# How to compute daily compounded backtest returns closer to real-world results?

I often run quick tests of trading strategies in my analytics suites by:

1. multiplying a vector of signal (lagged, {-1,0,1}) with a time series of daily percentage returns
2. doing a cumulative product of the resulting time series after adding 1 to each return

This is fairly standard but to be clear:

$$\text{NAV}_i = \prod_{ j = 1 }^i (1 + r_j)$$

When I have many assets, I do the first step on each return series, then element-wise sum, and then the second step.

Having run such strategies with real money, I know that the implicit assumption that the portfolio will be rebalanced to constant exposure relative to each day's NAV is unrealistic.

What I would like to know is:

• Does anyone have any other issues with this approach for running backtests? Particularly for multi-underlying strategies?
• To "make" the strategy trade on a monthly basis, would it be sufficient to sum daily returns intra-month (so that there is one summed-up return for each month) and then do the cumulative product in step 2 on the series of these summed returns?