Analytical Duration vs. Empirical Duration

A bond's cash flows are commonly used to determine its duration. Nothing new there.

What word might you use to describe this process of working from cash flows to a duration measure?

Not really; it's a clear calculation based on cash flows and timing. There's nothing random about that.

Not really. This is a standalone calculation invariant of time or outside forces.

Sure. It's analytical, but certainly not historical, or looking at any additional outside forces. So these calculated durations are called __analytical duration__.

But __empirical durations__ can be found from applying statistical techniques to historical events. And they aren't always the same. To see why, consider this: investors are nervous, so government bond yields are falling. What happens to the price of government bonds?

Of course. This is the typical inverse relationship between yields and prices.

No, prices would go up. This is the typical inverse relationship between yields and prices.

So with yields falling, bond prices are rising. For every basis point the benchmark yields fall, durations of bonds like 5 suggest a five-basis-point increase in the price.

But think about the "flight to safety" that happens in crisis situations. Investors dump risky bonds to get government bonds instead. What will that do to yield spreads?

Yes!

No, they will widen. Dumping high-yield bonds for government issues means that the prices will differ more greatly, and the yields will differ more greatly as well.

The result is that government bonds will rise in value, just as their durations suggested. But the high-yield bonds will be harmed by this drop in yields due to investor preference, which will cause prices of these bonds to rise more slowly, if at all. What does this mean for the empirical duration of these high-yield bonds?

No, this scenario is showing a clear difference between the two. Analytical durations would be positive as normal, but the empirical duration is closer to zero.

Right. These high-yield bonds may be moving very little due to the yield decreases, because of this negative correlation between yields and credit spreads that is typical in times of crisis. Isn't that something; after all of the fancy duration calculations, it ends up as a poor predictor of prices at times. But keep in mind that this is only the case in certain times. The economic environment and related variables can help guide you toward whether to use analytical durations or empirical durations. Maybe you'll want to look at both if you end up working heavily in the bond market!

To summarize this discussion: [[summary]]

No, higher empirical durations would suggest that they are becoming more valuable than what their analytical durations would suggest. But that isn't happening in this "flight to safety" scenario.

Random

Historical

Analytical

Prices go up

Prices go down

Yield spreads will widen

Yield spreads will narrow

They match their analytical durations

They are lower than their analytical durations

They are higher than their analytical durations

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