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 example considers a portfolio value defined as Brownian motion squared minus time. Applying Itô’s lemma to this function produces a drift term from the time derivative and the second derivative with respect to the Brownian state, alongside a stochastic…
The note explains why portfolio theory commonly plots expected return against standard deviation rather than variance. Its example combines a risk-free asset with a risky asset: scaling the risky position by one half scales standard deviation by one half,…
The responses survey reinforcement learning (RL) applications in quantitative finance, with portfolio allocation as the main example. They describe critic-only methods, which choose actions using learned value estimates; actor-only methods, which optimize…
The document describes a student fund’s effort to improve how it represents a domestic government bond index held through fixed-income ETFs. Its current approach treats the index as one bond, discounts projected cash flows, and feeds that estimated value…
The document raises a methodological question about applying principal component analysis to financial asset series. It compares using price levels with using returns, and asks whether the selected series should be standardized before calculating covariance.…
The document compares two ways to scale daily trading profit and loss: dividing by the previous day’s gross portfolio value or by the account’s initial equity. These choices describe different things. The prior-day value expresses each day’s gain relative to…
The document asks whether a proposed optimal holding for a CARA investor with normally distributed risky-asset payoffs is correct. Its setup compares expected payoff net of the risk-free investment cost with payoff variance, and suggests scaling expected…
The document asks whether Sharpe-style portfolio style analysis can explain equity fund performance using indices grouped by high, medium, and low ESG characteristics. It identifies suitable data as the central practical challenge and points to ESG scoring…
The document raises a portfolio optimization problem in which tracking error is constrained using a sample covariance matrix. It describes a case with 1,000 assets but only 60 monthly return observations, producing a covariance estimate that is not positive…
The answer demonstrates how a fixed-rate bond can be represented in QuantLib with an evaluation date, payment schedule, day-count convention, face amount, and coupon rates. The resulting cash-flow list contains coupon payments and the final principal…
The discussion distinguishes contemporaneous factor models from forecasting models for portfolio optimization. In the Fama–French three-factor setup described, an asset’s return is related to factor returns from the same period. That relationship can help…
The document examines how to interpret the stock and money-market components of a portfolio formed by holding a call and discounted cash equal to the strike. Under Black–Scholes assumptions, it combines the call price with the present value of the strike and…
The accepted answer explains how to minimize conditional value-at-risk, also called expected tail loss, using a scenario-based linear program. It introduces portfolio weights, a variable representing the value-at-risk threshold, and one auxiliary variable…
The document describes a simulation designed to compare covariance transformations for minimum-variance portfolio construction. For each lookback window, the author samples portfolios of 100 assets, estimates a sample covariance matrix, transforms it, and…
The document proposes a quadratic program for finding an efficient frontier between expected alpha and a portfolio’s residual variance relative to a benchmark. It expresses residual variance as portfolio covariance risk less the benchmark variance scaled by…
The document asks how to construct an efficient frontier by optimizing portfolio weights at specified volatility levels, rather than relying on random sampling. It describes maximizing expected portfolio return subject to a volatility ceiling and nonnegative…
The document considers how to estimate a portfolio variance-covariance matrix when assets began trading at different times. One direct method is to use only the period in which every asset has data, which avoids mismatched histories but discards older…
The document describes how to express an unhedged US investment’s performance in euros. First, turn the dollar return series into a total-return price index, using an arbitrary starting value such as 100. Next, convert each index value into euros using the…
The document poses a fixed-income immunization question involving a mortgage asset with fixed payments, prepayment and option-adjusted spread models, and calculated price, duration, and convexity. The asset and a blend of liabilities are assumed to trade at…
The document asks which risk-free rate to use when constructing a maximum Sharpe ratio portfolio from a rolling estimation window of monthly returns. It frames the problem within mean-variance portfolio theory, where the Sharpe ratio measures expected…
The document explores reducing a large ETF or equity universe before portfolio optimization. Suggested approaches include clustering return series using correlation-based distances, examining PCA loadings to group assets with similar behavior, and using…
The document considers a heterogeneous portfolio in which inverse-volatility risk parity can assign very large weights to instruments whose estimated volatility has fallen relative to the rest. It describes a proposed cap that compares risk-parity weights…
The document explains how to account for inflation when calculating an internal rate of return. Its method is to build a price index from the inflation rate, convert each cash flow into real terms by deflating it with the corresponding index, and then…
The document describes difficulties implementing Black-Litterman with analyst-consensus views. The author reports portfolio weights that become negative or exceed the full portfolio allocation, as well as returns below a market-weighted benchmark. In one…