Coastal Quant
@coastal_quant
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Seasoned quant researcher.
New York, NY
Joined July 2015
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Player A and Player B play a coin tossing game where the person who flips more heads wins. Player A gets to flip a fair coin 20 times while Player B gets to flip 21 times.
What is the probability Player B wins the game?
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Given the a fair coin, what is the expected number of coin flips needed to get three heads in a row?
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Restarting my quant interview questions series, this time with a more stats focus than prob brainteasers.
I have a univariate linear regression y ~ X*beta with 100 observations. I accidentally load my data twice so now I have 200 observations. How does the beta estimate change?
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Hanguk's content is STELLAR. Excited to try this course and highly recommend to both novices and experienced traders.
QT201📔📔 Statistical Methods in Quant Trading (new quant lecture recordings)
I'm doing a giveaway for people who show some love to my work so...do your thang
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67% (!) of people chose 1/2, which is wrong ☠️
Intution would say knowing one of the children is a girl doesn't impact the odds of the other child's gender. This is wrong. We can see it by enumerating all the possibilities of the genders of the two children.
G - G
B - G
G - B
A woman has two children. I tell you one of them is a girl. What is the probabily the other child is a boy?
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A lot of great responses here and some did get the correct answer: Player B has a 50% chance of winning this game.
Didn't see a lot of great explanations, so here's an elegant one via symmetry. If A only flips 20 times while B flips 21 times, B must end up with either more
Player A and Player B play a coin tossing game where the person who flips more heads wins. Player A gets to flip a fair coin 20 times while Player B gets to flip 21 times.
What is the probability Player B wins the game?
44
5
72
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Two random variables X and Y have correlation 0. Are X and Y necessarily independent?
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A group of people wants to find their average salary on the condition that no individual would be able to find out anyone else's salary. They have no way to communicate except by speaking to each other. Can they do this?
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This gets an A+
@quant_questions
Not spectacularly shown work nor the most efficient, but 14 flips. Also included a snippet of Python code that runs 1M simulations of the scenario and comes to the same conclusion.
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I have two envelopes. Inside one I put some amount of cash (say $X) and in the other I placed twice that amount ($2X).
You can pick one envelope to keep. After you look inside, I give you the opportunity to switch envelopes if you’d like. Are you better off switching?
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What is the expected number of cards you need to draw to see an Ace in a normal 52-card deck?
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@quant_wiz
I started with n=100 and k=1,2,3 to build intuition. The expected value of k rolls depends on the expected value of k-1 rolls and you can use this to determine what to do depending on the outcome of the kth roll (stop or keep rolling) and probability you take each decision.
My
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@ecamupdate
@alphaarchitect
@alphaarchitect
What's going on here? BOXX was supposed to not generate dividends, it's why almost everyone bought it over SGOV. If it pays dividends going forward, might as well switch to SGOV for the true risk-free return
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Going to start sharing questions commonly asked in quant finance interviews. If anyone has topics they'd particularly like to see covered, let me know. I'm a current quant with many years of experience in the industry.
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@harodihg
All coin flips are independent - A's flips don't impact B's. Your line of reasoning is the Gambler's Fallacy, see below:
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How many trailing zeros are there at the end of 100! (100 factorial)
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@lecPokrandt
Althought I appreciate the resourcefulness, this is actually wrong!
@OpenAI
here's a bug test for you :)
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@macrocephalopod
Which is why I post some daily for people to practice! These questions are still VERY commonly asked
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@__paleologo
@AffectiveAutism
Crowding is tricky - I can imagine at a lot of “lesser” funds a large part of their alpha can be attributed to crowding and orthogonalizing to that factor removes a big portion of their alpha.
It’s probably really difficult for a PM to naturally construct a crowd-neut book.
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@theodoore__
@__paleologo
You need to be careful about roles in risk.
First and foremost, you need to make sure you're doing risk RESEARCH and not simple monitoring/operations.
Second, your work needs to feed directly into investing decisions. That's how you know you're valued.
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@__paleologo
The Embedded Leverage paper by Frazzini is a great behavioral explanation of the anomaly
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@nope_its_lily
Not to mention that retail traders actually get pretty good execution on market orders because of price improvement from PFOF... large players need to spend a ton of time on slippage/impact analysis while retail gets amazing execution
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@0xfdf
Slightly off topic but from previous posts I understand you're a quant PM? I'm curious how much you think about risk modeling/management day-to-day vs. pure alpha research.
