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Assume:

  1. You can't time the market bottom
  2. You have a finite amount of cash to buy equities
  3. There are P dip/bear periods you're gonna purchase the equity

2 Problems:

  1. You deploy too much cash early, you limit your upside because equities dip more.
  2. You delay or commit too little cash, you miss the rebound oppurtunity. Again you limit your upside.

I guess we could by stating that the bigger the magnitude of the dip, the proportianally bigger the cash deployment. The average amount of repeated 'bad' weeks(period) follow some kind of normal? distribution and could be from 3 - 5, with a mean of 4 for 6 week bear market.

So we have some kind of subset sum division problem. Suppose you have 100 units of cash. And you deploy it in 4 periods linearly such as 10+20+30+40=100. Can someone point me to a relevant paper or can we model such situation better? Maybe sub-quadratic splitting ? Or propability weighted splitting?

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