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Lets say I have 2 time-series, how would I standard beta hedge them against each other? For example, what if the position in 1 timeseries is 100 shares at 16 USD per share. Another time-series is 25 USD per share. Covariance of the two is 50 and the standard deviation of time-series 1 is 5 and of time-series 2 is 7. So I know that:

`beta = Cov(ts_1, ts_2)/(SD(ts_1)*SD(ts_2)) beta = 50/(7*5) beta = 1.428 `

How would I determine the position of ts_2 that I should short?

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To standard beta hedge you would make your positions dollar values inversely proportional to their Betas. So if your standard position is 1000 USD long vs 1000 USD short when the Betas are 1, then you would have 909 long vs 1000 short when the betas are 1.1 and 1. In general $1000//beta_1$ long of security 1 vs $1000//beta_2$ short of security 2..

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