Yield to Maturity vs. Holding Period Return

There are many yields associated with bonds. For example, there are yield to call, yield to worst, current yield, running yield, nominal yield (coupon rate), and yield to maturity (YTM). Most investors are concerned with the yield to maturity because if an investor purchases a bond and holds it until maturity, his return will be equal to the yield to maturity (YTM). On the other hand, if the investor does not hold the bond until maturity (a common practice for long-term bonds), the total return will be equal to the yield over the length of holding, or the holding period return (HPR). Due to uncertainty about interest rate fluctuations and holding period duration, the holding period return can be more difficult to calculate than YTM.

Yield to Maturity

Yield to maturity (YTM), also known as book or redemption yield, reflects the yield an investor receives for holding a bond until it matures. It does not account for taxes paid by the investor or incurred dealing costs. The YTM, often stated as an annual percentage rate (APR), assumes that all coupon and principal payments are made on time. The YTM rate may differ from the coupon rate. The formula for calculating YTM, if done correctly, should account for the present value of the bond's remaining coupon payments. The YTM formula can be seen as:

 YTM = F V P V 1 where: F V = Face Value P V = Present Value \begin{aligned} &\text{YTM} = \sqrt \frac{ FV }{ PV } - 1 \\ &\textbf{where:} \\ &FV = \text{Face Value} \\ &PV = \text{Present Value} \\ \end{aligned} YTM=PVFV1where:FV=Face ValuePV=Present Value

YTM is different from standard yield calculations because it adjusts for the time value of money. Since inverting time value of money values requires a lot of trial and error, YTM is best left for programs designed for that purpose.

Holding Period Return

Bond investors are not obligated to take an issuer's bond and hold it until maturity. The return on a bond or asset over the period in which it was held is called the holding period return (HPR). There is an active secondary market for bonds. This means that someone could buy a 30-year bond that was issued 12 years ago, hold it for a five-year period, then sell it again. In such a circumstance, the bondholder doesn't care what the yield of the 12-year old bond will be until it matures 18 years later. If an investor holds the bond for five years, they only care what yield they will earn between years 12 and 17.

The bondholder ought to attempt to calculate the bond's five-year holding period return. This can be approximated by slightly modifying the YTM formula. The bondholder can substitute the sale price for the par value and change the term to equal the length of the holding period. The holding period return formula is as follows:

 Holding Period Return = I + E P V I V I V where: I = Income E P V = End of Period Value I V = Initial Value \begin{aligned} &\text{Holding Period Return} = \frac{ I + EPV - IV }{ IV } \\ &\textbf{where:} \\ &I = \text{Income} \\ &EPV = \text{End of Period Value} \\ &IV = \text{Initial Value} \\ \end{aligned} Holding Period Return=IVI+EPVIVwhere:I=IncomeEPV=End of Period ValueIV=Initial Value

If the bond is still owned, use the current market price rather than the selling price to determine the present holding period return yield.

Sometimes, investors use the holding period return yield to assess the yields of different bonds. The results identify which bonds are more favorable investments.

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