Hello,

I'm a newbie and I'm currently trying implement a basic algorithmic trading strategy using historical returns data for a range of equities and indexes. However, when I was reading Ernie Chan's 'Quantitative Trading' he states that

"*Unfortunately, we cannot trade on the mean reversion of returns.* "

I'm not exactly sure why this is. Is it because the returns do not necessarily randomly distribute around a mean of zero? If I only have historical *returns* data, does this mean I'm confined to a momentum-based strategy?

Apologies if this seems basic, however I'm new to this field and while I would feel more comfortable implementing a mean reversion type algorithm, I just want to understand why this is apparently not possible with the data I have.

No. you can't trade on mean reversion on returns. You buy/sell the asset under question. The returns are generally stationary. (Which implies they mean revert) Check that using Phillips-Perron test.

Now, to check if the means of the returns are 0, you would have to run a t-test to check if mu = 0.

Now based on the mean reversion, run a regression of returns that mean revert against the returns of indices as factor. Check that residuals are stationary and uncorrelated by using a box-ljung test.

What if your indices are correlated among each other? You could standardize the explanatory variables, or run a ridge regression instead since If the indices are infact correlated, (X^t X)^-1 might not exist.

You could perhaps then create a trading strategy based on the signals of the residuals.

Is this a pairs trading beta neutral strategy you are trying to implement?

I'm not sure if I answered your question correctly as I haven't read that book yet. But I assume that's what he meant by saying you can't trade on mean reversion on returns.