crnt2 · HackerTrans

10 ปีที่แล้วdiscuss

I don't think you really understand the Sharpe Ratio -

    Sharpe = E[Return - Financing] / StDev[Return - Financing]

You could only have infinitely high Sharpe if the standard deviation of your returns, minus your financing cost, is zero. That means that Return = Financing + Constant. Now, some people are able to achieve that because they have abnormally low financing (e.g. they are an insurance firm with a large float, or a bank which is able to loan money at a higher rate than it borrows) but for most investors, the only way to make that equation hold is if the constant is zero or negative.

Going long 3 month T-bills does not give an infinitely high Sharpe Ratio (if it did, everyone who could would lever it up and do it in large size).

As an experiment, I simulated holding a long position in the nearest to expire Eurodollar futures contract (which give a return similar to the 3 month T-bill return) and rolling every 3 months, which gives a Sharpe of 0.92, an annualized return of 0.65% and annualized standard deviation of 0.7%.

Similarly, a long position in nearest-month two year treasury futures contracts gives a Sharpe of 0.94 with 1.59% annual return and 1.67% volatility.

These are attractive Sharpes (better than equities!) but they are certainly not infinite, and to juice up the returns to anything approaching an equity investment you need to be looking at 5-10x leverage.

Your point about selling puts, with skewness/kurtosis risk which is not priced by Sharpe, is a fair one, and probably the most common method of gaming returns, but it is a side-issue.

crnt2

10 ปีที่แล้วdiscuss

There are strategies that rarely lose money and have a great risk-adjusted profile. But they are generally at least one of

a) Not scalable (e.g. most intraday market-making or scalping strategies)

b) Only available at a very high fee (think north of 3/30)

c) Not available at any price (e.g. Renaissance Medallion, which has been closed to outside investors for 20+ years)

So I'm not sure that it's particularly relevant to this discussion, which is about fee pressure on traditional, long-only asset managers.

crnt2

10 ปีที่แล้วdiscuss

The difficult part is getting regulated, and raising money.

Robo-advisers are subject to the same regulation as traditional asset managers - a regulatory burden which is only likely to increase over time. The legal fees associated with regulation are not cheap.

Compounding the problem, a competitive robo-adviser needs to offer lower fees than a traditional asset manager. Probably they need to be in the 0.25-0.5% range, which means that for each $1m under management they are picking up $5,000 of revenue. Out of that they need to pay salaries, infrastructure costs, legal costs, rent, taxes etc. Let's be conservative and say that these costs are $2.5m per year. That means that a robo-advisor needs about $0.5bn under management before it begins to turn a profit.

I don't think it's really suitable as a side project.

crnt2

10 ปีที่แล้วdiscuss

I made an attempt to do this elsewhere in the thread, take a look at

https://news.ycombinator.com/threads?id=crnt2

The result - the factor is actually surprisingly large!

crnt2

10 ปีที่แล้วdiscuss

Here is my attempt to work through the math and figure out how "surprising" this result is.

Clearly, we should expect that for small primes (< 100e6) it is less likely that a prime ending in K (in base B) will be followed by another prime ending in K - because for that to happen, none of the B-1 numbers in between can be prime.

A (very naive) model of the distribution of primes says that every number n has probability p(n) = 1/log(n) of being prime. Assume that a number n ends with a k in base b. Define p = 1/log(n). Then the probability that the next prime ends in k+j is, roughly,

  q(j) = p * (1-p)^(j-1) * sum_{i=0}^{infinity} (1-p)^(i*b)
       = p * (1-p)^(j-1) / (1 - (1-p)^b)

In this formula, j takes values 1 to b (where j = b represents another prime ending in k).

For n ~ 1,000,000 and working in base b, under this model we would expect to see around 6.97% of primes ending in k followed by another prime ending in k, whereas we expect to see 13.7% of primes ending in k+1 (it is apparent how naive the model is, since in fact we never see a prime ending in k followed by a prime ending in k+1, except for 2,3). It would not be hard to extend the model to rule out even primes, or multiples of 3 and 5, but I have not done this.

Around n ~ 10^60 the distribution starts to look more equal, as the primes are "spread out" enough that you expect to have long sequences of non-primes between the primes, which blurs out the distribution to be roughly constant.

I think this is what the article is getting at when it quotes James Maynard as saying "“It’s the rate at which they even out which is surprising to me". With a naive model of 'randomness' in the primes, you expect to see this phenomenon at low numbers (less then 10^60) and for it to slowly disappear at higher numbers. And indeed, you do see that, but the rate at which the phenomenon disappears is much slower than the random model predicts.

