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The document explains why an attempted R calculation returned zeros: it subtracts the logarithm of each price from the logarithm of that same price. Log returns instead compare prices at different observations, commonly by taking the difference between…
The document considers a portfolio formed from several contingent claims whose prices depend on one underlying asset. It explains why differentiating the portfolio value as a weighted sum can be misleading: the weights may change over time, but the…
The document distinguishes the mechanical effect of interest rates on a stock forward price from the broader economic effect of rates on the underlying share price. Under a no-arbitrage carry argument for a non-dividend-paying stock, the forward price is the…
The document describes a direct way to interpret a finite set of equally probable portfolio-return scenarios for Value at Risk. With 250 scenarios, sorting the outcomes from worst to best makes the 25th-worst outcome the 10% VaR under the convention…
The document explains how the stochastic discount factor prices a payoff through its expected value and its covariance with that payoff. When covariance is zero, the payoff has no exposure to the priced source of risk represented by the discount factor. Its…
The document explains when a cross-currency swap can be viewed as two interest rate swap legs. For a typical physically delivered fixed-for-fixed or fixed-for-floating structure, each currency has its own interest cash flows, and principal exchanges must…
The document explains why changing interest-rate or dividend-yield inputs can make an option implied-volatility smile appear unusual, especially for in-the-money options. Under Black–Scholes intuition, a higher interest rate raises a call’s modeled value; if…
A deliverable FX forward exchanges the two contracted currencies at maturity. A non-deliverable forward instead calculates a net payment in a settlement currency from observed exchange rates on a fixing date, usually before maturity. NDFs are used where…
The document asks how to obtain long-run daily or weekly returns for MSCI factor indices, including momentum, minimum volatility, small cap, and enhanced value. The replies explain that index providers commonly restrict benchmark data, so full historical…
The question investigates why a USD zero-coupon inflation swap’s fixed-leg payment can remain unchanged when its maturity date moves by a few days, then jump to the next annual compounding amount. The answer proposes interpreting the 1/1 convention through a…
The question asks whether Black–Scholes can use an expiration measured in hours after converting that duration to years, and why an option calculator returns a different value when the input changes from a day to an hour. The answer interprets the change as…
The document describes a question about fitting an Asymmetric Laplace Distribution (ALD) to daily NIFTY 50 log returns and determining whether the fitted distribution has finite variance. The post gives fitted location, scale, and asymmetry parameters and…
The discussion outlines ways to study high-frequency quotes and trades when observations arrive at uneven intervals. It recommends first defining the target, such as volatility or correlation, and accounting for how measurement intervals affect the…
The document explains how derivative volatility relates to the volatility of its underlying asset through elasticity, also called leverage or lambda. Elasticity measures the derivative’s percentage price response to a one-percent change in the underlying,…
This document considers how to interpret significant cross-correlations with opposite signs at adjacent lags in two time series. Its example frames interest rate data as sound signals and reports a strong positive correlation at zero lag alongside a stronger…
Bond yields are generally quoted using a compounding frequency that matches the coupon payment schedule. Some markets instead standardize yields to the frequency used for local government bonds, which makes comparisons with benchmarks and across issuers…
This document asks how to translate an earnings event volatility estimate into an implied one-day expected return using a formula from a volatility trading text. The formula combines the exponential of half the event variance with the normal cumulative…
The document considers how to estimate volatility when a return series contains complete monthly observations plus a final observation covering only part of a month. It proposes a weighted variance calculation: first scale the partial-period return to an…
The document explains how to calculate a portfolio’s cumulative return across several periods and why the calculation depends on whether the portfolio is rebalanced. For buy-and-hold, multiply each asset’s returns across periods, apply its initial portfolio…
The document explains a formula for estimating a one-period total return on a ten-year Treasury note using its yield at the start and end of the period. The formula values the note’s coupon stream as an annuity discounted at the ending yield, adds the…
The document explains style factors as interpretable characteristics used to describe the risk and returns of assets or portfolios. They give portfolio managers and other decision-makers a consistent way to discuss exposures, in contrast with less directly…
Mean-variance optimization is a general portfolio framework that evaluates portfolios by expected return and variance or standard deviation of returns. Under suitable distributional assumptions, it identifies efficient portfolios: those offering the best…
The document frames a market-impact question: how typical transaction cost models would estimate the long-term price effect of buying shares equal to 1% of a company’s outstanding stock. It converts that quantity into trading volume using an assumption of…
The document examines a structural default model in which a firm's unobserved assets follow a geometric Brownian motion and default is linked to a debt threshold. It contrasts measuring default at a fixed horizon by checking whether assets finish below the…