Portfolio diversification and Sharpe ratio

Question

I have a given trading strategy T and say 3 assets in my universe. The hold time is one day. The trading strategy can general signals for the 3 assets in any given day (so signal can trigger for any one or all 3). In case the signal is generated for more than one asset, the goal is to find the optimal capital allocation between the two (or three) assets, according to "some" criterion". One criterion could be minimizing overall return variance where return is the yearly return of the strategy say.

We are given historical OHLC data for the 3 assets. So it is possible to compute daily return series, and the variance/covariance between the returns across the 3 assets.

In general I want to apply mean variance to the problem but am a bit confused when it comes to treating the dynamic nature of the problem (its not as simple as optimizing a portfolio of assets). The signal generation is conditioned on some events being true so its stochastic. I can set up a backtest and compute the realized returns (keeping weights on the assets unknowns, in days where signals came for two/three assets say).

I am curious if someone can help structure the problem or drop some pointers to set it up. Is this in the camp of Stochastic dynamic asset allocation?

Answer 1

You should start looking at Merton's Portfolio problem. A lot of papers elaborated on the top of it. The principle is "simple":

• optimize the allocation between one risky asset (Brownian) and a riskless one;
• such a way you maintain a portfolio from which you consume money (for instance to pay some expenses).

The main result is the optimal allocation is the same as Markowitz one. It is probably why people did not focus that much on it. Nevertheless as soon as you change assumptions, you obtain very interesting results, like for instance in On portfolio optimization in markets with frictions.