Correlation

Covariance is the raw co-movement: did the two series wander away from their averages in the same weeks? Correlation rescales that raw number so it sits between −1 and +1. You can compare a correlation of 0.20 with a correlation of 0.80. You cannot glance at two covariances and know which link is tighter, because covariance still carries the size of each series.

On the return risk page, beta uses this link. Beta is correlation times the investment’s volatility, divided by the benchmark’s volatility. Correlation says how lined-up the pair was. Beta says how large the investment’s move was for a move in the benchmark.

Take two assets, equal weights, each with a 15% volatility. The portfolio volatility is not automatically 15%. It depends on the correlation.

At a correlation of 0.20, the portfolio volatility is about 11.6%. The mix is quieter than either asset alone, because the two do not always move together. At a correlation of 0.80, the portfolio volatility is about 14.2%. The mix is still a little quieter than 15%, but much less of the bounce cancels.

A planning assumption might use the calm correlation, 0.20. A stress window for the same two assets might print 0.80. Nothing in the calm number promised that the stress number would match. Equity and credit, or two equity markets, often move together more tightly when prices are falling than they did in the quiet sample.

That is the breakdown the picture is about. The diversification was a property of the calm sample. In the stress sample the assets share more of the move, so the portfolio width rises toward the width of the pieces. A negative correlation can break the same way: a hedge that used to move opposite the asset can start moving with it.

The same idea applies inside an asset-liability book. Asset values and liability values can fall together, or they can move apart. A rate decline can mark long liabilities up by more than the assets. An equity decline can mark a stock sleeve down while a fixed liability does not move with it. Correlation between the asset and the liability is one way to say how often those two sides share a shock.

The later pages separate the shocks on purpose: a rate move, a credit move, an equity move, and a volatility move. Combining them is a scenario. Assuming they stay as loosely linked as they were last year is an assumption, and the stress picture is the reminder to say so.