Utility Theory

Economics 101 tells us that people have 'convex' utility curves.

Which means there are diminishing returns to having more, but losing what you currently have diminishes your well being precipitously.

Convexity is such a human property, it shows up again and again in unexpected places.

Eyeballs, boobs and butts to name a few examples.

In finance convexity shows up in the form of our risk aversion. The aforementioned convex utility curve means we generally fear large losses more than we lust after large gains.

Quant finance eschews this risk aversion and assumes risk neutral pricing, which means that financial models may overestimate the price a human is willing to buy a very risky asset at and underprice very safe assets - assuming humans are doing the trading of course.

The reason why risk neutrality is necessary is because we all have subjective risk appetites, neutrality removes the subjectivity and in turn produces only one price.

While volatility represents risk in most strategy appraisals it assumes symmetric up and downsides. Obviously our utility functions are convex and our view of ups and downs are like apples and oranges, which means analysing both separately is important.

I have analysed many well known strategies in this way, comparing their 'Upside Betas' against 'Downside Betas'.

Here's a summary.

Apart from anything else, it's good to note how much beta you get with 'High Beta', it's like free leverage!

In any case the net beta 'spreads' are easier to read.

The financial naming convention changes a little; positive convexity, gamma or beta spreads means a situation where the index loses less than the market on the downside and more on the upside.

At -9% Momentum is the big loser whereas Growth and High Beta are the winners.

Bad gamma is something to be aware of, which begs the question, why limit yourself to well known strategies which generate negative gamma in an ad-hoc-externality way?

How about intentionally producing negative gamma returns which coincidentally make massive profits?

Hedge funds have been doing this for years with option writing strategies, but you could probably come up with an imaginative 'delta one' style strategy which emits a tonne of negative gamma and seemingly juicy profits.

Investors generally hate losing a lot of money, but they may not realise for a few years.

On the other hand, if you are considering an investment style for your own money, there are perfectly profitable ways to invest with positive gamma. Meaning fewer nasty surprises, and perhaps the odd nice windfall every now and again!

More analysis:

If you have any other suggestions, let me know: John.Orford@gmail.com