The holding period return yield formula may be used to compare the yields of different bonds in your portfolio over a given time period. This method of yield comparison lets investors determine which bonds are generating the largest profits, so they may rebalance their holdings accordingly. In addition, this formula can help evaluate when it is more advantageous to sell a bond at a premium or hold it until maturity.

Key Takeaways

  • A bond's bolding period return/yield is equal to the total return earned on an investment during the time that it was held by an investor.
  • The holding period is the period of time the bond is owned by an investor, which may be from purchase until maturity, or else the period between the purchase and sale of the security.
  • Holding period return is useful for making like-comparisons between returns on various investments purchased at and held for different periods in time.


What Is the Holding Period Return Yield Formula?

A holding period is the amount of time that an investment is an investor's possession. For a long position, the holding period refers to the time between an asset's purchase and its sale. For bonds, the holding period may also cover the time from purchase through to its maturity. Holding period return is thus the total return received from holding an asset or portfolio of assets over that period of time, generally expressed as a percentage.

Depending on the type of asset involved, different holding period return yield formulas can be applied to account for the compounding of interest and varying return rates. However, bonds generate a fixed amount of income each year. This rate of return, known as the coupon rate, is set at issuance and remains unchanged for the life of the bond.

Therefore, the formula for the holding period return yield of bonds is quite simple:

HPRY = ( Selling Price P ) + TCP P where: P = Purchase Price TCP = Total Coupon Payments \begin{aligned} &\text{HPRY}= \frac{(\text{Selling Price} - \text{P}) + \text{TCP}}{\text{P}}\\ &\textbf{where:}\\ &\text{P = Purchase Price}\\ &\text{TCP = Total Coupon Payments}\\ \end{aligned} HPRY=P(Selling PriceP)+TCPwhere:P = Purchase PriceTCP = Total Coupon Payments

If you still own the bond, use the current market price of the bond instead of the selling price to determine the current holding period return yield of your bond.

Example

Assume you purchased a 10-year, $5,000 bond with a 5% coupon rate. You purchased the bond five years ago at par value. This means the bond has paid $1,250, or 5 * $5,000 * 5%, in coupon payments over the past five years.

Assume the bond has a current market value of $5,500.

If you sold your bond today, the holding period return yield of the bond is:

 = ( ( $ 5 , 5 0 0 $ 5 , 0 0 0 ) + $ 1 , 2 5 0 ) / $ 5 , 5 0 0 = ( $ 5 0 0 + $ 1 , 2 5 0 ) / $ 5 , 0 0 0 = $ 1 , 7 5 0 / $ 5 , 0 0 0 = 0 . 3 5 , or  3 5 % \begin{aligned} &=(\left(\${5,500}-\${5,000}\right)+\${1,250})/\${5,500}\\ &=(\${500}+\${1,250})/\${5,000}\\ &=\${1,750}/\${5,000}\\ &={0.35}\text{, or }{35}\%\\ \end{aligned} =(($5,500$5,000)+$1,250)/$5,500=($500+$1,250)/$5,000=$1,750/$5,000=0.35, or 35%

However, like all bonds, the repayment of your initial investment is guaranteed by the issuing entity once the bond matures. If you hold the bond until maturity, it generates a total of $2,500 in coupon payments, or 10 * $5,000 * 5%, and the holding period return yield is:

 = ( ( $ 5 , 0 0 0 $ 5 , 0 0 0 ) + $ 2 , 5 0 0 ) / $ 5 , 0 0 0 = $ 2 , 5 0 0 / $ 5 , 0 0 0 = 0 . 5  or  5 0 % \begin{aligned} &=(\left(\${5,000}-\${5,000}\right)+\${2,500})/\${5,000}\\ &=\${2,500}/\${5,000}\\ &={0.5}\text{ or }{50}\%\\ \end{aligned} =(($5,000$5,000)+$2,500)/$5,000=$2,500/$5,000=0.5 or 50%