# Buying at highs and lows: Thinking in Probabilities

Mining past returns of the MIDCAP 100 index, if you invested for 50 days, the probability of returns greater than 10% is 32% and the probability of returns greater than 15% is 18%. On the flip side, over the same holding period (HP,) the probability of returns lesser than 0% is 35% and the probability of returns lesser than 5% is 52%. These data points are the first row of the following tables:

Suppose you want to hold for 50 days, then to maximize your returns, you will have to buy at the 500-day low to have an even shot at making a return greater than 10%. The better outcome would be if the holding period were to be extended to 200 days. At which point the probability of even making less than 5% is very low and that of making more than 15% is more than 80%.

Using this table, one can lookup the odds of different holding period returns at different highs and lows.

Code is on github.
Related: Highs and Lows

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