Math & Probability

If there's one thing that trips up most investors, it's math, and especially probability. But it doesn't have to be a big obstacle. To excel at investing you don't have to have an advanced degree in math or statistics. You just need to grasp a few straightforward concepts that are important and relevant to investing.

Ratios

If you are fluent in grade school arithmetic and high school algebra, you have all the math training that you need as an investor. And you can even be terrible at algebra (like I am) and still be able to grasp the math of investing. Take ratios for example. You don't have to compute them yourself because they are readably available on most brokerage platforms and research reports. Your task is to interpret them.

Ratios like price-to-earnings, price-to-book value, and price-to-free cash flow are standards of measurement for judging whether a stock is cheap, fairly priced, or expensive. By comparing these ratios to other stocks in the same industry, you can get an idea of the relative value of a stock.  

Compound Annualized Growth Rate (CAGR)

This number is based on the idea that as time goes by, you are not just earning a return on the money you initially invested. You're earning a return on that money plus the interest and capital appreciation you have gained along the way. Put another way, compound growth is earning more money on the money you already made. 

The formula for CAGR is a little complicated, but thankfully it is also published on websites like DQYDJ.com. This site has a multitude of free calculators that will do the heavy lifting for you so that you don't have to spend time figuring out how the formulas work.

The Time Value of Money

Simply stated, a dollar in your pocket today is more valuable than a dollar you will get in the future. Why? Because of inflation. How does this relate to investing? Because the value of a company is determined by the growth of earnings and dividends that will come in the future. But those cash flows are not worth as much as they would be in today's dollars. There is a discount applied to the cash flows, and that is one of the key principles of investing math.

You don't have to do these calculations, either. Analysts and brokerage firms do them for you when they publish their version of the "fair value" of a stock. Fair value takes the time value of money into consideration. You can get fair value for virtually any stock by visiting Morningstar.com.

Probability

Investing is not a purely mathematical endeavor. There are emotions involved. When investors are happy and optimistic, they will pay more for a stock than they would if they were worried and pessimistic. That's where probability comes into play.

If you have ever participated in a game of chance, like poker or horse racing or the state lottery, you have experience with probability. In fact, we all use probability every day for decisions like whether or not to take an umbrella (probability of rain), which lane to choose when we drive somewhere (probability of arriving at our destination faster) and which checkout line to choose when we shop at the grocery store (probability of getting stuck behind someone who needs a price check or some other kind of help). 

When it comes to making investment decisions, we usually rely on our instincts to guess the probability that the stock we're considering will go up instead of down. This is where analysts' ratings (strong buy, buy, hold, sell, strong sell) come in handy. These analysts follow the companies closely and their ratings reflect how confident they are about the future prospects of the stocks they cover.   

The worst odds of winning are found in the state lottery. Very low probability of winning, and very high payout if you do happen to win. Many investors are attracted to penny stocks (stocks that are trading for less than $1 per share) because they are cheap to buy and they have the potential to pay off in a big way. But the risks of investing in penny stocks are so great that most professional advisors will discourage their clients from investing in them. 

In cards, if you are skilled you can tip the odds of winning in your favor, so that is a probability-rich environment for skilled players. Likewise, in investing, someone who has the right set of skills has an advantage over the majority of investors who tend to buy and sell based of nothing more than their gut feelings that day.

In the stock market, the odds are stacked against you. Unless you have some kind of an edge. Your edge can be something like an intimate familiarity with a certain company, and their prospects for future growth. Or it could be a superior strategy that is unique and profitable. Other examples of having an edge include being self-aware, thinking critically, and having a well designed investment plan that keeps you on track.

Without an edge, the probability of beating the market consistently are slim to none.