Five questions, answered from the data.

The yield curve is what you get by plotting what the US government pays to borrow for different lengths of time. It normally slopes upward, because lenders want more for tying money up for ten years than for three months. When it slopes the other way, the bond market is pricing short-term rates to fall, which usually means it expects the Federal Reserve to cut because the economy is weakening. That is the whole theory, and it is why an inversion gets so much attention.

Read the chart from the left and the rule looks weaker than its reputation. The recessions of 1957, 1960 and 1990 arrived with the spread narrowing but still above zero. On this measure the signal belongs mostly to the period after 1966, and the table below gives every case, including the misses.

The false starts matter as much as the hits. The curve inverted for 5 months in 1966 and the economy kept growing until the end of the decade. The inversion that began in November 2022 lasted until November 2024, reached −1.57 points at its deepest, and the NBER has not dated a recession since. The NBER dates recessions many months after they begin, so for now that reads as "not yet" rather than "no".

One of the hits deserves an asterisk. The 2019 inversion counts because a recession began nine months later, but that recession was caused by a pandemic, and no bond market saw it coming. The tally flatters the signal by at least one.

Most of the risk numbers you will meet, from volatility to value at risk, start from the standard deviation. It is a good summary of an ordinary month. It says much less about the months that matter, because under a normal distribution a move of four standard deviations should turn up about once in 1,300 years of monthly data. This sample has 9 of them in a hundred.

The middle is different too. More months sit close to the average than the normal curve predicts, and fewer sit a moderate distance away. Excess kurtosis of 7.3 measures the two effects together: a market with more quiet months, more violent ones, and fewer in between than the bell curve would give it.

A histogram shows how often. It does not show what a bad run feels like from inside, which is what an investor has to live through.

The 1929 fall took until January 1945 to recover, 15 years even with every dividend reinvested. The other four falls in the table took between three and six years to make back.

Correlation measures how closely two returns move together, from 1 for lockstep to 0 for no relation at all. Ten industry portfolios is a deliberately blunt test. Each one holds hundreds of stocks, and between them they cover the whole market. If the line between energy and healthcare fades in a sell-off, the line between two stocks you picked will fade too.

The peaks line up with the crises you would name: 1929, 1987, 2008 and 2020. The highest reading, 0.94, came in October 1987, when almost everything fell on the same day. The next chart asks the question more directly, one quarter at a time.

A straight regression line through these dots would explain only 5% of the variation, and it would suggest there is little to see. That is because the effect is one-sided: correlation rises in falling quarters and does not drop in rising ones, so a single straight line averages the two halves into something flat. The averages by tenth show the shape a line hides, which is why the chart uses them.

The latest reading is unusually low. Low correlation is what makes a portfolio look well diversified, and it is a description of calm markets. The history above shows what a sell-off has tended to do to it.

CAPE is the index price divided by the average of the last ten years of earnings, both adjusted for inflation. Averaging over ten years takes out the business cycle, so a recession's collapse in profits does not make the market look expensive just as prices are falling. Robert Shiller popularised the measure, and the monthly data behind it go back to 1871.

In the ten-year panel, each ten points of CAPE has come with about 4.0 percentage points less real return a year. That is the useful reading. The less useful one is to treat the line as a forecast. The dots sit a typical 4.4 points a year either side of it, which is the difference between doubling your money in real terms over a decade and barely keeping up with inflation.

The high end of the chart is thinner than it looks. The ten years after a CAPE of 25 or more ranged from −5.9% to 9.8% a year, and almost all of those months fall in two episodes, the late 1920s and the years around 2000. The dataset's latest CAPE of 35.2 sits beyond most of that history, which says prices are high relative to past earnings and says nothing about when that changes.

A factor is a rule for sorting stocks, held as a long-short portfolio: buy the stocks at one end of the sort and sell short the ones at the other. Size, value, momentum, profitability and investment are the best documented of them, with records that run back decades. The heatmap shows why a long record is not the same thing as a dependable one.

This is the backtester's problem in its plainest form. A rule can work for eighty years and then spend fourteen losing money, and nothing in the first eighty would have told you when. When a backtest of your own draws a smooth line, the question to ask is how much of the history sat in a shaded stretch like these, and whether you would still have been running the rule at the end of it.