Asset Allocation and Bet Size

by George Hatjoullis

The most important decision any investor makes is the cash to risk assets ratio. In my blogs I have repeatedly asserted the validity of 70% cash v 30% risk assets. Most have regarded my allocation as overly conservative. A paper published in the Journal of Portfolio Management suggests it might even be aggressive. The Paper, Rational Decision Making under Uncertainty: Observed betting patterns on a biased coin by Victor Haghani and Richard Dewey, is worth a read. It is very accessible though the concepts will be alien to non-finance professionals. A link can be found on the Elm Funds website which is a very interesting source of information.

The thrust of the paper is that if you have a prospect with a positive expected value then you should invest (bet) a constant fraction of your investable wealth. They refer to the Kelly* formula which is 2xp-1, where p=the probability of winning. This assumes utility from playing the game takes a particular form but this is not critical to the argument. If you believe there is a 65% chance of your bet or investment paying off then you bet 2×0.65-1 which equals 0.3 or 30%. Of course, equity investment is a long way from a binary betting game but the principle is similar.

The logic of the approach is that if you bet too much you could run out of money and if you bet too little it is sub-optimal. The Kelly formula gives you some way of getting a handle on how much to bet. Many lifestyle funds use 50/50 as the asset allocation. This implies a 75% probability of positive returns. The logic is that in the long run this is true. It probably is but what if you get an unlucky run over the next few years? It makes sense if you are adding new cash to your portfolio each year so the invested value is growing. It may be too aggressive if you have a fixed wedge to invest for a finite number of years, as do most pensioners.

The other implication is that passive funds may actually be more risky than we realise. The funds match a market value weighted index. Nothing in the Kelly formula or this fine piece of simulation suggests investing more in larger companies. There may be other reasons for doing so, such a liquidity, but a case can be made for equal weight for each individual asset. Unless you have special knowledge about one asset that changes the probability of success there is no probability reason for anything other than equal weights. An index is weighted towards large cap stocks by construction and not their prospects.

So for a fixed lump sum investor, not being too aggressive makes sense. I stick with 70/30. Diversify as widely as possible so that individual asset risks do not overly impact the total portfolio. Where possible opt for equally weighted passive portfolios unless you are not well diversified or have better knowledge of some component assets.


Kelly, J.L., Jr. “A New Interpretation of Information Rate.” In The Kelly Capital Growth Investment Criterion, edited by L.C. MacLean, E.O. Thorp, and W.T. Ziemba, pp. 25-34. Singapore: World Scientific, 2012.