Position Sizing with Forecasts and Transaction Costs
Summary
The document examines how to choose a position when forecasts provide expected returns and volatility over multiple future horizons. It starts with the growth-oriented rule of sizing in proportion to expected return divided by variance, then considers applying that rule daily when forecasts are available. A transaction cost on position changes makes frequent resizing expensive, creating a need to account for the cost of trading and the forecast horizon.
One proposed approach compares forecast Sharpe ratios across future bars after incorporating transaction costs, then selects the horizon with the highest ratio and sizes using that horizon’s expected return and variance. The text frames this as a question rather than a validated solution: it gives no simulation results, cost model, or derivation showing that selecting a single horizon is optimal. Forecast error, the path of future position changes, and how costs accumulate remain unresolved considerations.
Key ideas
- Growth-oriented sizing scales exposure with expected return divided by return variance.
- Daily resizing from forecasts can become costly when each position change incurs transaction costs.
- The proposed heuristic compares transaction-cost-adjusted Sharpe ratios across forecast horizons.
- The selected horizon’s expected return and variance then determine the suggested position size.
- The document poses this as an open problem and supplies no evidence that the heuristic is optimal.
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Full text
# Optimal Position Size with Transaction Costs given Forecast Mean and StDev # Optimal Position Size with Transaction Costs given Forecast Mean and StDev I have rather a challenging question. I'm hoping that someone can share their experience. I will build up the problem in steps. Let's start our thinking with the idea of a buy and hold strategy of an stock whose returns are expected to be 10% (annualised) in excess of the market and a standard deviation of 20% (annualised). If we have £1000 to invest, Chan suggests an optimal leverage to maximise expected growth of mean/stdev^2 = 0.10/0.04 = 2.5 times. In other words we should borrow £1500 to invest along with our £1000 in order to get the best growth. Yes there is a chance that this may blow up so in reality we may choose a smaller multiple such as half of that. So far so good. Ok, so now let's consider the next step. We have just hired a guru quant who believes that each day he can provide an estimate of the next day's mean and standard deviation of returns. Assuming there are no transaction costs, it actually simulates well if we use our same formula of mean/stdev^2 to resize each day. Ok, next we discover that we need to pay a transaction cost of 2bp on any changes we make to position size. This condition actually changes things substantially. Clearly in this case we don't want to be chopping and changing our position size too much otherwise it will get expensive quickly. We think about the problem for a while and decide that in order to beat this, we need to look further into the future, not just at the next bar's forecast. We give our guru quant a payrise and he's able to now not just give us an estimate for the mean and stdev of the next bar, but also n bars ahead, all the way out to N days. Each day he gives us N mean predictions and N stdev predictions. The question becomes, how do we optimally size based on this information? One simple solution is each day to examine the mean and standard deviation predictions at each of N bars in the future. For each we calculate the Sharpe Ratio, ie mean/stdev, for each incorporating transaction costs and chose the highest. We then trade this in quantity mean/stdev^2 for that duration. Any ideas?
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