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The document discusses an options-text exercise comparing two quarterly interest-rate payoffs: a spread involving a five-year swap rate and compounded SOFR, and a spread between compounded SOFR and a Treasury bill rate. It reports that the solution manual…

The document asks how to annualize a Sharpe ratio for an intraday strategy evaluated with prices sampled every ten seconds. The trader describes computing each interval return, summing those returns to form a daily result, and then applying the usual…

The document raises a question about why the COS method presents a characteristic-function relation specifically for Lévy processes. It notes that if a log price is represented as an initial log-moneyness plus a random log-price change, the characteristic…

The document explains why rolling multi-day returns are statistically dependent and how that dependence affects covariance. It expands the covariance of two overlapping two-day return series into same-day covariance terms and cross-time covariance terms.…

The document describes a study design for sorting S&P 600 stocks into three portfolios according to historical return volatility. The proposed process estimates each stock’s volatility over a formation year, assigns stocks to terciles at the year end, and…

The document asks how to generate many asset return histories that match summary statistics from capital market assumptions, including expected returns, quartiles, volatilities, and incomplete correlation information. One response suggests initially setting…

The document discusses how to construct USD yield curves from publicly available data for valuing interest rate swaps and FX forwards. It distinguishes a discount curve from a LIBOR projection curve: the response recommends bootstrapping an OIS curve for…

The document asks how to adapt the differential Sharpe ratio reward used in a trading reinforcement learning system so that it instead reflects the Sortino ratio. The proposed motivation is that the traded assets are volatile and positively skewed, making…

This note distinguishes a local trading hedge from protection against large portfolio losses. For a position in one asset hedged with another, a correlation-based hedge weight can help manage small, day-to-day changes in portfolio value. A tail-focused hedge…

This note examines an apparent arbitrage in put-call parity when a stock follows a zero-drift Black-Scholes process, with no interest or dividends. For a strike equal to the current stock price, parity makes the call and put prices equal. The apparent puzzle…

The document outlines an Euler–Maruyama simulation for log asset prices under a local volatility model, using volatility that varies with time and the asset level. It asks which drift to use for option valuation versus estimating the real-world chance of an…

The document explains why Fama–French style time-series regressions use returns on factor portfolios, such as SMB and HML, rather than a stock’s size or book-to-market characteristics directly. Factor portfolio returns represent the payoffs associated with…

The document asks how the persistence coefficient in an AR(1) model for consumption growth affects the process. It identifies a zero coefficient as the case where growth has no dependence on its previous value; if the innovations are independent and…

The document asks whether the average strike and, where relevant, average implied volatility of a set of calls can be entered into one Black-Scholes calculation to approximate the portfolio’s average delta. The scenarios hold the underlying, expiry, rates,…

The document compares two ways to infer expected Federal Reserve rate changes across upcoming meetings: differences between successive overnight index swap rates, and implied average rates from fed funds futures. It gives a dated example using swap quotes…

The document presents an unfinished R simulation of traders whose buy, sell, or neutral decisions are updated using sampled decisions from other traders. Initial actions are assigned probabilistically, each trader observes a subset of peers, and the…

The document describes a user’s attempt to create a risk-return scatter plot from quarterly portfolio returns that include missing values. Replacing missing entries with zero does not resolve the problem: the assignment expression passed to the plotting…

The document considers how to balance minimum-variance portfolio construction with maximum diversification. It presents several responses: the minimum-variance and maximum-diversification portfolios are each unique and generally differ; treating both…

The document derives lower and upper bounds for a European call using payoff dominance. A call payoff cannot exceed the underlying asset’s payoff, so its price is at most the asset price. It also dominates both zero and the payoff from holding the asset…

The document studies the stochastic integral of an exponential deterministic function against a Wiener process over a finite time interval. It identifies the integral as a Wiener integral, which is normally distributed with mean zero. Its variance follows…

The document considers an Australian government bond issued in US dollars and asks which interest rate curve should measure its rate risk. The answers distinguish the bond's currency exposure from the issuer's country: because the payments are denominated in…

The discussion explains why a cash-or-nothing digital call cannot generally be replicated exactly using ordinary calls and puts at strikes spaced five dollars apart. In theory, a digital payoff can be approached by a call spread whose strike gap shrinks…

The document compares monthly and daily regressions of a portfolio described as 70% India and 30% USA against SMB, HML, WML, and a market excess return. It reports different coefficient estimates and significance levels across frequencies: the monthly…

The document asks how the Hayashi–Yoshida estimator for asynchronously sampled asset returns relates to realized variance and Pearson correlation. It describes realized variance as the sum of squared returns and the Hayashi–Yoshida covariance estimator as a…