For a portfolio formed by summing two dependent random variables, the note explains that VaR is still a one-dimensional quantile: first find the distribution of their sum, then take its target quantile. It gives an integral for the sum’s cumulative…
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2,013 documents
The document asks how bond ETF managers turn coupon payments from underlying holdings into the fund’s monthly distributions, including whether the timing of coupon receipts determines the payment month. The answer cites BlackRock’s explanation of the general…
The discussion addresses how to store daily or lower-frequency economic and financial observations that may be revised after their initial release. Its central method is to keep the observation’s reference period separate from the date each version becomes…
This discussion recommends literature for readers with a mathematical background who want to study optimization in finance. The suggestions range from treatments of efficient frontier calculations and Markowitz portfolio construction to a technical book…
The document asks whether data are available in aggregate on European banks’ use of credit risk approaches for regulatory capital. It describes the distinction between the Foundation and Advanced Internal Ratings-Based approaches, the additional role of…
The document explains why a currency swap’s future payments are valued by discounting them at current market yields. Under annual compounding, a future cash flow is converted to present value by dividing by one plus the relevant yield raised to the time…
The document considers how to model dependence when individual market series have heavy-tailed, approximately Student t marginals. It explains that a conventional multivariate t distribution imposes a t copula with a shared degrees-of-freedom parameter,…
The document considers adding vanilla interest rate swaps to an existing Monte Carlo VaR process for foreign exchange and commodities. The proposed simplified method estimates volatility and correlation from daily changes in par swap rates, simulates rate…
The document asks how to estimate future values for a portfolio containing a stock, a long-term coupon bond, and a European call option. It provides example daily inputs for the stock price, required yield, volatility, and short-term interest rate, and asks…
The document outlines a proposed portfolio framework that combines probabilities for four market states, historical asset data, simulated returns, and an investment committee’s views on distribution moments. It focuses on the difficulty of generating…
The document explains why Ledoit–Wolf covariance estimation blends a sample covariance matrix with the identity matrix. The blend shrinks estimated covariances toward zero and variances toward a common scale, limiting the influence of extreme sample…
The note asks how commodities relate to real assets and physical assets, drawing on a CFA reading that classifies commodities and tangible property as physical assets. It distinguishes commodities such as metals, energy, and agricultural products from real…
The document explains why pricing a multi-index structured option requires more than estimating historical average returns and covariance, then simulating under a multivariate normal distribution. It identifies risk-neutral pricing as the framework: discount…
The document asks what an estimated equilibrium return on 90-day Treasury bills means when it appears as the risk-free rate in a reference portfolio review. The accepted answer interprets the figure as a long-run estimate of the policy-rate environment,…
The document addresses an apparent contradiction in descriptions of Federal Reserve reserves: reserves are liabilities held by commercial banks, yet banks can request physical currency from the Fed. The key accounting point in the accepted answer is that…
The discussion distinguishes directional strategies, which take a view on an asset’s future movement, from relative-value approaches that trade multiple assets against one another. It names trend following as a clear example and also points to systematic…
This question considers approximating a recently launched fund with a set of market indices because the fund has a short history of daily net asset values. The intended use is to build conditional return distributions for bull and bear markets from the…
The document asks whether expanding the money supply can fund public services in a low-growth, deflationary economy, and whether quantitative easing should be understood as government money creation rather than genuine borrowing. It points to central-bank…
The document asks whether a source provides historical real yield curves across a broad set of countries. Real curves describe yields on inflation-linked bonds, and the question distinguishes them from nominal curves, which many central banks publish. The…
The discussion distinguishes real-world probability modeling for risk measurement from risk-neutral measures used in pricing. For counterparty exposure, the proposed perspective is to model the relevant risk factors and contracts together across currencies…
The document explains why converting a portfolio’s VaR from one reporting currency to another requires information about both the asset and the exchange rate. For a linear position, one approach estimates volatility directly from the asset price expressed in…
The document asks how to interpret and calibrate selling intensity and loss intensity in a liquidity stress test for a portfolio of equities and bonds. It introduces a cash conversion factor that combines a liquidity factor, based on selling intensity over…
The document shows how to compute the covariance of a weighted return index with one of its component assets or with another asset. Using the linearity of covariance, the covariance between a weighted sum and a variable is the sum of each component’s…
The document addresses a QuantLib change affecting construction of cross-currency basis swap curves for collateral posted in a currency different from the asset currency. It identifies ConstNotionalCrossCurrencyBasisSwapRateHelper as the apparent replacement…