Read beta and correlation figures and explain why both go up when markets fall hard.
Open your brokerage account, line up the monthly returns of each holding for the past few years, and find the month where the account did worst. Count how many holdings fell that month. If nearly all of them fell together, the number of names in your account overstates how many separate bets you hold.
Marcus, a retail investor in Singapore with SGD holdings, has eight holdings and considered himself diversified. When he lined up their monthly returns, seven of the eight fell in his worst month. Only his T-bills did not. His eight names were closer to three bets. Correlation and beta explain this, and they measure different things.
Correlation measures how closely two return series move together, on a scale from minus one to plus one. Plus one means the two rise and fall in perfect step, zero means there is no consistent relationship, and minus one means one rises exactly when the other falls. Correlation says nothing about the size of moves: 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 about one and a half times as much, and 0.5 about half as much. Beta combines correlation with relative volatility:
beta = correlation x (holding's volatility / market's volatility)
Using the made-up ten years of data from Lesson 2.3, Marcus found his portfolio had a correlation of about 0.98 with the world equity index. His volatility was 11.3% and the index's was 12.5%, so 0.98 x 11.3% / 12.5% = about 0.88. His portfolio moved almost in lockstep with world shares, about 12% less far. Despite his stock picking, it was mostly a slightly toned-down version of the index.
Put monthly returns for the holding and the market in two columns, usually covering three to five years. CORREL on the two columns gives correlation. SLOPE gives beta, with the holding's returns as the first range and the market's returns as the second. To check the result, multiply the correlation by the holding's volatility divided by the market's volatility.
Beta is a backward-looking estimate. A company that changes its business or takes on debt can have a very different beta the following year, and any quoted beta depends on which index, which period and which return frequency was used. Write down your index, period and frequency each time you calculate one.
Correlations are measured from history, and history does not hold still. Assets that seemed unrelated in calm years can fall together when investors sell everything at once to raise cash or cut risk, and their correlations rise towards one. In late 2008, shares in almost every market fell together within weeks, along with corporate bonds, REITs and commodities. March 2020 followed the same pattern. The shared driver in both episodes was investors' need to sell.
For much of the two decades before 2022, high-quality government bonds tended to rise when shares fell, cushioning share losses. In 2022, with high inflation and fast-rising interest rates, shares and government bonds both fell in the same year, and portfolios relying on bonds to offset share losses were hit twice.
Diversification does not fail overall. Over long periods, holding assets with differing returns smooths the ride and lowers the chance that one bad bet sinks you. A single company can go to zero; a broad index of thousands of companies is very unlikely to. It protects little during the weeks of a sharp market-wide fall, which is when people most want it. So assume that in the next crisis most of your risky holdings fall together, and check you could live with the portfolio's drawdown on that basis. Lesson 11.5, Correlation clusters: hidden bets across your holdings, turns this assumption into a sizing rule.
A correlation matrix is a grid with holdings along the top and down the side, where each cell shows the correlation of one pair. The diagonal is all ones, because each holding moves perfectly with itself.
Marcus built one from five years of made-up monthly returns for his five largest holdings: a world equity ETF, an SGD bond fund, an STI ETF, local bank shares and a US chip designer. Bank shares against the STI ETF came to about 0.88, which fits with banks carrying a large weight in the STI. The world ETF against the US chip stock came to about 0.82, since large US technology companies are a big part of a world equity index. The bond fund against each share holding was between 0.1 and 0.3.
Pairs with a correlation above 0.8 behave like one position. 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. He does not have to sell either, but he can no longer count them as diversifiers.
To build your own, take your five largest holdings and get their monthly returns in SGD over the same months for every holding. Lay the holdings along the top and down the side, fill each cell with the CORREL result for that pair, and colour any cell above 0.8 so the clusters stand out. Treat each coloured pair as one position when you judge how diversified you are.
Your activity: build a correlation matrix of your five largest holdings from their monthly returns, with every pair above 0.8 marked.
Use monthly returns to build a correlation matrix of your five largest holdings, and mark every pair above 0.8.
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