2. Correlation and diversification: why holding assets that move differently reduces risk

Theory 4: Risk, return and diversification

You put several risky assets together in a portfolio, and the risk of the whole comes out lower than the average risk of each one on its own. This is not an accounting trick. It is mathematics.

Measuring the volatility of an asset in isolation, as we did in the previous module, is only half the story. The other half is correlation: how two or more assets move in relation to each other.

It is also what explains why something called a 'portfolio' exists at all, instead of simply picking the single best individual asset.

A number between minus one and plus one

Correlation is measured with a number between -1 and +1. The three reference points are these:

• A correlation of +1: two assets always move in the same direction and with the same relative intensity. If one rises 2%, so does the other, in perfectly proportional fashion.
• A correlation of -1: the opposite extreme. When one rises, the other falls, again in perfectly proportional fashion.
• A correlation of 0: there is no detectable linear relationship between their moves. Knowing what one did tells you nothing about what the other did.

In practice, almost no pair of real assets sits exactly at these extremes. Most fall somewhere in between, with a stronger or weaker relationship depending on the period analyzed.

The idea that won Markowitz a Nobel

This is where the central idea of diversification comes in, first formalized by Harry Markowitz in the middle of the twentieth century, and rewarded with the Nobel Prize in Economics.

Combine assets in a portfolio that are not perfectly correlated with one another. The total risk of that portfolio — measured, again, as standard deviation — can be lower than the weighted average of the risk of each individual asset taken separately.

This is not an accounting trick or a coincidence. It is a direct mathematical consequence: when one asset falls, another with low or negative correlation tends to offset part of that fall, smoothing the combined movement of the portfolio.

From that follows the practical rule. The lower, or the more negative, the correlation between the assets combined, the greater the diversification benefit obtained, all else being equal.

Diversifying is not piling up positions

This explains why 'diversifying' does not simply mean 'holding many different positions'.

Holding 30 different growth technology stocks does not diversify real risk very much. They all tend to move in the same direction in response to the same factors: interest rates, sentiment toward the technology sector, the broad economic cycle. Their correlation with each other is usually high.

Combining things that respond to different drivers tends to deliver a far larger diversification benefit:

• Stocks from different sectors.
• Bonds of different maturities.
• Some commodity exposure.
• And, depending on the risk profile, some cash.

That mix diversifies more than simply multiplying the number of similar stocks, even if the total number of positions is smaller.

The problem: correlation moves

It is also essential to know that correlation is not a fixed constant over time. It tends to change with the market regime, and with one particularly inconvenient tendency.

Many assets that show low or even negative correlations in normal periods tend to converge toward much higher correlations during severe crises. That is, precisely when diversification is most needed.

This phenomenon is sometimes summed up like this: 'in a crisis, all correlations go to one'.

It does not invalidate the value of diversifying. In most periods, and over the long run, it still works reasonably well. But it is a serious warning against the complacency of believing that a 'diversified' portfolio is protected in every scenario, including the most extreme ones.

What diversification cannot do

Diversification does not eliminate risk: it transforms it.

It reduces, sometimes substantially, the specific risk of each individual asset: the risk that one particular company does badly for reasons of its own.

It does not eliminate systematic or market risk: the risk that hits virtually every asset at once when the economy as a whole goes through a severe crisis.

Understanding this distinction between specific risk (diversifiable) and systematic risk (non-diversifiable) is the foundation on which the next module builds the idea of risk-adjusted return.