I think that is why it is surprising.

crnt2

10 ปีที่แล้วdiscuss

Miscalculation - obviously no primes end in 0 (base 11) so I should have said "10% as you would naively expect".

I take your point about primes being closely packed at low numbers, but I think this is a small correction (i.e. you might expect 8-9% of primes ending in 2 to be followed by another prime ending in 2, but certainly not <4%)

crnt2

10 ปีที่แล้วdiscuss

The results are particularly striking in base 11 - looking at primes below 100 million, only 4.3% of primes ending in 2 are followed by another prime ending in 2 (compared to the 9.1% you would naively expect) with similar numbers for other pairs.

A prime ending in 2 (in base 11) is also unlikely to be following by a prime ending in 5, 7 or 9, whereas it is particularly likely to be following by a prime ending in 4 or 8.

It would be interesting to know what structure there is (if any) in this NxN "transition matrix" for various bases.

   1: ( 1,  4.3%) ( 2, 13.0%) ( 3, 14.3%) ( 4,  7.7%) ( 5, 11.5%) ( 6,  6.3%) ( 7, 18.0%) ( 8,  9.0%) ( 9, 10.7%) (10,  5.2%) 
   2: ( 1, 10.0%) ( 2,  3.7%) ( 3, 11.3%) ( 4, 14.1%) ( 5,  7.5%) ( 6, 12.1%) ( 7,  5.3%) ( 8, 17.5%) ( 9,  7.8%) (10, 10.7%) 
   3: ( 1,  6.1%) ( 2, 10.3%) ( 3,  3.7%) ( 4, 12.5%) ( 5, 14.0%) ( 6,  9.2%) ( 7, 12.1%) ( 8,  5.6%) ( 9, 17.5%) (10,  9.0%) 
   4: ( 1, 11.1%) ( 2,  6.1%) ( 3,  9.9%) ( 4,  4.1%) ( 5, 11.5%) ( 6, 14.5%) ( 7,  7.7%) ( 8, 12.0%) ( 9,  5.3%) (10, 18.0%) 
   5: ( 1,  9.6%) ( 2, 12.7%) ( 3,  6.3%) ( 4, 11.5%) ( 5,  4.0%) ( 6, 13.6%) ( 7, 14.5%) ( 8,  9.2%) ( 9, 12.1%) (10,  6.4%) 
   6: ( 1, 17.9%) ( 2,  8.5%) ( 3, 10.6%) ( 4,  5.0%) ( 5,  9.6%) ( 6,  4.0%) ( 7, 11.4%) ( 8, 14.0%) ( 9,  7.5%) (10, 11.5%) 
   7: ( 1,  6.0%) ( 2, 19.1%) ( 3,  8.8%) ( 4, 11.1%) ( 5,  5.1%) ( 6, 11.6%) ( 7,  4.1%) ( 8, 12.5%) ( 9, 14.1%) (10,  7.7%) 
   8: ( 1, 12.0%) ( 2,  5.5%) ( 3, 17.5%) ( 4,  8.8%) ( 5, 10.6%) ( 6,  6.3%) ( 7,  9.9%) ( 8,  3.7%) ( 9, 11.3%) (10, 14.3%) 
   9: ( 1,  8.8%) ( 2, 12.4%) ( 3,  5.5%) ( 4, 19.1%) ( 5,  8.6%) ( 6, 12.7%) ( 7,  6.0%) ( 8, 10.3%) ( 9,  3.7%) (10, 13.0%) 
  10: ( 1, 14.3%) ( 2,  8.8%) ( 3, 12.0%) ( 4,  6.0%) ( 5, 17.8%) ( 6,  9.6%) ( 7, 11.1%) ( 8,  6.1%) ( 9, 10.0%) (10,  4.3%)

crnt2

10 ปีที่แล้วdiscuss

This is explicitly ruled out in the article -

> Lemke Oliver and Soundararajan’s first guess for why this bias occurs was a simple one: Maybe a prime ending in 3, say, is more likely to be followed by a prime ending in 7, 9 or 1 merely because it encounters numbers with those endings before it reaches another number ending in 3. For example, 43 is followed by 47, 49 and 51 before it hits 53, and one of those numbers, 47, is prime.

> But the pair of mathematicians soon realized that this potential explanation couldn’t account for the magnitude of the biases they found. Nor could it explain why, as the pair found, primes ending in 3 seem to like being followed by primes ending in 9 more than 1 or 7.

crnt2

10 ปีที่แล้วdiscuss

The first three comments were all variations on "this isn't new" so let's take that point for granted, and see what else this article gives us.

