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The document asks where to obtain historical implied volatility rank or percentile data for US equities. The questioner distinguishes those measures from an options data feed that provides implied volatility alongside historical realized volatility, and…
The discussion examines why fundamental equity risk models, such as Barra-style models, often assign securities a binary exposure to their country, industry, or world factors. A one-zero membership indicator is a simple way to define exposures and estimate…
The document asks how to estimate the CEV model’s parameters, which determine the scale and price dependence of stock volatility, for simulations of CPPI and OBPI portfolio strategies. The answer recommends calibrating the model to vanilla equity or index…
The discussion explains how bond DV01s measure each bond’s approximate price sensitivity to a one basis point move in its own yield, under a parallel shift assumption. Because the 5-year and 30-year bonds respond to different points on the yield curve, a…
The discussion compares position sizing in proportion to inverse volatility with sizing in proportion to inverse variance. In a simple portfolio of normally distributed assets, inverse volatility sizing is associated with risk parity: it treats assets as…
The document explains ways to identify a portfolio with zero beta when no risk-free asset exists. One practical approach begins with a portfolio of assets, estimates its beta by regressing its returns on market returns over a chosen horizon, then offsets the…
The document examines whether replacing the CAPM’s constant expected factor return with its realized time-varying return in time-series regressions creates an errors-in-variables problem that invalidates the GRS test. The proposed test runs asset-return…
The document shows how to derive the price of a 10-year zero-coupon bond from two 10-year coupon bonds with different coupon rates and known prices. The replication scales a long position in the lower-coupon bond and a short position in the higher-coupon…
The document discusses whether brokerages offer web APIs for market data and order entry. It gives examples of a URL-based trading interface and reports that TD Ameritrade provided web APIs requiring an account, while noting that broker access varied. The…
The document explains the distinction between clean (quoted) and dirty (cash) bond prices when specifying a bond option. Its answer emphasizes that over-the-counter contracts can define their strike and underlying price according to the parties’ chosen…
The document presents an attempt to forecast VIX using a constant-mean GARCH(1,1) model fitted to daily log changes in the VIX. It shows a historical sample, a training cutoff, a multi-step forecast, and forecasted conditional variances across dates and…
The document asks for the distribution and exponential moment of an Itô integral whose integrand is the sign of a Brownian motion. The answer observes that the integral is a continuous, square-integrable martingale and computes its quadratic variation from…
The document compares geometric Brownian motion (GBM) with the Ornstein–Uhlenbeck (OU) process and presents them as parts of a broader diffusion model. In that framework, setting the mean-reversion coefficient to zero gives a non-mean-reverting process,…
The document raises a measurement question about calculating Sharpe ratios from a vectorized backtest. Its example constructs a strategy-return series by retaining bar-to-bar log returns only between an entry and an exit, while recording zero returns outside…
The document addresses how to summarize a sequence of trading gains and losses when positions occupy capital for different lengths of time. It recommends using the internal rate of return (IRR) on actual dollar cash flows rather than averaging return per…
The document introduces the skew stickiness ratio (SSR) as a way to describe how at-the-money-forward implied volatility responds when the underlying asset moves. It uses this measure to distinguish two common smile-dynamics assumptions. Under sticky strike,…
The document surveys ways to estimate how an option’s implied volatility may respond to a hypothetical market move, with portfolio risk simulation as the motivation. It describes modeling the joint behavior of forward at-the-money volatility and the first…
The document frames portfolio construction as choosing weights across return series to maximize the Sharpe ratio, defined in the question as average portfolio return divided by its standard deviation. It provides a small sample return matrix and a CVXPY…
Reverse stress testing starts with an unacceptable outcome, such as a specified portfolio loss or capital shortfall, and works backward to find market scenarios that could produce it. When many combinations could reach the threshold, assumptions about how…
The document explains why the Kelly criterion chooses a position size by maximizing expected logarithmic wealth growth rather than expected wealth or simple return. Because wealth compounds multiplicatively across repeated bets, log returns add across…
The document explains an equivalence between a caplet paying a floating rate above a fixed strike and a put-style payoff on a zero-coupon bond. Its economic interpretation treats the caplet as the right to sell a one-period coupon bond with a predetermined…
The document addresses how risk managers can respond when portfolio managers argue that tighter limits kept them from benefiting from rallies or rebounds. Its central recommendation is to agree with senior management on a clear mandate for each trader,…
The document explains why a first principal component computed from asset returns may appear to represent the market with all-negative loadings and a strong negative correlation to a market index. This does not necessarily indicate a different economic…
The document outlines a probabilistic route from the Black–Scholes terminal-value problem for a European call to its familiar closed-form price. Feynman–Kac represents the solution as a discounted expected payoff under a diffusion. The derivation then…