can someone explain this statement pg 349 vol 3 ? If portfolio duration > liab duration the portfolio is exposed to price risk more if IR risk so this is not always the case
I could not understand the sentence above. However, Think of simple immunization. Basic condition is matching weighted average durations of assets to your liability, and of course PVs. So you assume portfolio is immunized. But what you have a bunch of various durations for your assets, only their average equals the liability duration. You have to make some assumptions regarding how durations would change if interest rates shift or what would be your reinvestment return to reach that mimimum level of portfolio at your horizon. Each assumption you have to make is a risk, basically in this case is immunization risk. They will determine how well your immunization work. In a different stroy, if you immunize your liability with an asset that exactly matches the horizon of liability, you don’t need to think of price risk or reinvestment risk. After all your asset will mature at the same date (no price risk, no reinvestment risk, no need to offset losses from price with gains from reinvestment etc.) and will fund your liability.
That makes more sense. I guess price risk is easier to control by setting the PV and is known in advance but reinvestment risk poses the biggest challenge. Thanks Hiya!