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The document asks how to calculate a firm's unsystematic risk from a market regression, given its R-squared and the regression's standard deviation. It distinguishes total return variability from the part left unexplained by the market. The answer points to…
The document discusses adding candlestick-pattern features to a machine-learning model that predicts whether a stock’s next daily close will rise or fall. The researcher scores patterns by the share of observed cases in which price moved in the pattern’s…
The document poses a hedging problem for a one-year payoff that activates only if a stock falls at least 20% from its initial level. If that condition is met, the holder receives the positive excess of realized volatility over a threshold; otherwise the…
The document derives the familiar annualization rule for covariance of asset log returns: multiply the per-period covariance by the number of periods in a year. It uses the covariance-of-sums identity. When returns within each period may co-move but returns…
The document considers a cross-sectional performance-attribution regression with asset returns as the response and style factors plus country indicators as predictors. It asks whether including a dummy for every country alongside a constant makes the model…
The document considers why the equivalent martingale measure is unique in the standard Black–Scholes setting. Its proof outline represents a candidate measure through a positive density process and uses the predictable representation property to express that…
The document explains how to obtain the probability that a stock price modeled by Heston will finish above a specified threshold at a future date. In options terminology, this probability is the undiscounted value of a digital call on the modeled spot…
The document derives the probability that an investment has a positive return over a chosen horizon under a geometric Brownian motion model. Starting with a price process whose drift is 15% and volatility is 10%, it applies Itô’s lemma to show that log…
The document explains why a latency figure is meaningful only when its start and end points are specified. It distinguishes order-to-accept latency, the round trip from sending an order until receiving an acceptance, cancellation, or execution response, from…
The document considers how to store and represent constraints in an asset-allocation program. It raises options such as classifying constraints into categories, defining a small domain-specific language and parser, or using a structured representation such…
The document asks how to attribute the total loss from a sequence of monthly returns to selected months. It points out that returns compound multiplicatively, so simply adding the monthly percentages and assigning a fraction of that sum to the ending loss…
The document examines whether Itô’s lemma can derive the risk premium of a derivative without assuming in advance that it shares the underlying asset’s Sharpe ratio. It applies Itô’s lemma to a value defined as the exponential of the risk-free rate times the…
The document asks why a rolling average of a compounded price series can appear to have the same variance as the underlying price levels, even as the averaging window grows. The question contrasts this observation with the familiar intuition that averaging…
The document investigates why a GARCH(1,1) fit differs from a variance model that replaces its lagged squared-return term with an external regressor. The example uses daily equity returns and compares fitted coefficients from the two specifications. The…
The document examines the moment generating function of a stochastic process formed by integrating Brownian increments against a response kernel whose argument depends on both integration time and the current time. Applying Itô’s lemma to the exponential of…
The document explains why forward Libor rates are often modeled as lognormal in Black’s framework, while clarifying that this distribution is a modeling choice rather than a requirement of no-arbitrage. By expressing a forward rate as a ratio of zero-coupon…
The question compares two ways to specify returns when modeling stock prices under the physical measure. A conventional GARCH model uses a constant conditional mean, with volatility changing through the variance process. An alternative adjusts the mean by…
The discussion surveys software and methods for testing options strategies, including multi-leg spreads. It explains why this work is harder than testing linear instruments: historical option chains are large, implied volatility histories may be unavailable,…
The discussion examines whether the risk-neutral measure, used to price securities, should also be used to forecast real-world returns. It argues for comparing predictive performance empirically rather than relying only on theoretical objections or strong…
The discussion distinguishes elicitation from backtesting. Expected Shortfall (ES) lacks a scoring function that uniquely elicits it as a point forecast, but that limitation does not by itself make ES impossible to backtest. The document cites work proposing…
The document addresses a mistaken either-or choice between modeling returns with a parametric probability distribution and using an autoregressive model. These describe different parts of a model: a distribution specifies the form of uncertainty, while…
The document surveys liquidity mechanisms beyond a central limit order book, including requests for quote, streaming quotes, single-dealer platforms, multi-dealer platforms, systematic internalisers, and dark pools. The response focuses on the trade and…
The document asks whether a long position in a quarterly bitcoin future and a short position in a perpetual swap can remain market neutral. It explains that perpetual swaps have no expiry and use funding payments to help keep their prices near spot. The…
The document discusses the Corwin–Schultz estimator, which infers bid-ask spreads from high and low prices over consecutive days. Its derivation relies on a geometric Brownian motion assumption and a relationship between one-day and two-day variance,…