Understanding Return

Variance

Variance is a statistical concept describing the range around expected return within which an investment return can be reasonably expected to fall.

Introducing Variance

In probability theory and statistics, variance measures how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean (expected value).

Understanding the concept of variance and three typical asset classes – money market, bonds, and stocks – can help you build a portfolio for any investor. Money market investments are very safe; they almost never go in the red, but they also do not pay high returns. Stocks are on the opposite end of the spectrum, going back and forth between red and black from year to year frequently, but over longer periods of time, they usually pay higher premiums. Bonds are somewhere in the middle. They are safer than a stock but riskier than a money market, and their average returns reflect that.

This table shows how to calculate the variance of an investment outcome.

How much do investors want to pay to have to take the good with the bad? Calculating variance is a three-step process once the expected return has been calculated. Calculate deviations from the mean (blue), square the deviations (yellow), and multiply the squared deviation by its original probability (orange). Get brownie points by taking the square root of that number and interpreting its meaning as a sentence.

You may not need to calculate variance, but you should still notice how we got it. In the figure, we started with three scenarios and a probability (P) and return (R) associated with each. We did some math and used the two blue columns to get the yellow one. Then, we multiplied the two yellow columns to get the orange one. We get the variance from adding up the numbers in the orange column.

Of the three numbers, we add (62, 0.34, and 128). Two are very big, and one is very small. The small number comes from the TC scenario, where the stock returns 10%, which is very close to our expectation of 9.25%. The bigger numbers come from extreme winters – when the stock performs way above 9.25% (HG) or way below it (WB). The standard deviation can be read as a percentage. This means that even though we can expect an average of 9.25% return on our stock over 50 years if we take any given year out and look at its performance, it is likely to be somewhere within 13.81% above or below that figure.

Variance in Relation to Expected Return

In the discussion of expected return, we concluded that, based on your research, you can expect the Ski/Snowboard Resort in Colorado to have an expected return of 9.25% based on three distinct weather outcomes. However, if you invest $20,000 in that company and expect to have $21,850 after a year, you must remember that this isn't a dice game that you can play over and over again. There will only be one result in this case, and at the end of it, you will have to make a down payment for a house. Is this a good investment idea?

What if your bid for a house will not be accepted unless you can put at least $20,000 down? There is an 85% chance that the winter is either hella gnarly (HG) or totally chillax (TC), and in either of those cases, you will still have over $20,000 to make a down payment. There is also a 15% chance that the year ends up being wicked bogus (WB), and if that is the case, you will lose 20% or $4,000 of your initial investment. Now you have $16,000, and suddenly, you are thinking tree fort.

Let's compare that investment to a CD at a bank that pays 3.25% no matter how much snow falls this winter. You can have an investment that is federally insured to pay you $20,650 one year from today, and you can be assured you have enough to make a down payment on your house.

If you can let that $20,000 investment sit for 10 years before you need it, there is a better chance you will end up in the black (experiencing a profit) than in the red (experiencing a loss). A 30-year-old with a 401K can be much more aggressive in his portfolio than a 65-year-old who will be retiring in one year. Every portfolio should be modeled with a time frame and risk tolerance considerations. It would be just as foolish for the 65-year-old to invest in aggressive stocks as it would be for the 30-year-old to buy conservative CDs in his retirement account.