title: @gemchange_ltd: In 2025, entry-level quants at top firms pulled $300K-$500K total comp....
author: gemchange_ltd
content_type: twitter_article
published: 2026-03-03T18:43:43+00:00
source_url: https://x.com/gemchange_ltd/status/2028904166895112617
word_count: 2697
In 2025, entry-level quants at top firms pulled $300K-$500K total comp.
AI/ML hiring in finance grew 88% year-over-year.
This article is everything I wish someone had handed me when i started my path laid out in the exact order you should learn it.
The path is like layers of a video game, where you can't skip levels.
Every concept builds on the last. But if you put in real work, not watching some lame ahh YouTube videos about finance, that's just wasting your time, actual problem-solving work - you can go from knowing nothing to being something in about 18 months. Disclaimer:
Not Financial Advice & Do Your Own Research & Markets involve risk.
My own project - @coldvisionXYZ
Forget everything you think you know about trading
Most people think quantitative trading is about picking stocks. Having opinions on Tesla. Predicting earnings.
Quant trading is about math.
You are mostly working with statistical relationships, pricing inefficiencies, and structural edges that exist because markets are complex systems run by humans who make systematic errors.
Part
: Probability is the Language of Uncertainty
Everything in quantitative finance reduces kinda to 1 question:
What are the odds, and are the odds in my favor?
That's probability. If you don't understand probability at a deep level, nothing else in this article matters.
Conditional thinking
Most people think in absolutes. Something is true or it isn't.
Quants think in conditionals. Given what I know, how likely is this?
The probability of A given B equals the probability of both happening divided by the probability of B. Profound implications.
A stock goes up 60% of days - that's the base rate. But on days when volume is above average, it goes up 75% of the time.
That conditional probability is a NOT BS. The raw 60% is NOISY BS.
Bayes' theorem
Your updated belief equals
(how likely you'd see this data if your hypothesis were true) * (your prior belief) / (the total probability of seeing this data under any hypothesis).
The denominator sums over all hypotheses.
In practice, you compute this with Monte Carlo sampling.
But the logic is the same. Bayes is how you update your conviction in real time.
A model says a stock should be worth $50. Earnings come out, revenue is 3% above estimate. The Bayesian posterior shifts upward. The traders who update fastest and most accurately win bread.
Expected value and variance your two best friends
Expected value is your conviction.
Variance is your risk.
If your strategy has positive expected value and you can survive the variance, you likely will make money.
Level 1 homework (3-4 weeks at 2 hours/day): 1. Read Blitzstein & Hwang, Introduction to Probability (free PDF from Harvard). Every problem in Chapters 1-6. 2. Code Simulate 10,000 coin flips, verify the law of large numbers visually. 3. Code 2 Implement a Bayesian updater takes a prior and likelihood, returns a posterior.
: Statistics
Once you speak probability, you need to learn to listen to data.
That's statistics and the #1 lesson statistics teaches is "most of what looks like NOT A BS is actually NOISY BS"
Hypothesis testing is the BS detector
You build a model. It backtests at 15% annual return. Is it real?
Set up H_0: "this strategy has zero expected return."
Compute a test statistic.
Calculate a p-value - the probability of seeing results this good if H_0 were true.
BUT If you test 1,000 random strategies, 50 of them will show p-values below 0.05 purely by chance.
That's the multiple comparisons problem.
Ur fix is Bonferroni correction divide your significance threshold by the number of tests
Or use Benjamini-Hochberg for false discovery rate control.
Every single beginner massively overestimates how much NOT A BS they've found. Your first 10 strategies will all be NOISY BS. Accept this now and save yourself a lot of money.
Regression decomposing returns
Linear regression y=Xβ+ϵ is the workhorse.
In finance, you regress your strategy's returns against known risk factors:
The intercept α is your alpha the return that can't be explained by known factors. If α is zero after accounting for factors, your "edge" is just disguised market exposure.
The OLS estimator:
The most important number is α.
Use Newey-West standard errors financial data has autocorrelation and heteroskedasticity, so default OLS standard errors are wrong. Using them is like driving with a cracked windshield.
Maximum Likelihood Estimation
Given data x_1,…,x_n, from a model with parameter θ:
Set the derivative to zero and solve. (or it's over gng)
MLE is how you calibrate every model in finance fit a GARCH model to volatility, estimate jump-diffusion parameters, calibrate option pricing to market quotes.
It's asymptotically efficient no other consistent estimator has lower variance for large samples (the Cramér-Rao lower bound).
When someone at a firm says they're "calibrating" a model, they almost, like always mean MLE.
Level 2 homework (4-5 weeks): 1. Read Wasserman, All of Statistics , Chapters 1-13. 2. Code Download real stock returns with yfinance. Test normality (they'll fail). Fit a t-distribution via MLE. Compare. 3. Code Run a Fama-French 3-factor regression on a stock portfolio using statsmodels. 4. Code Implement a permutation test shuffle dates 10,000 times, compare shuffled performance to actual.
: Linear Algebra
Linear algebra sounds boring. It's the machinery that runs everything: portfolio construction, PCA, neural networks, covariance estimation, factor models. You cannot be a quant without being fluent in matrices.
(if u skipped Algebra in school school doing that, it's over)
Thinking in matrices
A covariance matrix Σ captures how every asset moves relative to every other asset. For 500 stocks, Σ is 500×500 with 125,250 unique entries. Portfolio variance collapses to a single expression
This quadratic form is the core of Markowitz portfolio theory, of risk management, of everything.
Eigenvalues is what actually matters in a universe of stocks
Look at a 500-stock universe and the first 5 eigenvectors explain 70% of all variance. Everything else is NOISY BS.
The first time eigendecomposition u use it the whole world changes. Look at a 500-stock universe and the first 5 eigenvectors explain 70% of all variance. Dimensionality reduction, and it's the foundation of factor investing.
Level 3 homework (4-6 weeks): 1. Watch Gilbert Strang's MIT 18.06 lectures all of them. Non-negotiable. 2. Read Strang, Introduction to Linear Algebra . Do the problems. 3. Code PCA decomposition of S&P 500 returns. Plot eigenvalue spectrum. Identify top 3 components. 4. Code Markowitz mean-variance optimization from scratch.
: Calculus & Optimization
Calculus is the language of change. In finance, everything changes: prices, volatilities, correlations, the entire probability distribution shifts second by second. Calculus describes and exploits those changes.
Derivatives (the math kind): appears in every neural network backpropagation and every Greek calculation.