Reinvestment Risk vs. Price Risk

Can anyone explain to me the following 2 statements?

  1. If asset duration is lower than liability duration, the portfolio is exposed to reinvestment risk.
  2. If asset duration is higher than liability duration, the portfolio is exposed to price risk.

For the first statement, if asset duration is lower and interest rate decreases, the loss on reinvestment income will be greater than the gain on asset price. The liability will increase more than the asset, making it worse I guess? Overall it is a net loss.

Applying the same logic to the second statement, if asset duration is higher and interest rate increases, the loss on asset price will be greater than the gain on reinvestment income. But the liability will also decrease, reducing the loss? Overall it is still a net loss isn’t it? Do I even need to consider the liability here?

Thanks in advance.

Where did you read these?

I just searched the Level III curriculum, volume 4, and couldn’t find these statements.

The Fixed Income sections were changed in 2018, and those statements are from old materials. I guess they are still relevant to the current reading on bond immunization (and may still be asked?), so I’d like to ask here in case someone knows.

As far as I know, bond immunization means matching asset duration and liability duration. For a single liability, liability duration is approximately its maturity or time horizon, so we just need to match asset duration and time horizon. If they are matched, price risk and reinvestment risk should offset each other. If asset duration is less (higher) than liability duration, we are exposed to reinvestment risk (price risk), which is taught at level I. Is my understanding correct?

If you write “maturity” instead of “duration”, you’re definitely correct.

Thank you, but what exactly did you mean by that? To immunize a bond portfolio against a single liability, we should match the duration of the assets and the maturity of the liability, am I right? I thought because the maturity of the liability, which is also its MacDur in this case, is very close to its ModDur, we can just assume they are equal and say that we should match their durations?

I mean that if you have a liability due in, say, 5 years, then if you have a 10-year bond you have to worry about what it will be worth in 5 years (price risk), and if you have a 3-year bond you have to worry about the yield you’re going to get when you roll it over in 3 years (reinvestment risk).