#Expected Value

(Part 1 of 4) The convex payoff structure of prop firm accounts makes it possible to extract positive expected value net of challenge and activation fees, if you model the process—end-to-end—as a structured product. There’s obviously not an analytic solution to this optimization, but Monte Carlo simulation makes it possible to understand the optimal risk geometry for these accounts, and it allows us to determine the exact probability of passing, and net expected value, of a given strategy, given a backtest of its trades. This is how to pass a prop firm account challenge, and extract maximum net EV, even with a 0 (or low) expected value strategy. #propfirm #math #trading #quant

Quantitative trading interviews usually start with fast screening on probability, statistics, and mental math, then move into deeper problem solving under time pressure to test how cleanly someone reasons with uncertainty. Common rounds include brainteasers and expected value questions, linear algebra and calculus basics, coding in Python or C++ on data structures and simulation, and market microstructure topics like bid ask spread, slippage, and how an order impacts price. Later stages look like real work: designing a simple strategy from a described dataset, diagnosing overfitting, explaining how to validate signals, and handling risk sizing and drawdowns, often while being challenged with follow ups to see if assumptions stay consistent. 🚀 No Signals. Just Real Analytics. Be the first to access MacroGlide platform. Get Early Access — FREE (LINK IN BIO). Credits: HFT, Quant Blueprint, 2024 Edited for educational purposes. No ownership claimed. This content is for informational purposes only and does not constitute financial or investment advice.

Present Value (PV) #financestudent #collegestudent #youngprofessional #twenties

How quants actually use statistics in live trading decisions. Five concepts. What they really mean in a live trading environment. 1. Mean and variance: the two numbers every position starts with Before any trade, two questions get answered. What is the expected return? What is the variance, how wide is the distribution of outcomes? High expected return with unacceptable variance gets sized down or rejected. Every position sizing decision starts here. 2. Stationarity: the assumption every strategy lives or dies on A stationary process has statistical properties that stay constant over time. Most quant strategies assume stationarity, that what worked historically continues to work because the underlying relationship is stable. When stationarity breaks down, strategies fail. Testing for it before deploying is not optional. 3. Autocorrelation: measuring whether the past predicts the future Positive autocorrelation means yesterday’s return tends to predict today’s. Negative means it tends to reverse. Momentum strategies exploit positive autocorrelation. Mean reversion strategies exploit negative autocorrelation. Every systematic strategy is a bet on the autocorrelation structure of some signal. 4. Volatility clustering: why risk is not constant through time High volatility periods tend to be followed by more high volatility. Calm periods tend to persist. This is why static position sizing is dangerous. Quants model volatility dynamically and scale exposure accordingly. A strategy that ignores clustering takes far more risk than its designer intended. 5. The central limit theorem: why quant strategies scale Individual trades are nearly impossible to predict. But the central limit theorem guarantees that averages across large numbers of independent trades converge to a predictable distribution. This is why quant firms execute thousands of trades daily. Statistical convergence turns small positive expected value into consistent returns. That is the entire business model of systematic quant trading in one theorem. Comment STATS and I’ll send you the free study guide. Follow to break into quant trading with me.

