คลังความรู้

The document examines why ICE USD swap rate observations were absent during March and April 2020, while EUR observations remained available. It reports that the same gap appeared in data retrieved from both ICE-related time series and Thomson Eikon, and asks…

This answer derives how many shares to sell after a price change to restore an asset to its initial portfolio weight, assuming sale proceeds remain in cash and no outside capital is added. It writes the starting and ending portfolio values, equates the…

The answer treats the yield-curve model term as a Wiener integral with a deterministic integrand. Such an integral is normally distributed with mean zero, and its variance is the integral of the squared integrand over time. For an exponentially decaying…

This question describes fitting a probability distribution for an asset’s terminal price to discrete option quotes. It proposes using a distribution inferred from market implied volatilities as a prior, then minimizing relative entropy from that prior…

This exchange explains that mean-variance optimization does not inherently require portfolio weights to sum to one. That condition is an added modeling choice, commonly used to represent allocating all available capital to long-only positions, or to require…

The exchange presents a regression-based way to estimate how implied volatility may change when the underlying spot price moves. It points to a minimum-variance delta relationship in which the expected implied volatility change depends on the proportional…

The document asks for references surveying methods used to calibrate stochastic volatility models, including the Heston model. It notes that many calibration approaches exist and seeks a broad overview of research and practical projects. The response…

This exchange considers whether an asset with negative expected return can still be useful when combined with a portfolio, especially if its returns are negatively correlated or uncorrelated with the portfolio. The answer focuses on expected return relative…

The document asks whether market participants learn about unscheduled Federal Open Market Committee meetings before they occur. The included answer says investors know the scheduled meeting calendar, while emergency meetings are disclosed afterward through a…

The document asks how to evaluate intraday strategies whose long-only trades may benefit from an asset’s longer-term upward drift. Its examples enter an S&P 500 or gold position at the market open and exit around midday. The concern is that apparent strategy…

The document raises the problem of hedging a large fixed-rate bond issuance swap. A corporate issuer pays fixed on its bond and receives fixed in a swap to obtain floating-rate exposure; the bank on the other side must manage the resulting interest-rate…

The document explains how to track relative implied volatility at a specific option delta over time, such as comparing a 10-delta put with an at-the-money put. The suggested process begins with collecting option quotes across strikes and expirations for each…

The document asks how to extend mean-variance portfolio optimization with limits on factor exposures and individual positions. The objective is the familiar trade-off between expected return and variance, whose unconstrained solution depends on the inverse…

Convertible bond parity compares the value of the shares obtainable on conversion with the bond’s face value. When the stock and bond are quoted in different currencies, the share value must first be converted into the bond’s currency using the relevant…

The document asks how to infer a six-month LIBOR fixing from three-month Eurodollar futures. It identifies the futures-implied three-month rate as 100 minus the quoted futures price, expressed as a percentage, and asks how to extend that information to a…

The document frames corporate profit taxation as an option-like exposure: tax is owed when earnings are positive, while losses do not generate an equivalent tax benefit. On that view, the government holds a call-like claim on company profits, leaving the…

The document asks why traders use leverage if it does not improve a strategy’s risk-to-return ratio. Its answer distinguishes changing a ratio from scaling the amounts represented by that ratio: leverage increases both gains and losses, allowing a trader to…

The document considers a monthly return factor model in which one factor explains a substantial share of returns in some periods, but its relationship with returns reverses in others. Pooling the periods yields a lower overall R-squared. This pattern alone…

Market-neutral long–short portfolios can produce positive profit and loss while having little or no net invested capital, making a conventional return denominator unclear. The document presents two ways to define returns for Sharpe ratio analysis: divide…

The document discusses how to assess a market-making strategy that starts and ends each day flat, using a series of daily dollar profit and loss figures. One response says the annualized Sharpe formula based on mean and standard deviation is appropriate if…

The document considers a claim whose payoff is the time integral of an asset’s proportional price change. Its main replication argument is direct: hold one unit of the underlying’s inverse price, or equivalently one dollar of stock exposure, so the…

The document derives how delta hedging an options book can affect the underlying when hedge trades move its price. It starts with the delta-hedged profit and loss formula, then models price impact as proportional to the dollar demand created by rebalancing.…

The document discusses counterparty credit valuation adjustment for a European call bought from a counterparty. The key intuition is that the buyer has paid the premium and remains exposed to losing the value of the option if the seller defaults before…

The document explains how CAPM relates to modern portfolio theory and mean-variance optimization. MPT uses expected returns, variances, and covariances to construct an efficient frontier; combining a tangency portfolio with a risk-free asset gives a capital…