You will be able to read beta and correlation figures and explain why they rise when markets fall hard.
Marcus counts eight holdings in his account and thinks of himself as diversified. Then he lines up their monthly returns side by side and notices that in his worst month, seven of the eight fell. The only one that didn't was his T-bills. Eight names, it turns out, were closer to three bets. This lesson gives you the two numbers that show how many bets you really hold.
Correlation measures how closely two return series move together, on a scale from minus one to plus one. Plus one means they rise and fall in perfect step, zero means no consistent relationship, and minus one means one rises exactly when the other falls. It says nothing about size: two assets can have a correlation of 0.9 while one moves ten times as far as the other.
Beta measures how far a holding tends to move when the market moves. A beta of 1 means it has tended to move about as much as the market, 1.5 means about one and a half times as much, and 0.5 means about half. Beta mixes correlation with relative volatility: it equals the correlation multiplied by the holding's volatility divided by the market's volatility.
In a spreadsheet, CORREL gives correlation from two columns of returns. For beta, use SLOPE with the holding's returns as the first range and the market's as the second. Monthly returns over three to five years are the usual choice.
Using the made-up ten years from lesson 2.3, Marcus's portfolio has a correlation of about 0.98 with the world equity index and a beta of about 0.88. Check it with the formula: 0.98 times his volatility of 11.3%, divided by the index's 12.5%, gives about 0.88. In plain words, his portfolio has moved almost in lockstep with world shares, about 12% less far. For all his stock picking, his account has mostly been a slightly toned-down version of the index.
Beta is a backward-looking estimate. A company that changes its business or takes on debt can carry a very different beta next year, and the figure you see quoted depends on which index, period and frequency someone used. Write down your choices when you calculate it.
Correlations are measured from history, and history doesn't hold still. Two assets that seemed unrelated in calm years can fall together when investors sell everything at once to raise cash or cut risk.
Well-known episodes show the pattern. In late 2008 and again in March 2020, shares in almost every market fell together, along with corporate bonds, REITs and commodities, in the space of weeks. Assets that had looked like separate bets turned out to share one driver: investors' need to sell.
The relationship between shares and government bonds has shifted too. For much of the two decades before 2022, high-quality government bonds tended to rise when shares fell, which made them a cushion. In 2022, with inflation high and rates rising fast, both fell in the same year, and portfolios that relied on bonds to offset share losses got hit twice.
None of this means diversification fails. Over long periods, holding assets whose returns differ smooths the ride and lowers the chance that one bad bet sinks you. A single company can go to zero, and a broad index of thousands of companies is very unlikely to.
What diversification doesn't do is protect you much in the weeks of a sharp market-wide fall, which is exactly when you most want it. Plan for that. Assume that in your next crisis, most of your risky holdings fall together, and check that you could live with your portfolio's drawdown on that basis. Lesson 11.5, Correlation clusters: hidden bets across your holdings, turns this into a sizing rule.
A correlation matrix is a grid with your holdings along the top and down the side, each cell showing the correlation of one pair. The diagonal is all ones, since each holding moves perfectly with itself.
Marcus built his from five years of made-up monthly returns for his five largest holdings: the world equity ETF, the SGD bond fund, the STI ETF, his local bank shares and his US chip designer. The bank and the STI ETF came out at about 0.88, which makes sense because banks carry a large weight in the STI. The world ETF and the US chip stock came out at about 0.82, because large US technology companies are a big part of a world index. The bond fund's correlations with the share holdings sat between 0.1 and 0.3.
Pairs above 0.8 behave like one position. So Marcus's bank shares were mostly a bigger bet on the STI he already held, and his chip stock was partly a more volatile copy of his world ETF's largest holdings. Neither discovery meant he had to sell. It meant he couldn't count them as diversifiers.
When you build your own, use returns in SGD over the same months for every holding, and colour any cell above 0.8 so the clusters stand out. The activity asks for exactly that: a matrix of your five largest holdings from monthly returns, with every pair above 0.8 marked.
Build a correlation matrix of your five largest holdings from monthly returns and mark any pair above 0.8.
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