This is the infamous coin toss , also known as Peters’ coin toss. Dr. Ole Peters is a physicist at the London Mathematical Laboratory and External Professor at the Santa Fe Institute. I recently came across his work on ergodicity economics and honestly it blew my mind so much I had to make a video on it. So quick context — loss aversion is this idea that losing $100 hurts us about twice as much as gaining $100 feels good. Kahneman identified this and it partly won him the Nobel Prize. And look, loss aversion is real. We do feel losses more. But is it always irrational? That’s where things get really interesting. Economists basically call us biased for rejecting bets with positive expected value. But here’s what nobody tells you about EV — it treats gains and losses as if they’re symmetric. They’re not. You lose 50% of your money? Cool, now you need 100% just to get back to where you started. Your outcomes don’t just add up in life, they multiply. Every loss shrinks the base your next gain builds on. EV completely ignores this. That’s the whole idea behind ergodicity economics. what happens to the group on average is not the same as what happens to you over time. And why do I keep saying 300 years? Because EV as a decision-making tool goes back to Daniel Bernoulli’s 1738 paper. Ergodicity as a concept didn’t show up until physics figured it out in the 1870s. Economics was built on a framework that came before the math needed to spot the problem. Now for my economics friends — I know what you’re thinking. “Expected utility theory with a concave utility function already handles this.” And honestly I thought the same thing when I first looked at this. But here’s the difference — in EUT the utility function is a free parameter. You pick whatever fits. Ergodicity economics says the dynamics themselves tell you what’s rational. It’s not reinventing the math. It’s a perspective shift. And honestly whether you agree with it fully or not, it’s a field worth exploring further. Part 2 — why exactly the group gets richer while you go broke, and why this is so important for you to understand 🧠 Follow if you’d like to see it.

Most people treat prediction markets like sports betting. That’s why they lose. I approach it like a pricing problem. Markets assign probabilities. Those probabilities drift when sentiment, news flow, or positioning shifts faster than the odds update. I use quant models to track baseline probabilities and expected value. Then layer AI on top to scan news, speech, and flow in real time. The goal is simple. Find mispriced outcomes where implied probability does not match reality. No opinions. No narratives. Just numbers, reaction speed, and positioning. Edge comes from three things: • faster information processing • better probability estimates • disciplined execution If the market says 40 percent and the model says 55 percent, that gap is the trade. Over time, those small edges compound. Comment “quant” to follow along

WACC (Weighted Average Cost of Capital) is a concept that causes a TON of confusion. It’s usually taught with formulas and a bunch of finance theory, but the underlying point is often missed when this concept is explained. The critical thing to understand here is that any asset is by definition funded by capital (typically debt and equity). And further any capital provider will have a target rate of return based on the risk that they are taking. If we were to look at just the target return of one individual provider of capital, we wouldn’t capture the target rate of return for the entire asset, but rather the target rate of return of that individual capital provider based on their position in the hierarchy. So with the weighted average cost of capital formula, we take a weighted average expected return of all the capital providers which shows us the overall expected target return for the asset as if it was owned outright by a single person/entity. Follow @survivefinance to level up your finance game every day. #investmentbanking #privateequity #interviewprep #internships

#trading #expectedvalue #polymarket

💡Every choice has a cost. That cost is called Opportunity Cost — the value of the next best alternative forgone. Understanding this concept helps in better decision making in economics and daily life. 📌 Save for revision 📚 Follow @knittingknowledge #economicsclass #conceptart #microeconomics #studygram #concept

The law of large numbers is a fundamental idea in probability that explains how randomness becomes predictable when repeated enough times. It states that as you perform an experiment more and more times, the average of the results will get closer to the true expected value. For example, if you flip a fair coin, you might not get exactly half heads and half tails in a small number of flips, but as the number of flips increases, the proportion of heads will settle closer and closer to 0.5. This doesn’t mean outcomes stop being random; rather, the randomness balances out over time, revealing an underlying stability in the average. There are two common versions: the weak law and the strong law. The weak law says that the probability of the sample average being far from the expected value becomes very small as the number of trials increases. The strong law goes further and guarantees that the sample average will almost surely converge to the expected value in the long run. In practical terms, this principle is why averages in large datasets are reliable, whether in statistics, finance, or machine learning. It reassures us that while individual outcomes may fluctuate, long-term behavior becomes increasingly predictable. Like and follow @mathswithmuza for more! #math #statistics #law #foryou #study

You can now check if a stock is overvalued or undervalued in just 60 seconds! This will save you ample of time and energy. Also, please go with your gut! Don’t follow anything blindly. Please do your own research and invest in it accordingly. #financecontent

Enterprise Value ≠ Equity Value