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Problem 1

Momentum model with a window of 3 months and a reversal of 1 month. Long: top decile (equal dollars) and short bottom decile (equal dollars). Equal dollars means that each of the stocks in the decile is long or short the same amount. Since you have 50 stocks, the top decile will be 5 stocks and the bottom decile will be 5 stocks.

Problem 2

Add diversification. Instead of being long the top decile, be long the top half. 25 stocks long and 25 short.

Problem 3

Back to top and bottom deciles. However, instead of weighting equal dollars, weight each stock in the long and the short by their volatility over the previous 50 days, so that the long and the short have the same volatility (you choose some arbitrary number like 5% if you need).

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