SciFinance®

Science in Finance V: Diversification

One of the first lessons in any course on quantitative finance will be about portfolio construction and the benefits of diversification, how to maximize expected return for a given level of risk. If assets are not correlated then as you add more and more of them to your portfolio you can maintain a decent expected return and reduce your risk asymptotically to zero. (Risk falls off like the inverse square root of the number of different uncorrelated assets.) Colloquially, we say don’t put all your eggs into one basket.

Of course, that’s only theory. In practice there are many reasons why things don’t work out so nicely. Correlations never behave as they should, the relationship between two assets can never be captured by a single scalar quantity. We’ll save discussion of correlation for another time! For the moment I’m more worried about people or banks not even attempting to diversify.

Part of the problem with current mechanisms for compensation is that people are encouraged to not diversify. I don’t mean “not encouraged to,” I do mean “encouraged to not.” Imagine you have just graduated from a respectable Ivy League university with a thorough academic understanding of risk and return but without a similar level of appreciation of politics in an employment environment. You start your job as a junior trader determined to help your bank, and yourself, make money. You thus look for opportunities that diversify some of the bank’s risk while maintaining a good, solid return. Now if, as a result of the diversification you find yourself either losing money when the others make it, or making it when they lose it, then you are stuffed. Lose money when all around are making it, you’re fired. Make money when all around are losing it? Expect a big bonus? No way! Your profits will help to bail everyone else out and no one gets a bonus, even you. No, you should do the same as everyone else. As Keynes said, “It is better to fail conventionally than to succeed unconventionally.”

There are many ways to diversify, across contracts, asset classes, time horizons, what letter of the alphabet the contract starts with, etc. Even across models. I am in two minds about diversifying using different models possibly for the same contract. The scientist in me obviously wants to see each bank trying to find the best model, but I can appreciate that less harm might be done if people pick prices and greeks at random (my slightly cynical view of using multiple models!).

My scientist within would prefer each bank/hedge fund to have ‘one’ model, with each bank/hedge fund having a different model from its neighbour. Gives Darwin a fighting chance! I see so many banks using the same model as each other, and rarely are they properly tested, the models are just taken on trust. (And as we know from everyone's problems with calibration, when they are tested they are usually shown not to work but the banks still keep using them. Again, to be discussed later.)

There are fashions within investing. New contracts become popular, profits margins are big, everyone piles in. Not wanting to miss out when all around are reaping huge rewards, it is human nature to jump on any passing bandwagon. Again this is the exact opposite of diversification, often made even worse because many of those jumping on the bandwagon (especially after it’s been rolling along for a while) don’t really have a clue what they are doing. To mix metaphors, many of those on the bandwagon are in over their heads.

The key point to remember is something that every successful gambler knows (a phrase I use often, but shouldn’t have to), no single trade should be allowed to make or break you. If you trade like it is then you are doomed.

We all know of behavioural finance experiments such as the following two questions. First question, people are asked to choose which world they would like to be in, all other things being equal, World A or World B where

A. You have 2 weeks’ vacation, everyone else has 1 week

B. You have 4 weeks’ vacation, everyone else has 8 weeks

The large majority of people choose to inhabit World B. They prefer more holiday to less in an absolute sense, they do not suffer from vacation envy.

But then the second question is to choose between World A and World B in which

A. You earn $50,000 per year, others earn $25,000 on average

B. You earn $100,000 per year, others earn $200,000 on average

Goods have the same values in the two worlds. Now most people choose World A, even though you won’t be able to buy as much ‘stuff’ as in World B. But at least you’ll have more ‘stuff’ than your neighbours. People suffer a great deal from financial envy.

In banking the consequences are that people feel the need to do the same as everyone else, for fear of being left behind. Again, diversification is just not in human nature. Now none of this matters as long as there is no impact on the man in the street or the economy. (Although the meaning of ‘growth’ and its ‘benefits’ are long due a critical analysis.) And this has to be a high priority for the regulators, banks clearly need more regulatory encouragement to diversify.

Meanwhile, some final quick lessons. Trade small and trade often. Don’t try to make your retirement money from one deal. And work on that envy!

P