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 asks how to choose bond positions that replicate the issuer exposures of an equally weighted CDS index. Its two-issuer example contrasts investing equal bond notionals, which produces unequal market-value weights when the bonds trade at…
The document explains which risk-free rates to use when discounting project cash flows to today. A cash flow arriving at a future horizon should be discounted with the spot rate for that horizon, raised to the matching number of periods. A forward rate is…
The document addresses whether an internal rate of return should be described as a nominal or effective interest rate. It distinguishes a quoted rate with a specified compounding frequency from an effective rate converted to a different period. For instance,…
The discussion asks how small correlations might support reliable financial gains, while observing that strong correlations alone do not guarantee a dependable strategy. One answer links the idea to the Kelly criterion, which sizes bets according to expected…
The document describes how to encode an index-tracking portfolio in a genetic algorithm. The proposed chromosome represents which benchmark securities are selected, rather than their portfolio weights. For each selected subset, a separate quadratic…
The document asks how to choose weights in a weighted Frobenius norm when using alternating projections to adjust an equity correlation matrix that is not positive definite. It raises the possibility of weighting entries according to portfolio exposures, so…
The document explains what it means for SPY to track the S&P 500. The fund seeks to hold component weights close to those in the index, so its net asset value changes with the weighted returns of its holdings, after fees and expenses. The difference between…
The document considers how to estimate a Basel long-run average default rate when exposures enter and leave a portfolio during the year. It describes a simple estimator: at each year end, count the exposures still active, measure defaults among them over the…
The discussion distinguishes the first and second fundamental theorems of asset pricing. In the account provided, the first connects absence of arbitrage with the existence of a linear valuation rule that assigns zero value to traded cash flows. The second…
The document examines why adapting a long-only risk-parity objective to a dollar-neutral portfolio is difficult. Long-only risk parity seeks equal risk contributions, often by minimizing the dispersion of each asset’s weight multiplied by its marginal…
The document describes solving for the risk-aversion parameter in a mean–variance portfolio setup. Portfolio weights are expressed as a function of the parameter, expected returns, the covariance matrix, and a budget constraint. Those weights are substituted…
The document discusses portfolio optimization using an ETF and VIX futures, comparing minimum-variance and Sharpe-maximizing approaches across different rebalancing schedules. The response focuses on minimum-variance intuition: an asset’s weight is…
The document outlines a variance-covariance approach to estimating volatility for a portfolio of cryptocurrencies. It starts from daily price changes, forms a covariance matrix of daily returns, and scales that matrix by 365 to estimate annual variance,…
The document considers how to calculate the correlation between a stock and an index reconstructed without that stock. It defines the reduced index return by removing the stock’s weighted return from the full index return and rescaling by the remaining index…
The document raises an unresolved scaling question for dynamic portfolio optimization using the Modified Sharpe ratio. Because that ratio depends on portfolio skewness and kurtosis, the author needs co-skewness and co-kurtosis arrays to construct the…
The document presents a mathematical way to screen stock pairs before computing every pairwise correlation. For three variables, their correlation matrix must be positive semidefinite, meaning its eigenvalues cannot be negative. That constraint links the…
The document poses a portfolio-replication problem for a derivative whose terminal payoff is the time average of an underlying asset's price over the contract period, less a fixed strike. It assumes continuously sampled prices and a zero interest rate, then…
The document formulates the value of a portfolio that keeps equal weights in a set of stocks through continuous trading. For two stocks, it represents portfolio value as a function of their share prices and proposes partial-derivative conditions: each price…
The document demonstrates a fundamental valuation calculation for a pharmaceutical company using expected net income, book equity, a cost of equity, and long-run growth. It first subtracts interest expense from EBIT and applies the corporate tax rate to…
The document describes an attempt to check the optimal consumption and investment policy in Merton’s portfolio problem by simulating wealth paths and comparing average terminal utility with an analytical value function. It gives a discretized wealth update,…
The document presents standard matrix formulas for the global minimum variance and tangency portfolios, including their expected returns, volatilities, and weights. The question concerns a portfolio built from daily Dow Jones stock returns: its tangency…
The document examines why adding a gross-exposure constraint to a return-maximizing, risk-constrained portfolio can produce weights concentrated in a few assets. It describes a mean-variance setup that maximizes expected return subject to a covariance-based…
The document distinguishes maximum drawdown, measured from a running portfolio-value peak to a subsequent trough, from a longest run of negative returns. A drawdown can remain unrecovered at the end of the sample; recovery is tracked separately. The answer…
The document addresses how to estimate a portfolio’s beta when some holdings, such as recently listed companies, lack enough historical returns for reliable individual beta estimates. It considers estimating beta by regressing portfolio returns on index…