คลังความรู้

The document asks how to optimize an automated trading strategy when higher expectancy coincides with sharply fewer trades. It also notes that maximum drawdown appears to improve as trade counts fall, making it difficult to judge whether performance gains…

The document considers why a portfolio VaR based on a covariance matrix and normally distributed market factors may exceed its stated confidence bounds more often than expected. It proposes decomposing portfolio risk into component VaR to identify which…

The response defines delta-one products by their theoretical sensitivity to the underlying: a change in the underlying produces a corresponding change in the product’s value, giving a delta of one. It adds that the sensitivity should remain constant,…

The document outlines a proposed workflow for pricing a quanto option: estimate marginal distributions for the underlying asset and exchange rate, connect them with a copula, then calculate the expected payoff under the resulting joint distribution. Its main…

The response derives a closed-form present value for an infinite sequence whose cash flows follow a cosine pattern and are discounted at a constant rate. It notes that odd-indexed terms vanish, rewrites the surviving cosine terms as alternating signs, and…

This document asks why a 15-period binomial model gives an unexpected value for an American put under specified Black–Scholes assumptions. It does not provide a corrected price or a specific diagnosis. Instead, the response offers a general debugging…

The document asks how to modify the closed-form Markowitz efficient-portfolio weights so that every asset weight is positive. The supplied formula uses expected returns and the inverse covariance matrix to describe the unconstrained efficient portfolio…

The document addresses which bond data to use when estimating a portfolio variance–covariance matrix. Its central recommendation is to model returns rather than covariance of raw prices. For longer-maturity bonds, historical returns from traded prices may be…

The document explains a practical way to quote a binary call by approximating its payoff with a call spread. A seller of the binary can buy a spread around the strike; the spread’s cost provides a replication-based estimate of the option’s price. The…

The question derives a replication-error expression in which the difference between assumed local volatility and realized volatility is multiplied by option gamma over time. It interprets the sign: for positive gamma, assuming volatility above realized…

The document describes the gap risk a broker can face when it immediately hedges a customer's leveraged spot FX trade with a liquidity provider. If the market jumps through a liquidation level, the customer may incur a negative balance that cannot be…

This note examines a fixed-rate bond with a five-year first coupon period followed by semiannual coupons. In the described QuantLib setup, the calculated yield is below the coupon rate even though the bond is issued at par; the author reports that Bloomberg…

This note asks how to value a floating-rate note in a short-rate tree when the tree contains time steps between an IBOR fixing date and the coupon payment date. It proposes valuing backward from each fixing-date node by considering reachable payment-date…

The document considers when net income and operating cash flow can legitimately enter a backtest that trades around quarterly reports. Its key principle is to use information only after it became public. An earnings date may identify a press release, but…

The document addresses an interview puzzle about applying a fixed set of positive and negative returns to an asset and asks which ordering maximizes the ending value. Each return multiplies the current asset value by one plus that return. Since…

The document examines whether a bond’s coupon accrual period changes when a scheduled payment date falls on a non-business day and is moved by a forward business-day convention. Its central lesson is that there is no universal rule: the bond’s prospectus or…

The document asks where to learn econometric methods for continuous-time models when observations arrive at discrete times. It explains why the topic is relatively specialized: standard econometrics and time-series texts may give it little attention, and…

The document presents a time-series modeling problem: an ARFIMA(12,0,12) mean with an eGARCH volatility specification produces plausible one-step forecasts on a sample of 2,000 observations, but extreme mean and variance forecasts after fitting the same…

The document identifies research on whether academic publication eliminates stock return predictability and relates it to slow information diffusion. The suggested explanation is that information may take time to become fully reflected in prices, with the…

The discussion clarifies how risk-neutral pricing connects to delta hedging and the Black–Scholes equation. In a standard setup, a self-financing hedged portfolio is locally risk-free, so its return is tied to the financing rate. The stock’s real-world…

The document explains why very short-term U.S. Treasury yields can trade below the federal funds rate. One answer points to an imbalance between cash demand and Treasury bill supply: money market funds had abundant cash, the Federal Reserve’s reverse repo…

This discussion examines why a return calculated from an adjusted share-price series may differ from a reported total shareholder return with dividends reinvested. It explains that a total-return series is a constructed price history: dividends are treated…

This exchange clarifies the no-bankruptcy-cost assumption in the Modigliani–Miller framework. It means that financial distress or bankruptcy creates no direct costs, such as legal expenses, and no indirect costs, such as losses caused by disrupted operations…

The discussion asks whether random-walk assumptions imply that dollar cost averaging must always underperform a lump-sum investment. The responses distinguish the broad idea of investing gradually from any particular schedule or stock-selection rule. A…