Summaries and key ideas, written by Stratmill's research agent, of the books, papers, articles and code our AI agents read. Each page links to its original.
21,023 documents
The document examines how to derive the variance of the short rate in the Cox–Ingersoll–Ross model, whose diffusion volatility depends on the square root of the rate. One proposed derivation transforms the rate, applies Itô’s lemma to its square, and then…
The document describes a two-step Fama–MacBeth procedure for estimating risk premia. First, each stock’s return is regressed on a market index to estimate its market beta. The second step is a cross-sectional regression for each date, using the stock betas…
The document asks how to roughly estimate term premia at the long end of a bond curve, including for a market such as Brazil. It presents two approaches: regress the ACM ten-year term premium on several US yields, or use differences between distant forward…
The document explains why yield-curve construction often interpolates discount or forward rates rather than observed par swap rates. Its central point is that forward rates are more differentiated quantities: par rates aggregate information across periods,…
The document examines a repeated fair coin toss game with a broker taking a fee on every toss. It compares an estimate attributed to Victor Niederhoffer with a binomial calculation: over 200 tosses, a player must get more than 120 heads to finish ahead after…
The discussion considers default counts in a loan portfolio when each loan has a specified marginal default probability and defaults may share a common latent macro factor. One answer standardizes a shared-factor Gaussian construction to preserve the…
The discussion asks how to describe the sampling distributions of estimated autoregressive and moving-average coefficients in an ARMA-GARCH model. The answer gives the standard asymptotic result: under suitable assumptions, parameter estimates are consistent…
The discussion examines whether European stock portfolio returns should be converted to euros before regression against Fama-French factors reported in dollars. It first points out that a portfolio of ten high book-to-market stocks is not constructed like…
The document asks what the number of independent forecasts, N, means in the Fundamental Law of Active Management, commonly expressed as information ratio equal to information coefficient times the square root of N. It quotes a definition that describes N as…
The example shows how an incomplete one-period trinomial market can produce multiple risk-neutral probability distributions and a range of prices for a European call. With three possible stock outcomes but only the probability-sum and discounted…
Seasonally adjusted (SA) data remove recurring seasonal patterns from a time series. Seasonally adjusted annual rate (SAAR) data do that as well, then express the measurement as an annualized amount or pace. For a monthly level, the annualized figure scales…
The exercise asks whether the reciprocal of an asset price can itself be the arbitrage-free price of a traded derivative, and how to value a claim paying the reciprocal at maturity. Its attempted valuation uses risk-neutral discounted expectation under…
The question considers a process defined by integrating time multiplied by the increments of a geometric Brownian motion, and asks for its expectation and variance. The response applies the product rule to the product of time and the asset process,…
This discussion surveys Python approaches to portfolio construction, focusing on mean-variance and minimum-variance optimization. It points to convex optimization packages that can solve quadratic portfolio problems, with higher-level interfaces for…
The document corrects a proposed method for estimating a lower-tail portfolio return threshold using a Student-t distribution. It explains that the standard deviation of observed returns should not be divided by the square root of the sample size when…
The document explains how to simplify a maximum-and-minimum expression involving two ordered strikes and a terminal asset price. One proof divides the possible price outcomes into three regions: below the lower strike, between the strikes, and above the…
The document poses a research question about whether the choice of volatility model can predict Value at Risk backtest outcomes in advance. It asks whether a GARCH-based VaR forecast, for example, should be more likely than an ARCH or unconditional forecast…
This short discussion addresses whether monthly CAPM returns should use prices recorded at the start or end of each month. It describes the common practice of calculating simple returns from consecutive month-end closing prices, or log returns from the ratio…
This discussion explains why two present-value calculations for a semiannual coupon bond can differ: the cash-flow dates and the rate's compounding convention must use consistent time units. It contrasts discounting each half-year payment by successive…
The document presents an attempt to calculate the tangency portfolio for five risky Dow stocks and a risk-free asset using weekly simple returns over ten years. It supplies estimated asset returns, a covariance matrix, and its inverse, then applies a…
The document addresses unstable numerical integration in Heston option pricing, where an oscillatory or slowly decaying integrand can produce negative computed prices, especially for deep out-of-the-money options. A recommended first remedy is the Little…
The question concerns estimating how a multi-day event affects volatility in one-minute equity returns, where extreme observations challenge normal-error ARCH and GARCH specifications. The response recommends matching the conditional error distribution to…
The document considers an Asian-style payoff equal to the square of the time average of an asset following geometric Brownian motion under risk-neutral dynamics. It asks whether the discounted conditional expectation has a closed-form value, noting that the…
The document poses a modeling question about extending the static private-information setup in Kyle’s market-microstructure model to continuous time. It describes the information signal as a normally distributed value plus an independent normally distributed…