# Is intra-forecast-horizon rebalancing suboptimal?

Suppose that I have forward 1-month forecasts of returns that are updated daily. Is it suboptimal to rebalance more frequently than 1-month (e.g., daily or weekly)? Theoretically, if I forecast the stock to return 1% over a month, I will only realise the 1% (on average) if I held the stock for 1 month. If my forecast is noisy and I rebalance at a higher frequency than my forecast horizon, then I can think of a scenario where I pre-maturely sell the stock because of noise. If this is true, what would be the optimal rebalancing frequency?

#### "Is it suboptimal to rebalance more frequently than 1-month (e.g., daily or weekly)?"

This depends on the situation. On one side, if you rebalance your portfolio on a daily basis you will update the views of the portfolio more frequently and thus will (on average) be closer to your target metric over time. Generally, incorporating more (non-noisy) information into your forecasting model yields better predictive accuracy.

On the other side, rebalancing less frequently is a good way to cut costs, that can significantly hurt your annualized performance. If you have high transaction costs (or other additional hidden fees) associated with your financial products, it is usually more favourable to rebalance less frequently.

#### "[...] then I can think of a scenario where I pre-maturely sell the stock because of noise."

From your question, I assume that you have a $$h$$-step ahead forecast model $$f_{t+h}(r_t^d ; \theta)$$ with a parameter-set $$\theta$$, that is estimated on a daily return process $$r_t^d$$. Furthermore, I assume a fixed window-length of 1 year (252 days).

If you have estimated monthly forecasts by sparsely sampling your return process and thus calculated the 1-step ahead expectation, $$\mathbb{E}_t\left[f_{t+1}\right(r_{t}^m ; \hat{\theta}\left)\right]$$, then your monthly forecasts might contain less noise because: the model only use 12 monthly data-points to estimate $$\hat{\theta}$$ as opposed to 252 days (assuming no stability issues) and the noise inherently found in the daily sampled returns might diminish when considering monthly returns.

Also be aware that rebalancing on noisy estimates will not only create scenarios where you pre-maturely sell the stock, but also where you might unwantedly overbuy the stock.

#### "If this is true, what would be the optimal rebalancing frequency?"

The optimal rebalancing frequency depends on a few factors:

• Is the noise in reality a repeated pattern that your forecasting model is not accounting for? In this case, there might be some hidden features in your data that you are unaware of. A deep-dive investigation into your data, might uncover a new predictive pattern. Incorporating this into your model will increase its predictive accuracy and reduce the noise, which in turn, provide better portfolio weights. If this is the case, then going for a daily rebalancing scheme is favourable unless:

• The friction cost of rebalancing is high. Transaction costs, overnight-costs, slippage etc. all reduce your annualized performance of your trading strategy. If the costs are high, then rebalancing less often might be ideal.

In the end, it is best to do your own analysis: Do a backtest where you compare different rebalancing frequencies under different cost schemes. The increased annualized performance from daily rebalancing might diminish completely when considering a conservative cost scheme, and as such, a monthly rebalancing frequency is better (and vice versa). The paper of DeMiguel, V., Garlappi, L., & Uppal, R. (2009) is a good read on how to implement a generalized transaction cost scheme using portfolio turnover.

I hope this provide a bit of insight.

• This is a good overview of an issue that will in practice require a lot of detailed analysis to solve. Aug 28, 2022 at 7:38
• Thanks very much on your detailed response. This is spot on --- the feature set contains a mix of daily (e.g., price) and quarterly (e.g., financials) updated features. If the feature set only contains quarterly information then I won't be concerned about this. The question came about from an argument with a colleague and I was wondering if there's already a theoretical framework on this. Will have a look at the DeMiguel et al. (2009) paper. Thanks again. Aug 28, 2022 at 10:01