On Page 22, book 3 of Schweser, it says that “If portfolio duration is less than liability duration, the portfolio is exposed to reinvestment risk” and implies that this happens when interest rates decrease. I know that Duration=(Change in price/Change in yield), so if portfolio duration is less than liability duration, doesn’t that mean interest rates are INCREASING, not decreasing, because for (Change in price/Change in yield) to go down, yield must go up (i.e., the denominator of this fraction increases so that the duration decreases). My question is: Why is it that interest rates decreasing means that portfolio duration is less than liability duration?

First just ignore the “reinvestment risk” part of the statement and start by thinking of your assets as simply equal amounts of 2 yr bonds and your liabilities as 30 yr bonds (therefore the bond duration of security portfolio is less then your liabilities) in a declining interest rate environment the 30yr bonds are going to outperform the 2 yr bonds, in other words the 30 yr price appreciation will be greater. In this case your liabilities just grew at a faster pace then the assets. Now a risk that explains this phenomenon (out side of just the pure bond math) is reinvestment risk; one of the reasons the shorter bonds under perform their longer brethren is because the cash flows must be reinvested sooner into lower rate bond (again since rates are decreasing).

I believe it depends on what you have in your portfolio. If you have primary RMBS, callable bonds, in a falling interest environment, one will have greater prepayment thereby reducing duration, and callable bonds will tend to be called thereby reducing duration too. Agree on the statement of the above poster regarding reinvestments.

rellison Wrote: ------------------------------------------------------- > On Page 22, book 3 of Schweser, it says that “If > portfolio duration is less than liability > duration, the portfolio is exposed to reinvestment > risk” and implies that this happens when interest > rates decrease. > > I know that Duration=(Change in price/Change in > yield), so if portfolio duration is less than > liability duration, doesn’t that mean interest > rates are INCREASING, not decreasing, because for > (Change in price/Change in yield) to go down, > yield must go up (i.e., the denominator of this > fraction increases so that the duration > decreases). > > My question is: Why is it that interest rates > decreasing means that portfolio duration is less > than liability duration? Imagine you have a portfolio of zeros with a 2 year maturity and your liabilities are 30 years. If interest rates fall at the end of your 2 year zero you then have to reinvest the principal at the prevailing lower rates = reinvestment risk.