Knowledge Snippet

What is a factor?
I feel I never quite understood this idea until I started trading them very actively.
Factors are not anything special, they are just important alphas - NOTHING MORE.
You use factors to say:
Hey these alphas explain a large chunk of the variance and I don’t want to find them again. In crypto that might be a momentum factor so to avoid finding 20 versions of the same effect we use a xs regression to remove our momentum feature from returns and can then test against specific factor returns (returns minus the returns explained by factors basically).
The first factor is always the market, so in equities we take the beta to the S&P500 and then remove the return of the S&P * beta from the asset. This gets the idiosyncratic return. From here we can further remove factors.
In the end, a factor is just an alpha you think explains lots of the variance, there’s nothing “fundamental” or special about it other than that it’s very core to a lot of the things you find.
Alphas depend on what you research. If you are researching HFT and are predicting 1 min ahead you can still have factors. The best known is orderbook imbalance. As I said, a factor is just an alpha which explains lots of the variance and it’s well known that orderbook imbalance is a lot of the variance much like past ret * -1 is a lot of the variance for 1h timeframe. It’s also an alpha you’ll often accidentally find. In the HFT context it’s not like orderbook imbalance explains any risk adjusted returns, it’s simply an effect we’ll often find in our other alphas so hence its important to factor out of returns so we don’t confuse factor exposure (read as factor exposure = alpha we already found) for new alpha.
If you multiply the positions vector to the specific factor returns vector then you’ll get a flat line for an orderbook alpha since it’s already explained but a great line for idiosyncratic or raw returns — basically it shows you the performance in excess of what you know! Really useful!
They also are used for portfolio construction as a regularisation technique and few more applications but I want to explain that alphas and factors are really not that different. Factors are just the ones that we believe the most in and explain the most variance (and are at the biggest risk of being found in other alphas).