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Beta is the slope of a regression of a stock's returns against the market's. That's the whole definition. It says nothing about how risky the stock is, and once you put R-squared next to it, a 0.5-beta stock can be more volatile than a 1.8-beta one.
Everyone knows 2x leverage wipes you out at a 50% drawdown. Almost nobody does the other calculation: with a 30% house maintenance requirement, the margin call lands at a 28.6% decline. That is an ordinary bad year, not a crash.
A $1 million personal umbrella policy averages $300 to $400 a year. Each additional million runs $75 to $150. That pricing curve tells you what the product is: insurance against something that almost never happens, and the reason your liability is uncapped while your coverage is not.
Diversification lowers the risk of your portfolio without lowering your expected return. That combination is rare enough that economists call it the closest thing to a free lunch in finance. Here is how it actually works, and where it stops working.
Volatility isn’t the same thing as risk. It isn’t the same thing as direction. And the most-quoted volatility number on TV measures something almost nobody understands.
