When investors start looking at stocks and ETFs, the most common graph they see is a price chart, like the one below. We can see a rollercoaster of emotions we all experience, ranging from fear to joy, as prices fluctuate over time.
However, this is usually the wrong starting point to properly evaluate an investment. How do professionals think about investing more mathematically?
First, let’s take a look at the expected return of the investment — how much do we stand to make or lose each year?
- The first metric we can consider is past performance — on average, what has the investment returned per year? We often hear the disclaimer, “past performance is no guarantee of future returns,” so we must be wary. However, expected returns gives us a starting point that is much more scientific than guessing!
- The second metric to judge is the volatility of a security (how much the price fluctuates), which in statistics, is represented by standard deviation.
Stocks, Bonds and Standard Deviation
In modern portfolio theory, there is really only one concept we need to master that’ll make investing much more intuitive. Let us look at the two main security types, stocks and bonds. The chart below summarizes how the US stock and bond market has performed over the past 87 years.
How do these stats help us make informed decisions? We need to understand where standard deviation comes from: the normal distribution, also known as a bell curve.
Let’s break this down.
- The mean is the average number. For stocks, the mean return is +10% per year. For bonds, the mean return is +5%.
- Standard deviation (known as sigma) gives us an idea of probability. It tells us a range of what we can expect to make or lose. In statistics, 95% of the outcomes are within two standard deviation measurements of the mean. 68% of the outcomes are within one standard deviation.
Let’s start with bonds:
- For bonds, the mean performance is +5% and sigma is 8%
- Each year, we can confidently expect (95% of the time) that bonds will return +5% plus or minus 16%, “two standard deviations”. Two sigma equals a range of -11% to +21%. Unless an outlier occurs (5% chance), we can expect our investment to be between being down 11% and up 21%.
- Most of the time (68%), the 1-year return will be between -3% to +13%, or one standard deviation (8).
These numbers give us a frame of reference. Equipped with some general statistics knowledge, we no longer expect bonds to double (+100%) or go down by half (-50%) in one year, for example.
Moving on to stocks (S&P 500):
- The mean for stocks is +10% with a sigma of 20%, a much higher number.
- Using the same math, we expect stocks (95% of the time) to return +10% plus or minus 40, two standard deviations.
- Unless an outlier occurs (5%), that equals a large range of down 30% to up 50%. Most of time, the stocks’ return will be in the range of -10% to +30%.
As we can see, the larger the ranges (known in derivatives trading as volatility), the greater the risk.
The real world may not follow a perfect bell curve, but by applying statistics, we are better equipped to judge investments by more than gut feeling.
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