
portfolio-optimization

I have been looking to understand the H-model in finance, that is used for stock price valuation. In particular, I wanted to formally derive the final formula: $$PV=\frac{D}{r-g_2}\left[1+g_2+\frac{H}{2}(g_1-g_2)\right]$$ Here $PV>0$ is the present value (price) of the stock, $D>0$ is the constant dividend payment that is paid forever, $r\in(0;1)$ is the required rate of return on the stock and t…
We document a persistent intramonth momentum cycle in U.S. sector ETFs that yields meaningful risk-adjusted returns when properly sequenced. Using the nine original Select Sector SPDR ETFs and SPY as the market benchmark from December 1998 through June 2026, we show that trailing 252-day sector momentum generates a positive spread on the first trading day of the month—and then sharply reverses on…
I am building an event-driven capital allocator for three trading strategies. This is a portfolio-optimization and validation question, not a request for investment advice. This question follows an earlier question about pricing capital reserved for stochastic future signals . A new experiment appears to have resolved that particular issue, but it has isolated a different one: estimating the appr…
A rigorous guide to duration and convexity - Macaulay duration, modified duration, dollar duration, DV01, and convexity - with derivations, worked examples and Python code.

This article considers a three-dimensional latent factor model in the presence of one set of global factors and two sets of local factors. We show that the numbers of global and local factors can be estimated uniformly and consistently. Given the number of global and local factors, we propose a two-step estimation procedure based on principal component analysis (PCA) and establish the asymptotic …
Hello all, We hope you're enjoying the middle of summer. Here's a quick recap of the latest improvements and additions we've prepared for Quantpedia during the past month – API users can now directly download the full research papers written by Quantpedia – 10 new Quantpedia Premium strategies – 2 new related research papers – 7 new backtests – and finally, 5 new posts on our Quantpedia blog
A detailed look at Seeking Alpha Quant Growth & Income: all 30 current holdings, the exact buy and sell rules, portfolio yield and sector mix, what it costs, and who the strategy suits.

Optimize a portfolio of [Cash, Stock A, European Put on A (K, T = 6 months)] over a 1-month horizon. The portfolio is constructed today and held unchanged for one month. I have a stochastic volatility model for A calibrated to historical data (physical measure P). Optimisation is straightforward a) without the option or b) option valued only as ITM ignoring the remaining time value. The problem -…

I'm having trouble understanding pg. 93 of Cochrane's Asset Pricing textbook. As seen in equation 5.23, $$\frac{\sigma(m)}{E(m)} \ge \frac{|E(R^e)|}{\sigma(R^e)}$$ the Sharpe ratio on excess returns bounds the discount factor. However, to find a lower bound on $\sigma(m)$ for a given value of $E[m]$ , it seems like the author is varying the value of $E[m]$ , using the value to get a hypothetical …

`--- title: "Compute portfolio risk metrics (Sharpe, beta, correlation) via a free API — in JS and Python" published: false description: "Stop re-deriving Sharpe, Sortino, beta, alpha, drawdown, correlation and rebalancing. Send your price series to one endpoint and get the numbers back — with copy-paste JavaScript and Python." tags: javascript, python, api, tutorial If you've ever built anything…

Most retail investors track their portfolio in a spreadsheet. Some upgrade to a free app that shows total value and daily change. That's it. Neither tells you the numbers that actually matter: your annualized volatility, your Sharpe ratio, your beta against the market, your maximum drawdown, how correlated your positions really are with each other. Institutional investors have had this for decade…

I am a little confused. I have calculated the tracking difference of an Index and an ETF using the return getting 0,4% tracking difference per year. I have then leveraged both, the Index and the ETF to a lever of 2 getting 0.63% tracking difference per year. I have then done some testing with hypothetical value and got 10% unleveraged and 20% levaraged with an lever of 2. So, $$ \text{leveraged t…

Apologies as I suspect this is a basic question I've been too afraid to ask (as an academic without "real" trading experience)-- I've seen a lot of literature where trades are sized proportional to volatility raised to a power (usually -1 or -2). i.e.: Size proportional to return/vol in an attempt to normalize P&L across various opportunities and size to level playing field. Size proportional to …
Recent interesting research from Cakici and Zaremba, highlights an often-overlooked aspect of machine learning for equity return prediction: the choice of prediction target. Rather than focusing on increasingly sophisticated model architectures or feature engineering, the authors show that how returns are represented during training has a much larger impact on predictive performance. In particula…

I'm currently paying a 1.25% margin rate. This rate is based on the Fed Funds rate plus a margin. I would like to hedge against the possibility of this margin rate increasing. What is the best/cheapest way to do that? I have access to the futures market but not the market for swaps. Some hedging ideas: Short 2-year Treasury futures. Roll the futures every quarter and eat the cost of rolling since…

An examination of SpaceX's record-breaking IPO — whether the $1.77 trillion valuation reflects genuine growth or concentrates systemic risk in a single point of failure. 🎥 Video Tutorial 🎥 Watch Video: https://youtu.be/48MkY66hXfA Topics: quantitative finance, investment analysis, financial education, financial education video, trading tutorial

This might sound like a trivial question but would appreciate the answer. How would you calculate the return of the portfolio consisting of only equity and credit instruments? For example, consider only two assets S&P 500 and CDX IG and assume that they have equal weighting at 50%. In order to get daily portfolio returns we need daily returns for equity and credit. For equity it is simple (just d…

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