คลังความรู้

The document distinguishes two portfolio problems: choosing investments and sizing a group of trading strategies. For multiple strategies believed to be profitable and reasonably uncorrelated, one answer suggests allocating capital in inverse proportion to…

The document gives formulas for calculating a daily pivot point and the first three support and resistance levels from the prior period's high, low, and close. It shows these levels alongside price bars and existing MACD and moving-average signals, then asks…

The document examines whether a volatility surface for an inverse FX quote can be obtained by reversing call and put conventions around the at-the-money level. Its central explanation is that option delta depends on the currency used to measure the hedge. A…

The document explains how portfolio theory can be adapted when holdings and weights change over time. It describes dynamic optimization as repeatedly estimating allocations at scheduled rebalancing dates, using data available up to each date, rather than…

The document derives the expected stock growth factor over one time interval, restricted to cases where that factor falls below a threshold. Under geometric Brownian motion, the growth factor is lognormally distributed, so its truncated expectation can be…

The document asks why volatility forecasts from an ARMA(1,1)-GARCH(1,1) model decline slightly over a multi-step forecast horizon. The displayed output shows the standard deviation estimates decreasing across successive forecast steps, while the questioner…

The document considers a GARCH(1,1) model fitted to the spread between two correlated assets. Although the reported coefficient estimates appear unremarkable, the standardized residuals show a bimodal distribution, prompting the question of whether such a…

The note explains that a small negative Z-spread can occur for an investment-grade corporate bond. In the example, the observed spread is measured against LIBOR, which may sit above Treasury yields because it includes some bank credit risk. A highly rated…

The example considers a riskless asset and one risky asset whose dynamics are driven by two Brownian motions, while the information available to traders is generated by both. Although the asset equation can be rewritten using their scaled sum, that sum alone…

The note explains repo as a funding source for a long bond and reverse repo as a way to borrow a security for a short. It addresses why financing is tied to the bond being held: repo lenders apply security-specific haircuts, so the cash raised against a bond…

The document presents a closed-form expression for a zero-coupon bond price under an extended Hull-White short-rate model with time-varying drift, mean-reversion, and volatility parameters. The bond price is exponential-affine in the current short rate: one…

The document explains the distinction between Markit’s assumed and real recovery rates for credit default swaps. The assumed rate supports quote conversions between running spread and upfront payment, while the real rate represents the recovery used in…

The document discusses maximum-likelihood estimation for a linear Gaussian two-factor state-space model of commodity prices, using the Schwartz-Smith framework. The observed log price is modeled as the sum of two latent state components plus measurement…

The document considers how to measure the fit of a portfolio or linear combination of assets intended to reproduce another asset’s returns. It notes a weakness of relative error: dividing by the target return becomes unstable when that return is near zero.…

The document discusses using the difference between five-year and two-year Treasury Inflation-Protected Securities yields as an indicator of inflation expectations. The answer’s proposed intuition is that longer-term yields may rise more than shorter-term…

The document explains how a pension fund can use interest rate swaps within liability-driven investing to reduce the gap between asset and liability duration. Its example assumes a long-dated liability valued using a government bond yield, with only part of…

The document asks how to approximate a down-and-out call price when the underlying follows the Heston stochastic-volatility model. It states the option payoff with a barrier condition, contrasts the problem with a Black–Scholes closed-form expression, and…

The document explains why balance sheet and income statement items do not always appear in the same categories across companies. It uses Goldman Sachs to illustrate that financial firms may present liabilities by type and maturity without a single…

The document asks how to examine whether changes in the PCE index help explain daily stock return changes over time. The proposed approach is rolling Granger causality: repeatedly apply a two-variable Granger causality test to a moving window of…

The document asks how to choose the lag length when applying the Johansen cointegration test to two time series. It notes that test conclusions can vary with the lag specification: some choices may lead to rejection of the null hypothesis while others do…

The document raises a distinction among probability measures used in quantitative finance. It describes risk-neutral probability as the framework used to price derivatives under no-arbitrage conditions, while identifying physical probability as the relevant…

The discussion considers what an interface for monitoring an algorithmic portfolio should show. Its central design principle is to choose metrics and visualizations according to the strategy and the decisions the dashboard must support, rather than building…

The document discusses using importance sampling to estimate prices for far out-of-the-money barrier options under local volatility. It describes changing the distribution of simulated inputs from the original density to a shifted normal density, then…

The document poses a statistical question about annualized Sharpe ratios. It starts from the convention of multiplying a daily Sharpe ratio by the square root of the number of trading days in a year, under certain assumptions, and asks whether that scaling…