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@SahilPuri2310
@__paleologo
Are you saying apply mktcap filter and then equal-weight in the XS regression? Highly volatile megacaps (TSLA, NVDA) pass the filter but will implicity carry huge weight in the regression - you can see this if you try to estimate the industry ret of semis/tech without them
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@tickwide
The key to not lifestyle inflating is living as if that annual bonus didn’t come.
However the advice in this situation would be to use the bonus to pay down principal assuming your rate is higher than the current risk-free. Saves you more money in the long run and avoids taxes
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A woman has two children. I tell you one of them is a girl. What is the probabily the other child is a boy?
1/3
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1/2
87
2/3
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@oxbquant
The fact you’re working on this in your free time while also interning is amazing. You clearly want to kill it in this industry 🫡
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@systematicls
This is fantastic for those new to mid-freq systematic strategies. I'll say the true challenge is actually implementing these signals to make money!
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@hopbpatrick
@0xfdf
@systematicls
Yes, and you also run the risk of regressing out your alpha. Another concern is that more factors you orthogonalize, the more leverage you need to hit your target vol so based on your opt setup it could lead to large portfolio distortions.
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@__paleologo
The F-W-L theorem and the idempotency of the annihilator matrix are beautiful things :')
(c) and (d) are clearly best. Factor modelers would know this like the back of their hand but I know a lot of alpha folks who have lost basic linalg beacuse their job is 90% data cleaning.
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@0xfdf
Wondering how lenient the firms that you /
@systematicls
work at are with you posting educational content about quant portfolio management online? It’s obviously not IP but also could help others make money - I’ve heard of firms being very strict about these kinds of posts
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@idro___
As someone who's only really thought of low/mid freq trading, its crazy how much the spread demolishes your alpha. At low freqs you're paying a huge spread relative to the expected vol of your stock. Haven't found a good way to monetize alphas in this space
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@BeingHorizontal
@robothearth
If you do this enough it’ll drive the price necessarily to zero.
I’d go with rain control, you could probably get >$10k for each outdoor wedding you rescue
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@TyDClay
On the right track! Maybe in your initial insight, try to find some symmetry between Player A and B. The symmetry makes the annoying sum much easier.
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@0xfdf
@systematicls
If you are marketing your fund as a "global" portfolio, at some point you are going to need to vol-target your whole book as one entity instead of separate sub-portfolios. You can run all your signals within-country but you need to combine at the end for optimization.
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@altcryptodegen
Did I say X had to be an integer? Assume its any positive number. Admire the creativity though
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@__paleologo
A point on regression (b) - this is the return of a portfolio, namely the residual return of a portfolio with unit exposure to the new factor. It could be useful when you do not think the new factor doesn't belong in your residual return calc but you want to study its properties
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@therobotjames
@alphaarchitect
I’m wondering if AQR actually trades on this nonsense, especially given they’ve been spreading the gospel on classical econometric methods for years. This is the worst type of machine learning IMO
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@lecPokrandt
@OpenAI
Numerical simulation could get you super close though, just not this way. Something
@standupmaths
does a lot in his videos
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@skip_strike
@SecondA16110022
The definition of states is what leads to the counterintuitive result in this problem
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@__paleologo
One thing that I rarely see covered is error propagation in time series models. Moving from known firm characteristics to noisy time series estimations decreases confidence in estimated parameters
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@chuck_daniels_
Yes! The amazing thing is that this generalizes to any case where A gets n tosses and B gets n+1. The extra toss exactly offsets the chance of tieing.
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@SmityAndre82456
@__paleologo
You can’t fix this entirely with adjusted R2, but what can measure the difference between the 10 vs 100 factor example is leave-one-out cross-validated R2. R2 will mechanically go up as you add noise factors but CV R2 plateaus (or actually get worse, as you overfit factor rets)
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@HangukQuant
That's true. Although it can be tought to get precise vol control without a risk model
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@0xfdf
@__paleologo
@AffectiveAutism
A more behavioral argument is that all these fundamental PMs/analysts trained at the same banks, went to the same business schools, etc. Their way of thinking are naturally going to be similar and no good way to avoid that
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@quant_arb
Curious on your thoughts on Bryan Kelly’s recent work on ridgeless-regression regularized neural networks to predict returns? Seems like an interesting setup but could easily be snake oil
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