# Reinvestment Risk

Reinvestment risk is the risk inherent in a debt instrument such as a bond that results from the possibility that the coupon payments and the principal, if the bond is called earlier than its maturity, might need to be invested at a lower interest rate.

Bonds pay periodic interest payments called coupon payments and some bonds, the callable bonds, give the issuer an option to retire the bond earlier than its maturity by paying back the principal to the bond-holder. Typically, issuers retire bonds earlier when the market interest rates are low because they want to lock-in a lower interest rate. While it is good for bond issuers, it is unfavorable for the bond-holder because now he must reinvest the principal at the lower prevailing market interest rate.

Reinvestment risk is the function of cash flows that occur before maturity. A longer maturity coupon-paying bond has higher such cash flows and hence higher reinvestment risk. A non-callable zero-coupon bond or any other non-callable debt instruments that pay their principal plus all interest at the maturity date have zero reinvestment risk. Amortizing securities such as mortgages have highest reinvestment risk because their periodic cash flows constitute both principal repayment and interest.

## Example

Letâ€™s consider two bonds, both with a yield to maturity of 5%: (a) a $1,000 non-callable zero-coupon with 3 years to maturity and current price of $863.84 and (b) a regular $1,000 par value bond with 3 years to maturity, current price of $986.23 (as at 1 January 2018) and semi-annual coupon rate of 4.5%.

Since the zero-coupon bond is non-callable and it has no coupon payments, the investor can realize the 5% yield to maturity by just holding the bond to maturity.

In case of the second bond, the investor receives $22.5 coupon payment every six-months. The 5% yield to maturity can be realized only if each $22.5 can be reinvested at a rate 5% or higher. If the reinvestment rate available is only 4%, the realized yield on the bond will drop to Value of all coupon payment at maturity based on 4% reinvestment rate will be $14.93.

$$ FV\ of\ Coupons\\=$22.5\times\frac{\left(1+\frac{4\%}{2}\right)^{2\times3}-1}{\frac{4\%}{2}}\\=$141.93 $$

Comparing the future value of coupons plus the redemption value of $1,000 at maturity to its price at t=0 gives us a realized return of

$$ Realized\ Yield\\=\left\{\left(\frac{Future\ Value}{Current\ Price}\right)^\frac{1}{NPER}-1\right\}\times2\\=\left\{\left(\frac{$1,000+$141.93}{$986.23}\right)^\frac{1}{6}-1\right\}\times2\\=4.95\% $$