Quant finance terms explained like you're 15

Quant finance terms explained like you're 15 STOCHASTIC PROCESSES LINEAR REGRESSION y = Bo + Bix + E EXPECTED VALUE E[X] = sum xi * P(xi) MONTE CARLO SIMULATION CORRELATION MATRIX 1.00 0.72 0.15 0.30 -0.20 0.05 0.00 -0.20 0.30 0.65 0.05 0.10 0.30 0.35 1.00 -0.30 0.60 1.00 OPTIMIZATION min f(x) s.t. g(x) <= 0 1. STOCHASTIC PROCESSES A random process used to model how prices move over time. Example: Stock prices don't move in a straight line. They move randomly, like a random walk. Price Time Next move is uncertain, but we can model the odds. Think of it as: Trying to predict the weather, you can't know exactly, but you can estimate probabilities. 2. EXPECTED VALUE The average outcome you expect over the long run. Example: If you win $10 with 60% chance and lose $5 with 40% chance, the expected value is $4.00. OUTCOME Win $10 Lose $5 EXPECTED VALUE PAYOUT (X) $10 -$5 PROBABILITY (P) 0.60 (60%) 0.40 (40%) PxP $6.00 -$2.00 $4.00 FORMULA: E[X] = sum xi * P(xi) i=1 xi = possible outcome P(xi) = probability of that outcome Think of it as: If you could repeat the same situation thousands of times, the average result would approach the expected value. 3. LINEAR REGRESSION A way to find the line that best explains the relationship between variables. Example: Predict a stock's return (y) based on a market factor (x), such as the S&P 500 return. Each dot is an observation. The line shows the best fit. THE MODEL y = Bo + Bix + E y = dependent variable (what we predict) x = independent variable (what we use to predict) Bo = intercept (where the line crosses the y-axis) B1 = slope (how much x changes for a one-unit change in x) E = error term (the unexplained part) Stock Return (y) Best fit line Error (actual y minus predicted y) Market Factor (x) WHAT IT DOES Finds the line that minimizes total squared errors (the distance between the dots and the line). WHY IT MATTERS Helps us understand relationships, make predictions, and measure exposure (e.g., beta in finance). Think of it as: Drawing a trend line through a cloud of points to see the overall direction, even though individual points may be noisy. 4. MONTE CARLO SIMULATION Running thousands of possible scenarios to see a range of potential outcomes. Example: You invest $10,000 in the market. What could it be worth in 1 year? Instead of guessing one answer, we simulate thousands of possible paths. SIMULATED PRICE PATHS Portfolio Value ($) Time (1 Year) POSSIBLE OUTCOMES (AFTER 1 YEAR) 5th Percentile $6,200 Median $10,450 95th Percentile $15,800 HOW IT WORKS 1 Identify key inputs and their possible ranges (e.g., return, volatility). 2 Randomly generate thousands of scenarios using those inputs. 3 Calculate the outcome for each scenario. 4 Collect all results and build a distribution. 5 Analyze the range of outcomes and make better decisions. WHAT IT DOES Models uncertainty and shows a range of possible outcomes with probabilities. WHY IT MATTERS Helps us understand risks, prepare for worst cases, and focus on what's most likely. USE CASES Portfolio risk analysis, option pricing, forecast uncertainty, stress testing, and more. Think of it as: Rolling the dice thousands of times to see all the ways the game could play out, not just one guess. 5. CORRELATION MATRIX A table that shows how two assets move in relation to each other. Example: This matrix shows the correlation between different assets. Values range from -1 to +1. 1 means they move together, -1 means they move opposite, 0 means no relationship. CORRELATION MATRIX EXAMPLE Stocks Bonds Gold Real Estate Commodities Stocks 1.00 -0.20 0.10 0.65 0.30 Bonds -0.20 1.00 -0.15 0.25 0.10 Gold 0.10 -0.15 1.00 0.20 0.40 Real Estate 0.65 0.25 0.20 1.00 0.35 Commodities 0.30 0.10 0.40 0.35 1.00 WHAT IT TELLS YOU Positive (near +1) Assets tend to move in the same direction. Less diversification benefit. Near 0 Assets have little to no relationship. Good for building diversified portfolios. Negative (near -1) Assets tend to move in opposite directions. Great for risk management. WHY IT MATTERS Helps investors understand relationships, reduce risk, and build more efficient, diversified portfolios. HOW IT'S USED Used in portfolio construction, risk assessment, hedge selection, and more. REAL WORLD EXAMPLE Stocks and bonds often have low correlation, which helps balance risk in a portfolio. Think of it as: If your friends always make the same decisions as you, you're not getting new perspectives. A good mix of friends thinks differently, which balances things out. 6. OPTIMIZATION Finding the best possible solution from many available options. Example: You want the highest return for the lowest risk. Optimization helps find the best combination of assets to achieve that goal. RISK VS. RETURN: THE EFFICIENT FRONTIER 14 12 Highest return for this level of risk 10 Expected Return (%) 8 6 4 2 Lowest risk for this level of return Efficient Frontier (Best possible combinations) Possible Combinations (Higher risk for the same return) 0 5 10 15 20 25 30 Risk (Standard Deviation %) HOW OPTIMIZATION WORKS 1 Define inputs (Expected returns, risks, correlations, and constraints). 2 Set the objective (Maximize or minimize). 3 Run the optimization algorithm. Tests millions of possible combinations. 4 Find the optimal solution. The best portfolio for your goal. 5 Get the asset allocation. The weights of each asset in your portfolio. WHY IT MATTERS Helps you build portfolios that are more efficient, diversified, and aligned with your risk tolerance. COMMON OBJECTIVES Maximize return for a given level of risk, or minimize risk for a given return. Maximize the Sharpe ratio. Meet a target return with minimal risk. REAL WORLD USES Portfolio construction, risk management, asset allocation, pension funds, and robo-advisors. Think of it as: Packing a suitcase with limited space and weight. You choose the right items to get the most value without exceeding the limit.