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The document considers a market with one homogeneous good, multiple buyers and sellers, capacity limits, willingness-to-pay and reservation-price bounds, and utility functions. It outlines two standard game-theoretic formulations: Cournot competition, where…
The document gives a concise explanation for why a floating-rate loan is generally valued near par on a coupon reset date. At that date, the loan’s coupon is reset to the prevailing market rate. In the basic bond-pricing argument, an instrument whose coupon…
The document interprets ATOP in a strategy presentation as a likely abbreviation for annual portfolio turnover, expressed as a percentage of portfolio value. It describes a common calculation: compare total purchases with total sales over a year, use the…
The document explains why mean-variance optimization can assign nearly all capital to one asset as the asset universe grows. Its account centers on covariance structure: many assets share a small number of meaningful risk factors, leaving other variance…
The document explains why similar warrants from different issuers can imply distinct volatility surfaces. Issuers may add different markups to warrant prices, and those markups can depend on each issuer’s outstanding position in the product. As sales…
The document explains why the yield spread between a corporate bond and a risk-free bond cannot be read as a default probability on its own. The spread reflects expected default losses, including both the chance of default and the loss given default;…
The document explains how to value a payment of LIBOR fixed at time T and paid at T plus an accrual period. After the rate has been set, its value is the discounted payment amount. Before the fixing date, the price is the value of a portfolio holding a bond…
The document considers how to assess bid, ask, and volume data from two vendors when observations do not share exact timestamps. The questioner samples prices at regular time intervals, finds that plots look similar, but sees weak cross-correlation after…
A zero-coupon bond makes a single payment of face value at maturity and has no interim coupon payments. Its issue price reflects the present value of that future payment. With a positive yield, discounting makes the issue price lower than par; the discussion…
The document raises a market-structure question: when a futures exchange imposes daily price limits but the underlying spot market does not, can the two prices temporarily diverge? It asks whether that divergence would force a sharp futures adjustment when…
The document examines the relationship between required returns, variance, stock-index levels, and expected volatility measures. The response points to a decomposition of the market’s expected excess return that includes risk-neutral variance and additional…
The document asks how practitioners might extend a long-dated foreign exchange option hybrid model that captures volatility level and skew but may not reproduce the full smile. The questioner wants to retain a three-factor setup, avoid stochastic volatility,…
The document explains an inflation hedge in terms of how an asset’s return responds to inflation surprises, rather than whether its total return exceeds the inflation rate in a particular period. It presents a regression framework in which an asset’s excess…
The document asks how to bootstrap spot and forward curves from daily US Treasury yields when a coupon bond’s cash flows fall at maturities without quoted securities. For the two-year note, the missing one-and-a-half-year spot rate is needed alongside…
The document asks whether a plain-vanilla European option can have negative time value, defined in the discussion as option value minus intrinsic value. One response constructs a deep in-the-money put case: with a positive interest rate, the discounted…
The document examines how to annualize a cumulative return when capital was invested during separated intervals. It contrasts annualizing over the 450 days actually invested with annualizing over the full three-year span. The responses distinguish a…
The document explains why historical stock research can be biased when datasets omit firms that have gone bankrupt or otherwise left the market. It notes that some widely used finance sites focus on surviving companies, so researchers seeking bankrupt or…
The document clarifies the scope of the Gordy formula as described through its underlying asymptotic single-risk-factor credit model. The model represents an entity at the horizon as either performing or defaulted, and recognizes a monetary loss when default…
The document addresses whether individual-stock option volatility smiles become steeper after sharp declines. Its answer describes a common market pattern: implied volatility, especially for out-of-the-money puts, tends to rise after a stock price falls. A…
The document explains two practical ways to estimate duration and related small-shock risk measures for callable bonds, where issuer exercise can change the bond’s expected cash flows. One approach assumes the issuer exercises at the yield-to-worst call date…
The document considers whether official central bank exchange rate fixings can stand in for end-of-day spot forex data in lower-frequency analysis. The response points to the European Central Bank’s daily exchange rate series, noting that its rates are fixed…
The document responds to an observation that volatile Bitcoin prices seem to form a Weierstrass-like pattern across candlestick time scales. It explains that rough, fractal-like paths are not unique to cryptocurrency: Brownian motion and related stochastic…
The discussion examines how adjusted and unadjusted stock prices affect backtests, especially cointegrated pairs trading. Adjusted prices can remove artificial jumps from splits and dividends, which helps when measuring returns or momentum. But later…
The note addresses whether an information ratio should use average monthly returns or cumulative monthly returns. Its answer recommends dividing the average monthly return by the standard deviation, pointing readers to an external response for further…