How do MMs calculate Sharpe
I know there are a lot of MM PMs on here who are more experienced with this topic than me, hence my seeking wisdom.
If, for example, an SPM at MLP told me they ran a 2 sharpe last year on 10% returns, is it the case that this refers to a "simple" (zero risk-free rate, assume daily returns are IID) annualized Sharpe? I.e., the way to think about this is that, if I had a single time series of their daily returns, that looked something like +0.05%, -0.02%, +0.1%, -0.05%, etc... (with an n of 252, let's say, per convention), that the time series of returns would have a mean of +0.039%, and a standard deviation of about 0.31%, so that, in this calc, my "daily" sharpe is about .126, and I annualize it straight up by multiplying by sqrt(252) to get to an "annual" sharpe of 2 (on annualized returns of 10%, and annualized vol of 5%)?
If not, is there a different way to do the calc / are there different assumptions made when quoting a "Sharpe"? (That is, are there corrections for interest rates, autocorrelation, or anything else?)
And also, just to take the question a bit further / as an aside, given that mean and standard deviation, if daily returns were approximately normally distributed, is it the case that (just plugging in the values above), the chance of a down 1% day for this PM is (actually) 1 in 2500 trading days? (calculated by taking a z-score of -3.35) In other words, someone running a 2 sharpe on 10% returns, would have a 1% down day, once every 10 years?
Or is this where we'd say "no, it happens much more frequently than that, owing to the non-normality / non-IID nature of returns / owing to some other factor?
As a back of the envelope, how often would a PM running this type of performance expected to be stopped out (at a 5% max drawdown limit)? (I have run sims in Python, but I'm curious if those who have "lived it" have a way of thinking about how to translate these sorts of metrics to drawdown risk).
Based on the most helpful WSO content, here's how MMs typically approach Sharpe calculations and the nuances involved:
Sharpe Calculation Basics:
Your Example:
Adjustments and Assumptions:
Probability of a Down 1% Day:
Drawdown Risk and Stop-Outs:
In summary, while your outlined approach to calculating Sharpe and assessing probabilities is solid, real-world deviations from normality and IID assumptions mean that extreme events and drawdowns occur more frequently than theoretical models suggest.
Sources: Longevity of Hedge fund career: how long do people last in this industry?, Performance of the best PM’s at MM’s?, Random Thoughts on the HF Industry, Is the Multi Manager HF Experience Worth It?, Is the common view of financial risk completely wrong?
This is an amazing question. Bumping and following
following, good question
Interesting, I have no clue, but wouldn't be shocked if the statistics were applied incorrectly for self-marketing and ego purposes. Regarding the second part, I guess the PM typically wouldn't maintain their 2 Sharpe consistently over 10 years?
"Non-Normality: Financial returns typically exhibit fat tails and skewness. Some managers use modified measures like the Sortino ratio (focusing only on downside volatility) or Conditional Sharpe (accounting for tail risk)."
"Risk-free rate: Some practitioners subtract the risk-free rate from returns, which would lower the Sharpe if applied." ==> 4% risk free rate means the 2.0 Sharpe goes down to 1.2
"Drawdown risk is higher than Gaussian models predict due to non-normal return distributions and path dependence."
Just following / nothing insightful to add, but quant.stackexchange might be your best bet, some of those guys on there are cracked w.r.t questions like this
Not familiar with the exact MM calculations for Sharpe but I would almost never rely on the normal distribution for calculating several standard deviation probabilities in finance. The entire stock market has much fatter than normal tails and individual stocks/other financial products usually have even fatter tails than that so when applied to a portfolio it's highly likely the daily return distribution has fat tails as well as the correlation structure can also shift on these volatile days. For products with liquid options you can take a look at volatility surfaces to get a sense of implied vol across prices which implies non-normality if the implies vol is not constant (although there are also some supply/demand effects in options prices). For portfolios even ignoring intraday trading I don't think it is easy to theoretically estimate extreme values of the daily return distribution but several standard deviations events are almost certainly going to occur more frequently than implied by the normal distribution.
I think the question is not "how should it be done", but "how do pods/MMs actually do it"
You would generally assume a risk-free rate of 0% if you're at an MM because you can't actually earn the risk-free rate on your capital.
MM PMs are all trading on levered capital and therefore need to pay the borrowing costs on that capital. For example, I cannot just buy 1y US bills and earn ~4% on my 200m capital and get paid 25% on my 8m PNL at the end of the year. I have to pay the borrowing costs in the form of repo to be long those bills which basically offsets the yield. Given there is no risk-free rate to earn as an opportunity cost, it doesn't make sense to subtract it.
