Please read this one slowly (and, hopefully, more than once). Modern Portfolio Theory (MPT) is one of the most important concepts in investing to understand. It isn’t obvious: indeed, Harry

Markowitz won a Nobel Prize in economics for coming up with this idea in 1951. (So the idea isn’t really all that modern at this point.)

Most people think they understand the reason to diversify investments: you don’t want to put all your eggs in one basket. But the analogy is a sloppy one. If you have two eggs to transport and a 50% chance of dropping a basket, putting them in a single basket means that you will lose no eggs half the time and both eggs the other half. The average loss is one egg per trip.

What if you put the eggs into two baskets, one in your left hand and one in your right? The chance of dropping each basket is still 50%, so if you do four deliveries you would only expect one break-free trip on average, one trip during which you dropped the left basket losing a single egg, one in which you lost the egg in the right basket, and one in which you dropped both baskets, losing two eggs. That’s four broken eggs in four trips, which is still one egg per trip. Although you reduced the probability of a two-egg loss, from 50% when you used one basket to 25% when you used two, you didn’t change the average result, which remained a loss of one egg per trip. Reread this paragraph until you’re sure you understand it.

Got it? Great. But that is NOT how diversification of a portfolio works. When you apply MPT you reduce both the probability of maximum loss AND the average expected loss, while increasing the average expected gain. (This is a remarkable free lunch, if you think about it. Think about it.)

Assume you have the opportunity to invest in two different mutual funds named Coin Flip A and Coin Flip B. Each fund rises 100% (doubles) or falls 50% (halves) depending on whether the mutual-fund manager’s lucky coin comes up heads or tails that year. Both mutual funds, over the long term, can be expected to go nowhere, since they’ll be doubling half the time and be halved the other half. If you invested in either one, your most likely result over the long term is an annual rate of return of 0%.

But what if you split your money equally between the two funds each year? On average, one out of every four years will see both funds double; one out of every four years will see both funds halve; and two out of every four years will see one double and the other halve. Your wealth will obviously rise 100% when both double and fall 50% when both halve. But in the two years they move in opposite directions you won’t break even, you’ll GAIN 25%.

How so? Let’s say you had $100 to invest at the start of the year. $50 will go into each of the two funds. In one of them the $50 will double to $100 and in the other the $50 will halve to $25. You’ll now have $100+$25= $125.

In an average four years, starting from $100, your investments will grow to $156.25. This is the compounded result of the two years in which you made that 25% gain (the doubling and halving years cancel out). This is from two mutual funds which were each making 0%.

At this point, the mathematicians among you are ready to pounce on me for misusing the word “average” and the non-mathematicians are just assuming this has to be wrong. But I will explain myself in the next lesson.