Reinvestment Risk

Reinvestment risk is the risk that the coupons (and other intermediate cash flows) from a bond must be reinvested at a rate lower than originally anticipated, reducing the total accumulated return. A bond bought to yield j realizes that yield only if every coupon can be reinvested at j.

\text{Accumulated value} = \text{coupons} \cdot s_{\overline{n}|j'} + \text{redemption}

• If reinvestment rates j' fall below j, the accumulated value of coupons falls short of projection and the realized yield drops below j.
• Reinvestment risk is higher for bonds with more and larger intermediate cash flows — shorter duration and higher coupon rates — because more of the total return depends on reinvesting coupons.
• It is the counterpart of Price Risk: a zero-coupon bond has no reinvestment risk but maximum price risk, while a short-term bond has low price risk but high reinvestment risk.
• Redington Immunization and Cash Flow Matching both address reinvestment risk by matching asset and liability timing.

Reinvestment Risk on a Coupon Bond An investor buys a 3-year $1{,}000 bond with 8% annual coupons at par (yield = 8%), expecting to accumulate 1{,}000(1.08)^3 = \$1{,}259.71 over 3 years. If coupons are reinvested at only 5% instead of 8%, what is the actual accumulated value?

Answer Coupons of $80 are received at times 1, 2, and 3. Reinvesting at 5%, their accumulated value at time 3 is: 80\,s_{\overline{3}|5\%} = 80(3.1525) = \$252.20 Adding the $1{,}000 redemption value gives a total of 252.20 + 1{,}000 = \$1{,}252.20. The shortfall is 1{,}259.71 - 1{,}252.20 = \$7.51, so the realized yield falls slightly below 8% — the effect of reinvestment risk. A zero-coupon bond would have no such shortfall.