QUBO Portfolio Optimizer

How the stock-count recommendation works

For every count from 3 to 25 stocks, the tool builds the best possible equal-weighted portfolio of exactly that size (greedy selection, then a local-search polish), and scores each one with the same objective the main optimizer uses:

Adding stocks helps at first — spreading equal-sized bets across more names reduces company-specific risk. But because every position is forced to the same equal share, each additional, weaker stock doesn't just add harmless diversification — it dilutes your best picks by forcing them to give up part of their equal share. Past some point that dilution costs more than the extra diversification is worth, so the score gets worse again. That's why the curve has a real low point instead of just improving forever — the recommended count is exactly that minimum.

Your risk tolerance changes how heavily variance is penalized in that score, which is why Conservative, Balanced, and Aggressive can each recommend a different count for the exact same stock universe. If your capital is small enough that this count would push any single position below the minimum position size, the recommendation is capped lower instead — a practical floor, not part of the math.

How hedging works, and what this calculator does

Hedging, in plain terms: it means taking on a second position that's expected to move opposite your main portfolio, so a loss in one is offset by a gain in the other. It doesn't make your portfolio go up more — it narrows the range of outcomes in both directions: smaller potential losses, but also smaller potential gains, since you're giving up some upside in exchange for that protection. People hedge when they want to stay invested through a rough stretch without selling anything, not to make extra money.

What this tool actually calculates: it sizes a hedge by matching volatility (how big the swings are), not full risk. It takes your portfolio's dollar value and annualized volatility, and the hedge instrument's own volatility (editable above — 18% defaults to roughly what a broad market index like SPY has historically had), then works out how large a position in that instrument would need to be so its typical swing is about the same size as your portfolio's typical swing.

What it deliberately leaves out: correlation. A hedge only actually protects you if the instrument moves opposite your portfolio when it matters. This calculator assumes that direction is right and only matches the size of the swings — it doesn't check whether your chosen instrument is really negatively correlated with your holdings. If it isn't (or worse, moves the same direction), this sizing wouldn't protect you the way it looks like it would on paper.

This is sizing math only, for if you decide to hedge — it never tells you whether you should, or which instrument to use. Those calls are yours.

How the news-sentiment signal works, and its real limits

What it does: once a week, every S&P 500 ticker's ~10 most recent Yahoo Finance headlines are scored by an automated sentiment analyzer and averaged into a single number per stock, from −1 (very negative) to +1 (very positive). If you turn this on, that score nudges the stock's expected return up or down by up to ±5 percentage points before the optimizer picks — a real number pulled into the math, not decoration.

What "automated" actually means here, honestly: this is a general-purpose sentiment tool (VADER), not a financial analyst and not a language model reading for meaning. It reliably catches sharply negative headlines — recalls, lawsuits, a stock "plunging" — but it's weak on common positive financial phrasing. A headline like "Company beats earnings estimates, raises full-year guidance" scores as completely neutral, not positive, because words like "beats" and "raises" aren't inherently positive outside a financial context. Treat this as a real but crude signal, not equivalent to actually reading the news.

It's off by default for exactly this reason. When it's on, each stock's score is shown in the results table so you can see what moved the pick, not just that something did.

How "expected return" is actually calculated

The old way, and its real problem: every stock's "expected return" used to just be its own trailing 3-year average return. That's noisy and momentum-chasing — it can't tell "this run is durable" from "this run is about to reverse," and testing it against real history repeatedly showed the same failure: a handful of recent winners dominate the picks, and when the run doesn't continue, the portfolio gets hit hard.

What it does now: Black-Litterman. Instead of trusting each stock's own noisy average, this starts from the market-equilibrium prior — reverse-engineered from the S&P 500's REAL market-cap weights: "what returns would make the actual market portfolio the mathematically optimal one?" That's a much more stable starting point than one stock's own history, because it's anchored to how the whole market is actually priced, not to whichever names happened to run hot the last 3 years.

Honest tradeoff: this pulls expected returns toward looking more like the market itself, which means it should reduce both extremes — fewer disastrous concentrated bets on a stock about to mean-revert, but also less chance of an outsized lucky win. It's a real methodology change, noted in the footnote below every result, not a bigger version of the same historical-mean estimate.

Sector-lean and news-sentiment (if used) still apply as the same small, capped nudges as before — just on top of this better-grounded base instead of the old raw average.