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 explores reproducing corporate bond yield spreads under the Black–Cox structural credit model. It defines spread from face value, bond price, maturity, and the risk-free rate, then describes bond value as discounted debt recovery conditional on…
The document discusses plotting the historical minimum and maximum returns over holding periods of increasing length, alongside a central band, to visualize how observed outcomes vary by horizon. The accepted replies suggest variance ratios as a related…
The document asks whether a zero-mean, time-homogeneous Markov process starting at zero can have variance that does not increase over time. It gives a simple discrete-state example whose variance oscillates periodically, then considers a continuous-time jump…
The document poses a fixed-income valuation problem: how to calculate yield to maturity for a semiannual coupon bond that repays principal in installments before its final maturity. It provides a coupon rate, day-count convention, clean price, valuation…
The document asks why the estimated momentum coefficient in a Carhart four-factor analysis of mutual fund returns changes when the market benchmark is switched. The sample consists of 1,000 funds over 2000–2017. The reported momentum estimates are negative…
The document explains two features of a rewritten global minimum variance portfolio objective: the negative sign and the factor of one-half. A variance-minimization problem can be written as a maximization by negating the objective, which accounts for the…
The document offers a framework for choosing the sampling interval for intraday market research instead of assuming that five-minute bars are always appropriate. The researcher should match the data frequency to the trading horizon they can act on and to the…
The document shows how to count ordered outcomes for three six-sided dice according to their minimum value, then use those counts to reason about the expected payoff of a call-like contract with a strike of three. The counting method starts from rolls whose…
The document explains why several R functions for calculating price returns can produce different results. The key distinction is between arithmetic (simple) returns, calculated as the price change relative to the previous price, and logarithmic returns,…
This document examines fitting ARIMA models across rolling windows to track coefficient changes. Its central difficulty is that automatic model selection may choose a different order in each window, so the first reported coefficient may represent an…
This document surveys approaches to grouping time series that look similar, including curves with similar means but different variance or shape. One suggestion is to represent each series with informative features such as higher distribution moments,…
This document raises a question about why a five-day exponential moving average can differ when calculated from hourly closes versus minute closes. The finer series contains more observations over the same calendar span, and the author reports seeing…
This document explains how to allocate a market-cap-weighted crypto index when no constituent may exceed a chosen maximum weight. It presents a sequential calculation: start with each asset’s share of total market value, scale that share by the weight and…
The document asks how broadly to define mean-reversion and momentum strategies, including whether they correspond to particular latent-variable dynamics or more general properties of price processes. The accepted response gives informal meanings: mean…
The document asks how to calculate a firm's unsystematic risk from a market regression, given its R-squared and the regression's standard deviation. It distinguishes total return variability from the part left unexplained by the market. The answer points to…
The document derives the familiar annualization rule for covariance of asset log returns: multiply the per-period covariance by the number of periods in a year. It uses the covariance-of-sums identity. When returns within each period may co-move but returns…
The document considers a cross-sectional performance-attribution regression with asset returns as the response and style factors plus country indicators as predictors. It asks whether including a dummy for every country alongside a constant makes the model…
The document considers why the equivalent martingale measure is unique in the standard Black–Scholes setting. Its proof outline represents a candidate measure through a positive density process and uses the predictable representation property to express that…
The document derives the probability that an investment has a positive return over a chosen horizon under a geometric Brownian motion model. Starting with a price process whose drift is 15% and volatility is 10%, it applies Itô’s lemma to show that log…
The document considers how to store and represent constraints in an asset-allocation program. It raises options such as classifying constraints into categories, defining a small domain-specific language and parser, or using a structured representation such…
The document asks how to attribute the total loss from a sequence of monthly returns to selected months. It points out that returns compound multiplicatively, so simply adding the monthly percentages and assigning a fraction of that sum to the ending loss…
The document examines whether Itô’s lemma can derive the risk premium of a derivative without assuming in advance that it shares the underlying asset’s Sharpe ratio. It applies Itô’s lemma to a value defined as the exponential of the risk-free rate times the…
The document asks why a rolling average of a compounded price series can appear to have the same variance as the underlying price levels, even as the averaging window grows. The question contrasts this observation with the familiar intuition that averaging…
The document investigates why a GARCH(1,1) fit differs from a variance model that replaces its lagged squared-return term with an external regressor. The example uses daily equity returns and compares fitted coefficients from the two specifications. The…