It's not new that Wall Street is hiring Ph.D scientists and mathematicians (that's been happening since the 80s) but what's changing is the kind of role they are getting hired for.

From the 1980s up until 2005 or perhaps even later, most Ph.Ds were hired in "quant" roles, that is, to build mathematical models that could price and manage the risk of derivatives. They were generally not in trading roles.

More recently (i.e. in the last decade) it's common to hire Ph.Ds as traders - that is, to write algorithms that are used to make trading decisions. This requires a rather different set of skills - instead of being skilled in stochastic calculus, partial differential equations and numerical methods, the quant trader is skilled in statistics, data analysis, optimisation and machine learning.

It's true that Wall Street has Ph.Ds hired to build trading models for many years (e.g. Renaissance) but the change is that this is no longer an esoteric fringe pursuit. It is seen as standard that trading desks at investment banks will have a large number of quant traders. Large European investment banks have heads of trading who are quants. Quantitative hedge funds are no longer mysterious and exciting - many of them use well understood models that have been widely replicated across the industry.

To be honest, I am surprised that it has taken this long. Finance is so obviously suited to these kinds of quantitative methods that only an aggressive rearguard action by voice traders has been able to keep them at bay. The question is no longer whether quantitative traders and their algorithms will largely replace voice traders, but how long the voice traders will manage to hold out.

Jane Street is an interesting special case. From my (somewhat limited) interactions with them, they are neither wholly voice traders nor wholly algorithmic. Instead, their researchers and traders build algorithmic trading systems which can be "driven "by humans. For example, the system will continually calculate a set of useful metrics that a human trader uses to make a final buy/sell decision, and trade is then immediately executed by high frequency execution algorithms. Or the human trader decides to make a complicated spread bet (e.g. long an ETF vs. a cost-optimized basket of the underlying stocks) and the algorithm goes out to execute the basket as effectively as possible.

I think there's an interesting parallel to "Centaur chess" [0] where the combination of a computer and a human is much more powerful than either of them acting alone.

[0] https://en.wikipedia.org/wiki/Advanced_Chess

crnt2

10 ปีที่แล้วdiscuss

I think you misunderstood much of what tomp said, and willfully misinterpreted some of the rest.

The number of trades does not determine alpha, but it means that you can be much more certain about whether someone has alpha or not. For example, John Paulson made billions on (essentially) a single trade in 2007 and early 2008. Does he have alpha? It's hard to say, because all of those profits were from one trade, and he could have been lucky. Virtu Financial generates millions of dollars each year, by making tens of millions of trades. Do they have alpha? Absolutely - you can be certain of it, because it would be statistically impossible to get lucky tens of millions of times.

The idea "alpha becoming beta" is an extremely relevant one for many hedge funds today. As strategies become well known, they become commodified, and are often offered at a lower fee, both by hedge funds, ETFs and investment bank products. Frequently, they are offered for little or no performance fee, so they cannot be called "alpha" and are often referred to as "smart beta". For example, AQR Capital Management offers many low-fee funds giving exposure to value investing, momentum investing, managed futures, the FX carry trade and others. It sounds like you are using a very narrow definition of beta (exposure to the stock market) whereas the usage in the industry is much broader.

Pointing out that quant funds use "algorithms" to trade rather than "computers" is pointlessly picking holes. It's clear what he means.

crnt2

10 ปีที่แล้วdiscuss

That's not quite true. Scion was up in 2001 and 2002 (when the market was down) and they beat the market in 2003 and 2004 - in each of those years, they were primarily a long-only equity fund.

I'm not sure what the performance was in 2005. In 2006 they were down 16% (because of premiums on their CDS positions) which they then recouped in 2007 and early 2008.

crnt2

10 ปีที่แล้วdiscuss

I use MATLAB for 90% of my day to day work, for a combination of reasons -

1. Historically it is what has been used at my firm. We have a lot of code already written in MATLAB, interfaces to internal apis, external data providers etc. Everyone at the firm understands MATLAB code.

2. It really is very good for numerical work - both in terms of speed, and clarity of the code (much better than Python and R for clarity - probably on a par with Julia).

I also used KDB+/Q very heavily in a previous job. It is blazing fast in its domain (financial time series) and enables extremely rapid prototyping. The fact that it is a combined query language / programming language is very appealing for data-focused research. I wouldn't want to write a production system in it though (though I know people who have done!)

When I was studying for my PhD I wrote a lot of Fortran 77 and IDL. Essentially because my supervisor used IDL and had a lot of code written in it, and because we were using an external tool which consumed Fortran 77 files as input.