I have seen a lot of marketing pitches from top funds, and I’m pretty sure a lot of them use Monthly standard deviation when calculating Sharpe, which is the minimum required by GIPS if you remember that from your CFA exams. All of these decks have 5 pages of endnotes, so it should be disclosed there. Just like PE gets criticized (correctly) for understating volatility through its infrequent and subjective reporting, I am not aware of a lot of hedge funds marketing off a Sharpe derived from daily standard deviations (although there probably are some that do).
There are 2 distinct, but related things you're asking about: the mechanics of sharpe calculation, and inferences you can make from that calculation.
The calculation is just like you described. It is easier to use returns as opposed to dollar pnl numbers as allocated capital/book size can change over the course of the year. Usually GMV or allocated GMV is used as the denominator and dollar pnl is the numerator. You get your daily returns and compute sharpe as you described.
They track on both a daily and monthly basis for different purposes. Risk and the business verticals might use daily to monitor pod perf for risk and drawdown, and possibly payout purposes. For LPs the sharpe might be reported from fund level monthly returns. For individual pods, they are already trading on levered dollars so you can kind of assume that each pod has the same "leverage", i.e. the fund's overall leverage and, insofar as that doesn't change too much (which it usually doesn't), it doesn't really matter (since sharpe is leverage invariant).
As for inferences from sharpe - you are correct under assumptions of iid (like you said) but also, importantly, noramality. Return distributions in money managers are notorious non-normal with usually positive skew and fat tails. So make and inferences assuming normality at your own peril. Payout tiers can be tied to sharpe but the business/risk still know not to make confident "probability of x event happening" inferences using sharpe.
Thanks. I appreciate that - I agree with your splitting the question and appreciate the confirmation that the calculation is as described (and agreed re using daily returns in percentage space rather than in dollars space, and the nuance re daily vs. monthly returns.)
Agreed as well that the inferences don't work in practice for the reasons you describe. I guess I'm curious in practice if anyone has good data on what the empirical blow-out probabilities are like / empirical expected-lifetime-of-a-PM is. The other problem (which someone described) is that one might expect Sharpe to "decay" right before a blowout (even if that's a bit "convenient" as a way of explaining the blowout).
The returns are not only non-Gaussian but are correlated. There is an old paper by Andrew Lo, "The Statistics of Sharpe Ratios" that discusses these issues and has a correction factor to account for the correlation. But I don't think any big firms use this, as it makes the sharpe ratios lower and nobody wants to report a lower number for their own fund.
OP here. Thanks! Yes I'm familiar with and have read that paper.
My question truly was more trying to understand what calc people are doing when they say "I run a 2 sharpe book" - multiple actual SPMs at MLP have said this exact phrase to me (with a different number than 2), and I was curious what those people meant - i.e., what internal calculation was being performed.
Your answer is very helpful - I appreciate that, in fact, they are probably just running the no-autocorrelation number, in practice, and that I could replicate their calculation using the simple procedure described.
if it's a MM, they are quoting their annual return on GMV / their annualized vol calc'd daily. other poster is correct that funds will sometimes use monthly vol, but a MM PM is going to be quoting daily # since thats what they're looking at.
you don't adj for risk free rate bc MM PM's dont get paid rf as a baseline, bc they dont collect short borrow on first turn of leverage (whereas technically a SM running 200 gross / 0 net should be taking out rf since they are getting paid that). their pnl is just based on their L/S spread
for the -1% daily move -- people have rightly pointed out the power law distribution effects. market index (ie. SPX) returns under normal distribution would imply a 3 sigma event every ~1.5 yrs (370/252), whereas in reality a 3 sigma event happens every ~3 months. for MM portfolio returns, it's even more extreme bc you're running 80+ idio and 40% of idio vol is during EPS. if you use a t distribution with 3-5 degrees of freedom the p% of a -1% move given 5% annual vol goes up to 0.5% (implying 1.3x/yr) - 1.2% (which would imply 3x/yr)
on the 5% drawdown, it's same math but even more extreme bc now you have cumulative effects in prob distro to account for. so by definition if annual vol = 5%, then over a year a 5% drawdown is a 1 sigma event. but intra yr it is higher bc that 1yr number has +/- daily returns. the general point here is that we have a behavioral bias to underestimate degrees of randomness. empirically, even under a normal distribution, the rule of thumb is if vol = x%, prob of x% drawdown under normal distribution is ~40-50%. take a look at SPX annual vol vs max drawdown by year, lines up pretty well with this. when you move to fat tails, depending on assumption of how extreme that goes to 60-80%. which is why good PM's know when to cut risk early (and why the risk mgmt overlords will do it for you when you're 1/2 way there; also prob why avg PM breaks even)
Thx
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