Correlation between your signal and future returns is an important metric in quant trading. But what is a “good” correlation? Here’s a simple way to think about it.
We’ll use a simple model where future returns y over some time period tau are normally distributed with a mean of beta * x and a daily volatility of sigma (here x is a signal with std deviation 1)
We can easily work out the correlation between signal and returns and use that to express beta as a function of correlation, volatility and forecast horizon.
The key insight is that it should be easy to find signals that are not profitable if you take trading costs into account, since you won’t be able to action them anyway.
If we require that even a three standard deviation signal is unprofitable then we can bound the correlation —
What does that tell us? Say that we are interested in a stock with 3% daily volatility, trading cost of 5 bps and a forecast horizon of one day. Then we expect to easily find signals with a correlation of 0.5% with future returns
If we use factor hedging to remove non-idiosyncratic risk, we might halve the volatility and double the cost to trade (since we need to trade the factor hedge as well) so we expect to be able to easily find signals with 2% correlation with future idiosyncratic return.
Alternatively if we are trying to predict a short term (1 minute) fx return which costs 0.2bps to trade and has a daily vol of 0.3% then we expect to easily find alphas with a much higher correlation of 8.5%
You can think of these as absolute minimum correlations, you need to exceed these to be able to trade profitably. As a rule of thumb, a correlation which is 1.5x the minimum would be ok (you will have a trade to do in about 5% of periods) and 2x the minimum is very good (you will be able to trade 20-30% of the time)
This is one of the many ways that you can extend the law of active management to be more relevant to real world trading, a topic for another time maybe.
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In quant firms, proprietary signal research can uncover new, idiosyncratic alphas (which causes firms to decorrelate). But over time these ideas diffuse (researchers and PMs move between firms and take ideas with them) which causes them to correlate and crowd into the same names.
Use of the same “alternative” datasets also causes quant firms to converge, even more so now that many firms use data brokers to source new datasets (and the brokers will give little nudges like … “we’re seeing a lot of interest in this dataset, maybe you should take a look”)
Does the profitability of vol selling strategies depend on starting volatility level?
A short story.
We start with front month VIX futures beginning in 2005, shortly after the contract was launched, so ~20 years of data.
For each day, calculate the P&L from shorting one futures contract. By working in price space we ignore any issues from from calculating VIX returns.
Every 21 days, sample the starting VIX level, and calculate the P&L from being short one near-term contract, assuming we roll over to the next contract at expiry.
This means that we have a dataset of non-overlapping sample P&Ls with ~1 month holding period.
Many mistakes here, including confusing gross and net returns, and not understanding the the fund mostly paid out profits as a dividend, so you couldn't compound.
So if you invested $10,000 into Medallion at the start of 1988, how would you *really* have done after 30 years?
It's pretty easy to figure out, since the net returns are listed along with the fund size at the end of year year, so we can approximately know how much capital was allowed to remain within the fund and how much was returned.
Assume that if the fund size grew by more than the net return, then all capital remains within the fund. Otherwise assume that the difference was returned as a dividend and invested into treasuries.
A couple of people asked how to price this bet. As a reminder the bet Peter offered was 5-1 against that BTC/USD would hit $100,000 before the end of the year (i.e. he receives $20,000 if Bitcoin hits 100k, and he pays $100,000 if Bitcoin does not hit 100k)
Intuitively that seems mispriced, but how can we sharpen that up a bit? Let's convert it to a derivative contract. The bet (from Peter's pov) is equivalent to paying $100,000 to buy a contract that pays out $120,000 if BTC/USD hits 100k.
This is a "one touch digital option" -- digital because the contract either pays a fixed amount or it pays nothing, and one touch because the price doesn't need to finish the year above the strike, it only needs to touch the strike once.
I feel like some people talk about quantitative/systematic/automated trading as if they are all the same thing, which is not true, and blurring these lines causes confusion for people who want to enter the industry.
“Automated” trading (contrasted with manual trading) is the simplest to understand. If the strategy doesn’t require any human input as part of its execution, then it’s automated. If there is a human in the loop then it’s not automated.
(Though of course there is a bit of a spectrum and semi-automated or “grey box” trading is very popular at firms like Jane Street or Optiver)