies when considering how simplistic the model is and how many different market regimes witnessed during this period (note that the data runs from 2006 to today).

So the CAPM has shifted from becoming a tool used to explain market returns to one that we could use to manage risk. A measure of systematic risk is crucial for portfolio construction, and market participants rely on these measures to understand where they could lose all their biscuits. These become particularly important for funds that run long-short portfolios, especially those that aim to maintain a market-neutral position. The hard part is that there is a lot of subjectivity in these estimates. For example, which model should I use(single or multi-factor model?), which frequency do I use (daily, weekly, monthly, yearly?), how long do I run the regression for (how many months/years?), and how ofter should we re-estimate the model? Unfortunately, there are no clear answers to these questions. Still, that last question about re-estimating the model has become notably more relevant following the COVID-19 crisis as many quants believe the nature of systematic risk has changed.

Systematic risk in a post-apocalyptic world

The degree of systematic risk has changed since the COVID-19 crisis. The COVID-19 pandemic started as a health emergency that quickly morphed into a liquidity and financial crisis. The unusual nature of this crisis redefined systematic risk for most companies, reflecting a company's ability to operate under rolling global lockdowns. The right panel on the chart below shows how Beta's for S&P500 companies have increased slightly since the pandemic. Meanwhile, the panel on the left shows that the single factor model has better-explained changes in returns since the onset of the pandemic, as evidence by the increase in r-squared. Remember that the r-squared shows us how much of the variation in single stock returns are explained by variations in the market returns.

On a company-by-company basis, it is difficult to see how these changes have impacted the estimates of systemic risk. However, when we aggregate by sector, the story is a bit clearer. For example, the chart below takes the average change in a company's Beta for each industry over the last two years. We can see that systematic risk in utility, real estate, consumer discretionary, energy, and financials increased the most over the past two years, reflecting the operational challenges of the post-pandemic world. Meanwhile, healthcare, communication services, and technology all had their measures of systematic risk decrease over the past two years, reflecting how the pandemic has benefited these companies.

So what does all this mean? Well, the pandemic emphasized how notoriously difficult it is to estimate these measures of market risk. It also further stressed that the nature of systematic risk could change during extreme market events, or in this case, an extreme global event. As I had mentioned above, these changes in systematic risk can have enormous implications for funds that have long and short legs. For example, the most recent blowup came from the Dow Jones U.S. Thematic Market Neutral Momentum Index, which suffered a nearly 20 standard deviation decline in one trading day following the announcement of vaccine deployment in November of last year (Chart below).

This event deserves a separate post, which I will likely cover in the coming weeks. Still, a big reason for the collapse came from this shift in Beta risk and emphasized that understanding systematic risk is critical for investors. Although the basic CAPM model may have lost its ability to predict returns, the notion behind systematic risk is still very relevant to market participants over 50-years later. Now I'm not saying the CAPM is the best way to measure systematic risk, it most certainly is not, but it's not a model we should take behind the woodshed.

Thanks for reading,

Tiago Figueiredo