Predicted Values, Standard Error, Prediction Intervals, and Functional Forms in Regression
Why Prediction Requires More Than a Fitted Line Regression is often used because analysts want to predict something: next month’s asset return, a company’s sales growth, a credit spread, a fund’s factor exposure, or a macroeconomic variable. The fitted line…
Regression Assumptions, Residual Analysis, Goodness of Fit, Coefficients, and ANOVA in Finance
The first step in regression is estimating a line. The second, more important step is deciding whether the estimated line deserves the analyst’s confidence. A regression output can look mathematically precise while still being economically misleading. The slope can be…
Simple Linear Regression in Finance: Least Squares, Intercepts, Slopes, and Interpretation
Why Linear Regression Matters in Finance Investment professionals rarely observe relationships directly. They observe data: asset returns, earnings growth, inflation, interest rates, credit spreads, valuation multiples, factor exposures, transaction costs, fund flows, and other market variables. Linear regression gives the…
Monte Carlo Simulation in Finance: Modeling Asset Prices, Returns, and Investment Risk
Monte Carlo simulations are about producing many random variables based on specific probability distributions. This helps estimate the probability of various outcomes. We will give an example to illustrate the Monte Carlo Simulation implementation. Steps Involved in Project Appraisal Imagine…
Bootstrap Resampling in Finance: Estimating Uncertainty from Historical Data
Resampling Resampling refers to the process of repeatedly drawing samples from the original observed sample to make statistical inferences about population parameters. There are two common methods: Bootstrap and jackknife. Here, we’ll focus on the Bootstrap method. Bootstrap Resampling Bootstrapping…
Historical Simulation in Investment Analysis: Using Past Returns to Model Future Outcomes
Historical Simulation Simulation forecasts possible outcomes for a system by testing different scenarios. The process involves four steps: Three common simulation approaches differ mainly in how they source scenarios: A robust simulation system can handle scenarios from any of these…
Portfolio Return and Risk: Expected Return, Variance, Standard Deviation, Covariance, and Correlation
Portfolio Statistics Matter A portfolio is more than a list of securities. Each security contributes return, but each also contributes risk and interacts with the other holdings. A high-volatility asset may increase portfolio risk sharply if it moves with the…
Index Construction and Index Returns: Price, Equal, Market-Cap, Float, and Fundamental Weighting
Why Index Construction Matters A security market index is a financial indicator designed to summarize the performance of a selected group of securities. It may represent a broad market, a sector, an asset class, an investment style, or a custom…
What is the Difference Between Money- Weighted Return vs Time-Weighted Return?
Why Return Weighting Matters Investment performance is not measured in a vacuum. A portfolio may receive additional contributions, make distributions, experience withdrawals, and change in value between those cash-flow events. When those flows are large, the investor’s final wealth may…
Types of Financial Returns: Holding Period, Money-Weighted, Time- Weighted, and Log Returns
Introduction to Types of Financial Returns The previous learning module introduced the basic return framework. This learning module extends that framework by asking a more practical question: What type of return is the investor actually earning? A total return number…
