The Difference Between Beta and Correlation
Beta is 'movement relative to the market,' and correlation is 'the degree of moving together.' The two similar-looking metrics actually answer different questions. What's the difference?
Correlation — how much the direction matches
Correlation measures 'the degree to which two assets move together in the same direction,' on a scale from -1 to +1.
- +1: perfectly the same direction (when one rises, the other rises too). - 0: no relationship at all. - -1: perfectly opposite direction.
The important thing is that correlation looks only at 'agreement in direction.' It has nothing to do with magnitude (how large the move is). Whether A rises 0.5% or 5% when the market rises 1%, as long as the direction is always the same, the correlation is +1 in both cases.
Beta — how large the reaction is
Beta measures 'when the market moves 1%, how many percent does this asset move on average.' In other words, it looks at magnitude (sensitivity).
- Beta 1: moves by the same amount as the market. - Beta 1.5: swings 1.5 times more than the market (more aggressive). - Beta 0.5: moves only half as much as the market (more defensive).
If correlation asks 'is the direction the same,' beta asks 'how many times larger is the movement.' So even when the direction is the same (correlation +1), beta could be 0.5 or it could be 3.
The two are also linked by a formula: Beta = correlation × (asset volatility ÷ market volatility). In other words, beta contains both 'agreement in direction (correlation)' and 'the ratio of volatilities.'
Why you must distinguish the two
If you confuse the two, you can misread risk.
For example, just because beta is 1.2, it's a mistake to believe 'it sticks tightly to the market and moves 1.2 times.' If correlation is low (e.g., 0.4), the asset's direction frequently diverges from the market, so a beta of 1.2 means 'only on average.' In reality, there may be many days when it does its own thing separate from the market.
Conversely, if correlation is high and beta is also large, then when the market collapses, this asset shares the direction and moves even more, so it can get hurt especially badly.
To sum up, when designing diversification, 'how differently things move (correlation)' is the key, and when looking at an individual asset's aggressiveness or defensiveness, 'the size of its reaction (beta)' is the key. You need both lenses to see an asset's character fully.
よくある質問
Q. If correlation is 0, is beta also 0?
Yes. Because Beta = correlation × (volatility ratio), if correlation is 0, then beta is also 0. If there is no directional relationship with the market at all, it means the market's movement cannot explain that asset. But this means the sensitivity 'to the market' is 0—it does not mean the asset doesn't move.
Q. If beta is greater than 1, is the asset unconditionally risky?
A high beta means 'it swings more when the market moves,' so it's true it's more sensitive to market risk. But beta looks only at the risk that moves together with the market (systematic risk). Risk unique to an individual company isn't captured by beta, so you can't judge an asset's total risk by beta alone.
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