## December 2009

Recs

### 5

### Diversification Analogy

I think diversification is not very well understood, despite all that you hear about it. Most people don't actually understand the reason why diversification is necessary. Here is an analogy that was helpful for me...

Imagine you are playing a betting game using a coin. You will flip the coin once, and you have two choices - Bet A or Bet B.

Bet A: if you flip heads, you lose all your money. Otherwise, you get your 101 times your money back (10000% return).

Bet B: if you flip heads, you lose 10% of your money. If you flip tails, you get 1.2 times your money back (20% return).

Most people would take Bet A, because the expected return is enormous: 5000% (0.5 * 0 + 0.5 * 10000 = 5000), compared to Bet B's expected return of 5% (0.5 * 0.9 + 0.5 * 1.2 = 1.05).

However, if you change the game, so that instead of flipping the coin only once, you must flip it 1 million times, most people would take Bet B instead, since once you get wiped out once, you have no chance of coming back. If you took Bet A, you would most likely end up with nothing, and if you took Bet B, you would most likely end up very rich.

The reason is because, if you are looking at compounding over the long run, you cannot use an arithmetic average to calculate the expected return. You need to use the geometric average. You probably look at stocks' returns not based on arithmetic average return but compounded return. Also the reason many people prefer to use logarithmic charts instead of linear. Geometric average is basically the compounded return. For those of you who forgot this term from grade school, the geometric average is the product of all the numbers, taken to the nth root. So for example, the geometric mean of the numbers 1, 2, 3, and 4 would be (1*2*3*4)^(1/4) = 2.21. You might have noticed, this means the geometric mean for any set of numbers containing 0 is 0! This means that the expected return from Bet B over the long run is 0!

This coin flipping game is obviously an analogy for investing. For most people, investing is a life-long process (unless you plan to make your $$ in the market all at once and then just stop) so you need to look at it from a long-term perspective. Being too undiversified (or taking any unneeded risk in the market, really) can lead to huge winning streaks, but unless you are extremely good or lucky, eventually it will catch up to you, and one good year can undo amazing returns over many years (just look at what happened to Legg Mason Value Trust LMVTX managed by the famous Bill Miller).

Anyways, I am not a math major so there is probably an error or two in my explanation, but I hope I got the point across. By the way, if you are interested in this, there is a great book called **Fortune's Formula** that I highly recommend reading... after reading that book, I finally got a healthy respect for diversification. There is actually a mathematical formula called the "Kelly Formula" or "Kelly Criterion" that can be used for diversification, although that was not its intended purpose... it was first used at the racetracks and Vegas to make some good $$... really a fascinating read. [more]