# How to backtest a strategy with irregular in-out signal?

Hi I'm currently backtesting an event-driven strategies. Unlike factor strategy which has a regular rebalancing interval, event-driven strategy is conducted whenever there is an event. Since we do not know how many signals would pop up in the future in the past timepoint, I defined unit position size per one in-out betting.

I think there can be 2 possible ways to backtest such strategy.

1. (I think this would be a common case) Align every event-driven signal into one single timeline and check the mean return of the event. For example, if I want to test buyback event driven strategy, regardless of the announcement of the buyback event, set announcement date as 0 and last holding moment as 20 (1-month holding strategy, for example). And average the returns per day and check how long does buyback alpha persist from the announcement date.
2. (This is the case where I get confused) I want to calculate cumulative return of this strategy. (Final amount of money I can earn by conducting this strategy) However, since there is no fixed seed money at the very first time of the backtest, how can I calculate the return? Currently, I'm tracking
• unrealized return(evaluated return)
• realized return
• unit position price(number of currently held position * unit position size)
• unit position price averaged

and final return is calculated as (unrealized return + realized return) / unit position price averaged. But is it right way to calculate cumulative return of such strategy? How can I backtest cumulative return of a strategy without fixed seed money but flexible in-out position?