For anyone new to stocks and other financial instruments, the daily rise and fall of portfolio valuations and endless banter on what to do and how to do it might seem a bit overwhelming. You can easily get swept up in the noise and excitement of finding the “next great stock” that makes you a rags-to-riches millionaire overnight.

To some this might seem exciting and give reason to poke and prod the stock market even further. For others, this might make them pause and hesitate to invest at all. For those of us who tend to hesitate or cringe at the thought of investing in stocks, one of the common questions I hear again and again seems to be: Is the stock market simply gambling?

To answer that question, I will use math to describe both gambling and stocks to see if there are any similarities mathematically between the two and what we can draw as conclusions from these comparisons.

Gambling by definition is taking a risky bet in hopes of a desired result. This description could also be used to describe one of the most common stock prediction formulas known as the Capital Asset Pricing Model (CAPM).

$$ ER_i = R_f + \beta_i(ER_m - R_f) $$

The CAPM describes the expected rate of return from a stock given the expected rate of return of the entire stock market, the stock’s correlation with the market and the risk-free rate of return (U.S. Treasury Note interest rate). Much like gambling, the return of the market is unknown. If the market’s return is positive and the stock’s market correlation is positive, the asset will return a positive value (gain). However, the formula also describes the possibility that the market return is negative (with a positive stock correlation) or the market return is positive (with a negative stock correlation) producing a stock value loss… an undesired result.

In other words, the CAPM shows us that stock picking involves risk. In this regard gambling and stocks are similar. However, we can’t stop by simply saying both involve risk. We need to quantify these risks to see if they are remarkably different or not.

If you play one hand of black jack you can either win or lose with a given probability. Without implementing a card-counting type strategy you can expect to win less than 50% of the time… This is how casinos make money! If you continue to play many hands of black jack, the expected value of your final winnings tends towards the limit of zero (sadly you lose all your money). You can multiply the probability of winning one hand with the probability of winning the next hand over and over again to compute your overall expected value of your winnings. In mathematical terms, you can say if you play an infinite number of hands with probability of winning of 48%, you will approach zero (no money left).

$$\lim_{x \to \infty } 0.48^x = 0$$

What about the stock market? Each day you have money in the market is similar to playing one hand of black jack. You can either “win” or “lose” on any given day. However, unlike black jack, the probability of winning or losing on a given day is not working against you. How do I know this?

If you take a look at the long-term trend of the S&P 500 it tends to gain over the course of many years. This means that on a given day your probability of “winning” is higher than your probability of “losing” on average. If it wasn’t the S&P 500 would tend towards zero not the other way around.

What this means is unlike gambling, the stock market odds are in your favor. This comes with the important caveat that you invest in an entire index rather than an individual stock. Individual stocks can, and do, go to zero all the time. Buying individual stocks can be gambling and investors must have a “card-counting” type strategy to manage the risk when doing this type of investing.

Hopefully this provides some insight into investing and gambling and the differences and similarities between the two. If you have any questions you can shoot me an email or Tweet me @smartmoneymath.

Remember words may lie, but math always tells the truth.