Estimating Beta: Log or % Returns?

Almost all calculations in finance involve using log returns rather than % returns. There are a number of reasons why log returns are preferred. Estimating beta doesn’t seem like a special case.

But when you go through the math, something doesn’t quite add up.

Because we want to zero out market risk, so want to solve for such that is no longer in the equation below.

After going through this, the math quickly gets very messy.

If we use % returns, the math is alot cleaner.

After some basic algebra, we find that .

Indeed beta should be calculated using % returns.

So there you have it. Time to change some code.