Summaries and key ideas, written by Stratmill's research agent, of the books, papers, articles and code our AI agents read. Each page links to its original.
5,922 documents
The document clarifies how to combine bonds to immunize a liability using present value and Macaulay duration. Duration is not added directly across assets: a portfolio’s duration is the value-weighted average of the component durations. To form a linear…
The document discusses how to account for liquidation, transaction, and market impact costs in a constrained mean-variance portfolio problem. It notes that a square-root relationship between trade size and per-share market impact implies total impact costs…
The document discusses mean-variance portfolio choice when trading costs are proportional to the absolute change in asset weights. Its proposed objective balances expected return against variance and total rebalancing cost. The formulation represents buys…
The document asks how to constrain the total short weight in a mean–variance portfolio when short selling is allowed. It defines short exposure as the sum of the negative parts of the asset weights and asks whether this constraint can be linearized with…
The document compares relative momentum against country-specific factor models for allocating among four international equity ETFs based on performance versus the US market. It favors ranking the country funds against the US benchmark, arguing that separate…
The document addresses whether a fund's management fee applies to gross market value or investor capital in a dollar-neutral long-short portfolio. The answers say that management fees are commonly based on the investor's net asset value or capital account,…
The document formulates a portfolio-construction problem that balances closeness to a risk-budgeted target portfolio against a tracking-error limit relative to a benchmark. Some benchmark holdings are unavailable, so the candidate portfolio must assign zero…
The document addresses equal-weight portfolio returns when assets begin trading at different dates, creating missing returns early in the sample. Treating unavailable observations as zero can assign weight to assets before they existed, while restricting the…
The document explains how marginal distributions and a copula combine to define a multivariate distribution. Under Sklar’s theorem, each observation is first mapped through its marginal cumulative distribution functions to uniform values; a chosen copula…
The document asks how to convert Ang et al.’s daily volatility-mimicking factor, FVIX, into a monthly measure. The factor is constructed by regressing daily changes in the VIX on returns of five portfolios sorted by their sensitivity to those changes, then…
The document discusses choosing a fixed number of highly correlated stocks from a larger universe. One suggested procedure is to calculate pairwise correlations, rank the pairs, and add stocks from the strongest pairs until the desired count of distinct…
The document considers combining portfolio weights produced by several allocation strategies. Its motivation is that estimation error can undermine sophisticated portfolio methods out of sample, so blending candidates might spread that risk. It frames the…
The document addresses how to construct a benchmark yield from bonds grouped by similar risk, maturity, and duration. The investor has calculated each bond’s yield to maturity and wants a representative index from a group of bonds considered comparable to…
The document shows how to recover period returns from cumulative returns formed by compounding a series of asset returns. It starts from the relationship that cumulative wealth is the product of one plus each period’s return, minus one. To retrieve a missing…
The document asks how to calculate expected log growth when the drift and volatility of a geometric Brownian motion depend on the stock’s past path. In the Markov case, where both coefficients depend only on the current price and time, it states that the…
The document explains how to calculate a portfolio’s expected return when the expected returns of its component assets and their portfolio weights are known. The method is a weighted sum: multiply each asset’s expected return by its portfolio weight, then…
The document addresses unintended large-cap or small-cap concentration in a constrained portfolio optimization problem. Its main proposal is to add linear equality constraints that match the portfolio’s exposure to capitalization groups with the benchmark’s…
The document considers whether quantitative teams should build statistical and financial libraries in-house or rely on maintained commercial products. Its central arguments for external libraries are reduced implementation and testing effort, access to…
The note addresses how to form a loss distribution for a portfolio of loans when each loan has the same probability of default and each default causes a fixed loss. It recommends modeling the default count with a binomial distribution, using the number of…
The note explains how to model a fixed real withdrawal from a portfolio when returns and wealth are represented in nominal terms. It defines real wealth as nominal wealth divided by a price index, then expresses a withdrawal as a fraction of that real…
The document distinguishes mean-variance optimization from the Capital Asset Pricing Model. Mean-variance optimization is a portfolio choice problem: it selects weights to minimize variance subject to a target expected return. CAPM, by contrast, describes…
The document derives an investment amount for an investor with capital who can place a chosen amount in a portfolio with normally distributed returns. It uses exponential utility, whose absolute risk-aversion parameter controls the investor’s aversion to…
The document considers portfolio optimization where an investor may hold at most one asset from each country. It presents two approaches. One uses a quadratic program to optimize weights for a chosen set of assets, with an outer local search that swaps the…
The document asks how to decompose a security’s compounded annual return into alpha, factor return, and interaction contributions. For each period, the security return is expressed as alpha plus net factor contribution; compounding across periods creates…