June 25th, 2019

Using (Pseudo) Mathematics To Predict Stock Returns


Buy low, sell high. That’s the winning strategy to stock investing stated as simply as possible. While to the novice investor this might seem easily attainable, for the seasoned stock market veteran they realize just how difficult meeting this goal can be.

If you have your sights set on beating the averages (i.e. getting a better return than the S&P 500), you need to put in the time and effort to make it happen. Anyone can simply guess whether a stock will go up or go down, but what is the probability of successful long-term investing doing that? I can tell you from personal experience… not good.

My goal at Smart Money Math is to use mathematics to take guesswork out of stock selection. Today, I will introduce one of the first methods I have begun using to do just that. The equation below represents a simple regression equation used to model a stock's returns, \(C_{Ret} \), over a given time interval.


$$C_{Ret} = \omega_1 * M_{Ret} + \omega_2*S_{Ret} + \omega_3 +\sigma $$


This equation represents all the factors that influence the return of a stock. \(S_{Ret} \) represents the current return of the stock’s sector while \(M_{Ret} \) represents the current return of the market. The other \(\omega \) terms represent regression factors.


Company Factors


The first and most important of these factors is \(\omega_3 \) the idiosyncratic company variables. This includes the company’s financials, CEO, customers and anything else that can be attributed specifically to the company. These variables have a HUGE impact on the overall returns of the company, yet in the span of time they change very little. Company financial information is updated once a quarter and on-average we might only receive a couple of news stories a day updating us on the internal workings of a company. So, while these variables are highly important, we often go long spans of time without updated information on which to trade against them. Thus, it is usually easy to determine when these variables are actually affecting the return of a stock and when they are not. If the company reports bad news and the stock tanks it is likely caused by \(\omega_3 \). However, if the company tanks and nothing was reported on the company at all, then it is safe to assume \(\omega_3 \) was not the culprit.


Market Factors


The second most important factor is \(\omega_1 \) also typically known as beta (\(\beta \)) in the CAPM Model. This is the stocks correlation to the overall stock market and can be found on any number of websites. Because the stock market goes up and down every trading day, this factor frequently affects the performance of the individual stock’s return on a daily basis.


Sector Factors


The same can be said for the \(\omega_2 \) factor which is a stock’s relationship to its own business sector. This factor has grown in importance over the last decade as sector ETF’s and passive index investing have become larger in the overall market. This increase in sector ETF’s has led many companies to trade together within a given business sector despite the overall differences between the companies themselves.


Random Noise


The last variable is our random noise, \(\sigma \), which unfortunately is present in any stochastic process such as stock price movement. Figuring out what percentage this noise contributes to the overall stock return can be difficult, especially over a very short time interval. However, once you stretch out returns to weeks and even months the contribution of noise to the overall stock’s return should be minimized according to the efficient market hypothesis.

So why did I introduce this seemly simple equation to you? Because understanding why a stock is moving up or down is the first and most important thing to understand prior to buying or selling the stock itself. After all you want to know if you are getting a good deal on a good company or a bad deal on a broken company.


Getting To The Point


As I’ve mentioned before, you own a stock ultimately based on the individual company itself and not its relationship to the overall market or its business sector. If a stock is rising or falling because of its relationship to any of these variables other than \(\omega_3 \), there might be some market inefficiencies at play which you can capitalize on once these variables return to their normal states.

Let me give you can example, say stock XYZ drops 3% on a day the market drops 1%. You might ask yourself, is the 3% drop in value really justified? Was the large drop just due to its beta to the market (\(\omega_1 \)) or did another factor contribute to the decline as well?

If you look over the equation for the stock and can convince yourself that the drop was simply due to a down day for the markets or noise and the other variables are quite positive looking for the company itself, you might have found a winner that can beat the market in the coming days, weeks, etc.

However, beware that before you come to this conclusion you must first convince yourself that the greater-than-market decline is not justified by some other connection between macro events and the individual company itself. This is really the power of the equation. It’s not something that you really want to calculate to the decimal point. It’s more a thinking tool that should help you critically analyze what is going on within a given stock's return.