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Math that finds the “best” mix can backfire, because it trusts shaky estimates too much.

A smarter starting point: begin with the whole market, then nudge it with your opinions.

Instead of equal dollars, give each holding an equal share of the portfolio’s risk.

Over the long run, stocks have rewarded their stomach-churning ride with extra return.

Real markets have far more extreme days than a tidy bell curve predicts.

A common gauge of “how bad is a bad day” — useful, but it hides the very worst.

We feel losses far more than equal gains — and that warps the choices we make.

Prices reflect a lot of what’s known — but maybe not everything, and not always calmly.

Markets switch between long calm stretches and sudden stormy ones — and fear has a price.

There’s a math-optimal bet size for growth — and most pros deliberately bet less.

A strategy that looks perfect on past data often falls apart in the real world.

Great long-term returns come from durable, high-quality businesses — and judging that takes more than a number.

The only honest test of a strategy is how it does on data you didn’t use to build it.

The big ideas combine into one calm plan: diversify, manage risk, cut costs, and stay disciplined.

A prediction-market price is a real-money bet turned into a probability — useful, but not gospel.

Markets are linked, so when two that normally move together pull apart, the gap itself is worth reading.

When results land far from what the business did a year ago, the price often keeps moving that way for weeks.

A strategy that looked excellent on the data it was chosen from usually gives back much of that edge the moment it has to earn it forward.

Counting your holdings tells you almost nothing about how diversified you are — counting your independent exposures does.

A record only means something if the rule was fixed before the record started, and the failures are still on the list.