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 asks how Itô’s lemma can help derive Clark’s representation for a smooth, bounded function of Brownian motion at a fixed horizon. The stated formula expresses the terminal function value as its expectation plus a stochastic integral whose…
The document asks how to estimate the expected return of a broad stock index when calculating the market price of risk in a change from real-world to risk-neutral dynamics. It presents the relationship between that price and an asset’s correlation with the…
The document explains why effective interest formulas add one to a periodic rate, multiply the resulting growth factors, and subtract one at the end. The added one represents retaining the original principal as well as earning interest during each period.…
The document asks how to apply the FDR+ method to select trading rules that appear to outperform. It says the author has computed p-values using a stationary bootstrap, following a cited study, but provides no worked calculation, code, or detailed definition…
The document examines whether gross exposure divided by capital is a useful definition of portfolio leverage. It points out that this measure omits cash and can overstate risk when offsetting holdings are highly correlated, then derives a risk-based…
The document examines the parallel-shift assumption behind aggregating bond durations into a portfolio duration. It distinguishes shifts in the zero-rate curve from equal changes in the yields to maturity of individual coupon bonds, noting that coupon-bond…
The document explores whether investor reallocation can explain spillovers between asset returns. It starts from a mean-variance utility model and derives an unconstrained relationship between an investor’s holdings in two assets: the sensitivity of one…
The document examines the rare case where extending the maturity of a low-coupon bond trading at a deep discount can reduce its Macaulay duration. Duration is a present-value-weighted average payment time, so the maturity date alone does not determine…
The document explains a step in proving that an integrable stochastic process with centered, independent increments is a martingale. For times s before t, the increment from s to t is independent of information available through time s, so conditioning that…
The document considers how to infer a second asset’s covariance structure from that of a first asset and a relationship between their returns. One answer models the second asset’s return as a constant beta times the first asset’s return plus a small…
The document considers whether ordinary least squares can estimate the parameters of a GARCH model, which are commonly fitted using quasi-maximum likelihood. It summarizes a reference describing explicit OLS estimation for ARCH models through an…
The document shows how to estimate the real-world probability that a stock will finish within a specified price interval using a geometric Brownian motion model. It treats the stated required annual return as the drift and, for illustration, uses implied…
The document asks whether beta can be estimated using either excess returns or price returns. One answer challenges beta’s interpretation, arguing that regression results depend on whether beta exists in the data-generating process and whether the chosen…
The document explains two ways to simulate the return of a fixed-weight portfolio under a normal-return assumption. One method samples directly from a univariate normal distribution using the portfolio’s expected return and variance. The other draws asset…
This discussion surveys day-count conventions used to calculate interest accruals across bonds, money markets, floating-rate notes, and other instruments. It lists examples such as 30/360, Actual/360, Actual/365, Actual/Actual, and Brazil’s Business/252,…
This troubleshooting note concerns an error raised by the rugarch package while running a rolling GARCH forecast with ugarchroll. The reported setup estimates an sGARCH model with an ARMA mean specification, then forecasts one step ahead over a rolling…
The document explains how a t-statistic can test whether a trading strategy’s average return differs from a null value, commonly zero. A small statistic indicates insufficient evidence to reject the null of no excess return. Because return observations can…
The document presents a way to create a nonuniform numerical grid on the unit interval when a solution changes rapidly near both endpoints. It assumes a finite-difference problem, where grid density near sensitive boundaries can matter for accuracy. The…
The document explains how to express a Bachelier caplet as the difference between an asset-or-nothing payoff and a cash-or-nothing payoff. Under the stated forward-measure setup, the cash digital component is proportional to the strike times the probability…
The document asks for a more accessible derivation of the semi-closed-form price of a European call under the Heston stochastic-volatility model. It does not derive the pricing formula itself; instead, the replies point readers toward a paper with a…
The document examines whether stock prices should be martingales when profitable companies generate earnings and investors expect positive returns. Its replies distinguish ordinary prices from discounted or relative asset prices: under no-arbitrage…
The document describes a proposed stress-testing exercise for a zero-coupon yield curve built from daily observations. The curve combines a money-market-based short tenor with longer tenors interpolated from secondary-market Treasury rates. The author…
The document asks how to annualize a Sharpe ratio calculated from monthly returns when those returns are serially correlated. It notes that the usual square-root-of-time scaling assumes uncorrelated returns and raises a specific question about estimating the…
This discussion addresses why a consumer price index can look nearly linear over a selected historical period even though a constant positive inflation rate would compound. It distinguishes an index level from the inflation rate: sustained target inflation…