Yield to Maturity, Reinvestment Risk, and Realized Returns
Summary
The document clarifies that yield to maturity is the internal rate of return implied by a bond’s current price and promised cash flows. It is a comparison measure, rather than a guaranteed realized return at a particular investment horizon. The investor’s actual horizon return depends on what happens to coupon payments after they are received.
A numerical example compares the outcome when coupons are left unreinvested with the outcome when an interim coupon earns the bond’s YTM. The realized return matches YTM in the example only under that reinvestment assumption and when the bond is held to maturity. The discussion also notes that YTM relies on simplifying assumptions, including a flat yield curve, and that holding-period returns are distinct from YTM. Actual reinvestment rates can change, creating reinvestment risk; selling before maturity also exposes the investor to price changes.
Key ideas
- Yield to maturity is the internal rate of return implied by a bond’s price and promised cash flows.
- A bond’s realized horizon return depends on the investor’s coupon reinvestment policy.
- The realized return matches YTM at maturity only when coupons earn the assumed reinvestment rate.
- YTM is useful for comparing bonds but does not guarantee a particular investor outcome.
- Changing rates can affect coupon reinvestment, while selling before maturity introduces price risk.
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Full text
# Yield-to-Maturity and its assumption # Yield-to-Maturity and its assumption Reading about Yield-to-Maturity (YTM) I found out that two assumptions have to be made: - the bond holder must keep the bond until maturity; - coupons must be reinvested at the same YTM. Violating those hypotheses causes the bond holder incurring in two types of risks: the price risk and the reinvestment risk. So I was wondering: since interest rates are ever-changing, will a bond holder be automatically subject to the reinvestment risk? It is hard for me envisaging that he can still reinvest his coupons at the same YTM. I kindly ask you where my reasoning fails. ## Answer by John (score 5, accepted) https://quant.stackexchange.com/a/33680 It's simpler to just think of the yield to maturity as the internal rate of return of the bond given the current price. It's like the discount rate you would apply to the final payout and coupons, such that the result is the market price. A short paper by Forbes, Hatem, and Paul explains that yield to maturity ignores reinvestment. Strictly speaking, yield to maturity is an internal rate of return, not the return you would get at the horizon. The return you get at the horizon depends on the reinvestment policy. The return at the horizon only matches the yield to maturity if the coupons are invested at the same yield as the yield to maturity. For instance, assume a \$1000 bond with \$50 annual payments and 2 years until maturity and a 10% yield to maturity. The current price is \$913.22. The sum of the return and the coupons is \$1100. Ignoring reinvestment, the return at the end of two years is 20% cumulatively (1100 / 913.22 - 1) or 9.75% annualized. However, if the \$50 from year 1 is re-invested at a 10% rate, then the investor would now have $1105, generating a 21% return cumulatively (1105 / 913.22 - 1) or 10% annualized. Long story short, the yield to maturity is a bond's internal rate of return given its current price. It is only the return you would earn if you held the bond to maturity if you reinvest at that same rate. ## Answer by nimbus3000 (score 0) https://quant.stackexchange.com/a/33030 Yes, its called yield to maturity because you hove to hold it till maturity. For the reinvestment risk, suppose the day you get the coupon the coupon the day bond is trading at x%. Now with the money you get from the coupon, you can buy these bonds and realize x%. So the reinvestment risk is eliminated to the extent of the liquidity in the market. ## Answer by cykor21 (score 0) https://quant.stackexchange.com/a/33692 Just to add two things: - in fixed income world bonds are typically quoted by YTM instead of prices but if we go back to prices, then an analogous question would be: what conditions need to hold so that an investor who bought a bond at price X will realize the rate of return (YTM) of Y%? - I see YTM only in terms of a measure that allows me to compare similar bonds - the realized rate of return is a different thing - also: YTM assumes a flat yield curve so this is quite far from reality ## Answer by Randor (score -1) https://quant.stackexchange.com/a/33690 I think for not too large yield movements , you would earn the ytm by holding for bond duration (rather than till maturity) and reinvesting coupons in bond
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