Hedge ratio with non-whole betas

External question — Quantitative Finance Stack Exchange Author: CL40 Original post: https://quant.stackexchange.com/questions/42435 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. Pardon me if this is a simple question but it has been a while since I dealt with this. Last time was in my quantitative investment class. Let's suppose I have a couple highly correlated instruments $X$ and $Y$ . I would like to hedge these. The simplest way would be to run a linear regression on them. Suppose the result is: $X = .35Y + \epsilon$ To hedge this, I would need to buy $1$ $X$ and short $.35$ $Y$ . I dont know any brokers that will allow me to do this! If I take the floor of $\beta$ I get $0$ . So that won't work. If I take the ceiling I get $X = Y$ which will not be hedged correctly. In fact, it will be off quite a bit (though this may be the answer for something with a $\beta$ closer to a whole number). Mathematically I could also long $1/.35 = ~3.8$ $X$ and get the same result. This time taking the ceiling of $3.8$ gives me $4$ . Not perfect, but it doesn't allow much to slip. Is there a hard and fast rule to this? I vaguely remember my professor telling us to "just get the nearest whole number" but I don't exactly remember the entire discussion around it.

External answer — Quantitative Finance Stack Exchange Author: Bob Jansen Original post: https://quant.stackexchange.com/a/42436 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. This is only a problem with small numbers and even small (smart) retail investors would not buy one share or one index tracking ETF (because of fixed transaction costs). This problem disappears almost entirely if you buy 10.000 of something.