คลังความรู้

The document clarifies when the holder of a midcurve payer swaption must decide whether to enter the underlying forward-starting swap. The answer says the decision occurs at the option’s expiry, using the example of a one-year option on a five-year swap…

The document considers using principal component analysis on industry peers’ fundamental metrics to inform equity analysis. It provides variance shares and loadings for thirteen components, then asks what the first two components represent. The response…

The document compares a standard GARCH(1,1) conditional variance specification with a version that adds an asymmetric term. In the second model, a dummy variable activates an extra squared-residual contribution when the previous innovation is positive. The…

The document asks for the expectation of a time integral of Brownian motion with drift, weighted by exponential discounting. It specifies drift μ, volatility σ, and discount rate k, then applies Fubini’s theorem to move expectation inside the integral. Under…

The document questions media descriptions of US Treasury futures basis trades as arbitrage. It focuses on a cash bond and futures hedge, especially when the bond is the cheapest to deliver, and distinguishes a negative gross basis from a genuinely locked-in…

The document examines a formula for the weights of a conditionally optimal portfolio, called the unconstrained minimum-variance efficient portfolio, in a setting with multiple risky assets and no riskless asset. The weights depend on the conditional mean…

The document clarifies the meaning of a chart label describing preferred equity as purchased. Net preferred equity issued reflects both issuance and repurchases: when a company buys back preferred shares, that activity offsets prior issuance and can make the…

The document gives a quick approximation for the mark-to-market change on a fixed-rate interest rate swap after a small change in its quoted rate. The proposed method multiplies the rate move by the swap’s duration and notional, with the sign determined by…

The document asks how to interpret the cash-account changes in Piterbarg’s framework for pricing derivatives under collateral agreements. It distinguishes dividend income on a hedging stock position from the cost of financing that position, and asks why…

The document asks how to combine Barra factor exposures for individual assets into exposures for a long-short portfolio, with the eventual aim of attributing portfolio returns to factors. It raises a key weighting choice: divide each position’s dollar value…

The document poses an allocation question: how to split capital between an active fund and a passive ETF when the active fund’s risk relative to a benchmark exceeds the investor’s portfolio active-risk budget. It compares two proposed rules: divide the…

The document considers a stochastic differential equation whose drift switches between positive and negative values according to the sign of the state. The drift is bounded but discontinuous, so it fails the usual Lipschitz condition associated with standard…

The document asks how to measure and simulate gradual rises followed by sharp market declines. It presents threshold GARCH as a way to model return asymmetry, with APARCH as a related model family, and points to jump diffusions, often paired with stochastic…

The document investigates why AAPL and IBM have no prices for a particular historical date and how to research similar anomalies. The answer explains that U.S. exchanges were closed for Good Friday, a holiday whose date moves from year to year. It recommends…

The document concerns Japan’s benchmark interest rates, particularly TONAR and TIBOR, and asks how they differ from yen LIBOR and where to find TONAR’s calculation methodology. The response recommends an interest-rate instruments and market conventions guide…

The document compares the Fama–French market return with the Wilshire 5000 as market proxies in a three-factor regression of mutual fund returns. The accepted answer describes the Fama–French market portfolio as a value-weighted return on eligible…

The document asks what to call the overlapping strike prices in ordered lists of call and put options. Its answer uses the underlying spot price to explain the standard moneyness categories: calls with strikes below spot and puts with strikes above spot are…

The document explains why a candle can be green even when its close is below the previous candle’s close. In a common solid-candle convention, color compares the period’s close with its own open: green indicates the price rose during that interval, while red…

The document discusses when to roll a six-month call option into a longer-dated option, such as one expiring in nine or twelve months. Its main suggestion is to consider rolling when implied volatility in the existing LEAP is elevated and fewer than six…

The exchange explains the role of delta hedging in the Black–Scholes framework. A portfolio short the option and long the underlying in proportion to the option's sensitivity to the underlying cancels the shared stochastic price movement in the idealized…

The discussion addresses why summing trades only during regular New York market hours can produce a lower total than a published daily volume figure. For the NYSE end-of-day TAQ dataset described, the accepted answer says reported volume includes trades from…

The document asks how a Monte Carlo approximation of conditional value at risk can be expressed as a linear optimization problem. The approximation uses a threshold variable and the positive part of each scenario's loss beyond that threshold. Introducing one…

The discussion compares broad approaches to estimating fair value in corporate credit. It notes that cross-sectional regressions are common in published work, then frames structural models, stochastic pricing models, and hybrids that use distance to default…

The document shows how to account for a short position in open profit and loss using a signed position quantity. In its example, a short position is represented by a negative share count. When the current price falls below the entry price, the position has…