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 note considers whether an institution’s risk-aversion parameter can be inferred from observed trade profit and loss under a proposed power utility function. Its response cautions that utility is generally specified over wealth or consumption, rather than…
The document shows how to calculate a Sortino ratio for a weighted portfolio. It first forms a portfolio return series by applying asset weights to each period’s returns. Given a target return, or minimum acceptable return, it computes downside deviation as…
The document explains how to derive the correlation between two arithmetic baskets from the volatilities and pairwise correlations of their component assets. For two two-asset baskets, it first adds the four cross-basket covariances, expressing each…
The document examines a claim that active portfolios collectively have lower risk-adjusted returns than a passive market portfolio. It presents a numerical example with a market holding and an independent active holding, then constructs two funds with…
The document frames expected return estimation as a key input to Markowitz mean–variance portfolio optimization, where allocations balance expected return against variance according to an investor’s risk aversion. It asks what alternatives exist to…
The document discusses the approximate relationship between information ratio, information coefficient, and breadth: IR is often expressed as IC multiplied by the square root of breadth. It cautions that this is a useful but imprecise framework and that…
The discussion explains convexity for a portfolio containing two zero-coupon bonds with different maturities. It derives portfolio convexity by taking the second derivative of total price with respect to yield and normalizing by portfolio price. The…
The document considers what a third dimension could add to a mean-variance efficient-frontier visualization, whose familiar axes are portfolio volatility and expected return. It explains that these two statistics can describe the trade-off when returns are…
The note shows how to fill gaps in portfolio weight data between known rebalancing dates. The method treats the holdings established at the start of the period as fixed in share count until the next rebalance. Convert each starting weight into an invested…
The document explains why an ISIN should not be treated as a unique identifier for a company. An ISIN identifies a financial instrument, and one issuer may have multiple instruments, including different equity classes or a depositary receipt representing…
The document sets up Merton’s optimal portfolio allocation problem as a Hamilton–Jacobi–Bellman equation for an investor choosing a portfolio share between zero and one. It proposes discretizing that control and solving the value function with an implicit…
The document asks why portfolios sorted by lagged maximum return show a significant spread between extreme groups while the Fama–MacBeth regression coefficient on that variable is not significant. The response notes that these results concern different…
The discussion examines whether volatility exposure belongs in a portfolio as an asset class or is better understood as a risk factor. One view distinguishes volatility itself from the instruments that provide exposure, such as options and volatility…
The discussion clarifies the roles of variables in a factor return model. The question contrasts a familiar regression, where observed factor data are multiplied by estimated coefficients, with a formulation involving benchmark returns, pure factor portfolio…
The post examines whether a rise in the risk-free rate changes the efficiency of the market portfolio. Under CAPM, it rewrites expected returns so that higher-beta assets have lower expected returns and lower-beta assets have higher expected returns when the…
The document explains how portfolio weights can be negative or exceed one when an optimization allows short selling and leverage. A negative weight represents a short position, while a weight above one represents exposure greater than the investor’s capital,…
The document addresses how to weight a portfolio of long and short securities to remove directional exposure. Its proposed approach begins by defining the unwanted direction, often an equity index for an equity portfolio. Estimate each security’s beta to…
The document points readers seeking to understand bullet and barbell bond positioning toward literature on yield-curve analysis, convexity bias, and methods for assigning portfolio weights. It names a detailed treatment by Antti Ilmanen and a Lehman Brothers…
The document formulates the Markowitz minimum-variance portfolio for a target expected return, with weights summing to one. The question asks how to permit short selling while limiting the proceeds raised from short positions relative to initial wealth. The…
The document presents a household allocation problem: each year, divide excess earnings between stock investment and mortgage prepayment, with uncertain stock returns and mortgage rates. Its code simulates correlated outcomes, tests allocations on a grid,…
The document asks how to calculate a certain consumption equivalent for an agent with Epstein–Zin preferences. It first defines the idea under CRRA utility: find a fixed consumption level that gives the same lifetime value as a stochastic consumption stream.…
The document considers bond portfolio optimization when some securities are mandatory and others are eligible candidates, while the final portfolio may need to meet a limit on the number of holdings. It recommends filtering ineligible bonds before continuous…
The document asks why expected return is often related linearly to risk and whether the Sharpe ratio or a variance-based value-added measure should guide portfolio choice. The answer connects linear expected excess returns to covariance with a stochastic…
The answer describes how bond portfolios can immunize a liability or another bond against interest-rate changes using duration and convexity. Given the ability to short, two bonds with different durations can match a target duration, while three…