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.