Yield to maturity
Encyclopedia
The Yield to maturity or redemption yield of a bond
or other fixed-interest security
, such as gilts
, is the internal rate of return
(IRR, overall interest rate) earned by an investor who buys the bond today at the market price, assuming that the bond will be held until maturity
, and that all coupon
and principal payments will be made on schedule. Yield to maturity is actually an estimation of future return, as the rate at which coupon payments can be reinvested when received is unknown. It enables investors to compare the merits of different financial instruments. The YTM is often given in terms of Annual Percentage Rate (A.P.R.), but more usually market convention is followed: in a number of major markets the convention is to quote yields semi-annually (see compound interest
: thus, for example, an annual effective yield of 10.25% would be quoted as 5.00%, because 1.05 x 1.05 = 1.1025).
The yield is usually quoted without making any allowance for tax paid by the investor on the return, and is then known as "gross redemption yield". It also does not make any allowance for the dealing costs incurred by the purchaser (or seller).
of this cash flow, 100/(1.1)30 = 5.73). Over the coming 30 years, the price will advance to $100, and the annualized return will be 10%.
What happens in the meantime? Suppose that over the first 10 years of the holding period, interest rates decline, and the yield-to-maturity on the bond falls to 7%. With 20 years remaining to maturity, the price of the bond will be 100/1.0720, or $25.84. Even though the yield-to-maturity for the remaining life of the bond is just 7%, and the yield-to-maturity bargained for when the bond was purchased was only 10%, the return earned over the first 10 years is 16.25%. This can be found by evaluating (1+i) from the equation (1+i)10 = (25.842/5.731), giving 1.1625.
Over the remaining 20 years of the bond, the annual rate earned is not 16.25%, but rather 7%. This can be found by evaluating (1+i) from the equation (1+i)20 = 100/25.84, giving 1.07. Over the entire 30 year holding period, the original $5.73 invested increased to $100, so 10% per annum was earned, irrespective of any interest rate changes in between.
Here is another example:
You buy ABC Company bond which matures in 1 year and has a 5% interest rate (coupon) and has a par value of $100. You pay $90 for the bond.
The current yield
is 5.56% ((5/90)*100).
If you hold the bond until maturity, ABC Company will pay you $5 as interest and $100 par value for the matured bond.
Now for your $90 investment, you get $105, so your yield to maturity is 16.67% [= (105/90)-1] or [=(105-90)/90].
Bond (finance)
In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest to use and/or to repay the principal at a later date, termed maturity...
or other fixed-interest security
Security (finance)
A security is generally a fungible, negotiable financial instrument representing financial value. Securities are broadly categorized into:* debt securities ,* equity securities, e.g., common stocks; and,...
, such as gilts
Gilts
Gilts are bonds issued by certain national governments. The term is of British origin, and originally referred to the debt securities issued by the Bank of England, which had a gilt edge. Hence, they are called gilt-edged securities, or gilts for short. The term is also sometimes used in Ireland...
, is the internal rate of return
Internal rate of return
The internal rate of return is a rate of return used in capital budgeting to measure and compare the profitability of investments. It is also called the discounted cash flow rate of return or the rate of return . In the context of savings and loans the IRR is also called the effective interest rate...
(IRR, overall interest rate) earned by an investor who buys the bond today at the market price, assuming that the bond will be held until maturity
Maturity (finance)
In finance, maturity or maturity date refers to the final payment date of a loan or other financial instrument, at which point the principal is due to be paid....
, and that all coupon
Coupon (bond)
A coupon payment on a bond is a periodic interest payment that the bondholder receives during the time between when the bond is issued and when it matures. Coupons are normally described in terms of the coupon rate, which is calculated by adding the total amount of coupons paid per year and...
and principal payments will be made on schedule. Yield to maturity is actually an estimation of future return, as the rate at which coupon payments can be reinvested when received is unknown. It enables investors to compare the merits of different financial instruments. The YTM is often given in terms of Annual Percentage Rate (A.P.R.), but more usually market convention is followed: in a number of major markets the convention is to quote yields semi-annually (see compound interest
Compound interest
Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding...
: thus, for example, an annual effective yield of 10.25% would be quoted as 5.00%, because 1.05 x 1.05 = 1.1025).
The yield is usually quoted without making any allowance for tax paid by the investor on the return, and is then known as "gross redemption yield". It also does not make any allowance for the dealing costs incurred by the purchaser (or seller).
- If the yield to maturity for a bond is less than the bond's coupon rate, then the (clean) market value of the bond is greater than the par value (and vice versa).
- If a bond's coupon rate is less than its YTM, then the bond is selling at a discountDiscounts and allowancesDiscounts and allowances are reductions to a basic price of goods or services.They can occur anywhere in the distribution channel, modifying either the manufacturer's list price , the retail price , or the list price Discounts and allowances are reductions to a basic price of goods or services.They...
. - If a bond's coupon rate is more than its YTM, then the bond is selling at a premiumPremiumPremium may refer to:* Premium , a promotional item that can be received for a small fee when redeeming proofs of purchase that come with or on retail products....
. - If a bond's coupon rate is equal to its YTM, then the bond is selling at parPar valuePar value, in finance and accounting, means stated value or face value. From this comes the expressions at par , over par and under par ....
.
Variants of yield to maturity
As some bonds have different characteristics, there are some variants of YTM:- Yield to call: when a bond is callable (can be repurchased by the issuer before the maturity), the market looks also to the Yield to call, which is the same calculation of the YTM, but assumes that the bond will be called, so the cashflow is shortened.
- Yield to put: same as yield to call, but when the bond holder has the option to sell the bond back to the issuer at a fixed price on specified date.
- Yield to worst: when a bond is callable, puttable, exchangeable, or has other features, the yield to worst is the lowest yield of yield to maturity, yield to call, yield to put, and others.
Example
Consider a 30-year zero-coupon bond with a face value of $100. If the bond is priced at an annual YTM of 10%, it will cost $5.73 today (the present valuePresent value
Present value, also known as present discounted value, is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk...
of this cash flow, 100/(1.1)30 = 5.73). Over the coming 30 years, the price will advance to $100, and the annualized return will be 10%.
What happens in the meantime? Suppose that over the first 10 years of the holding period, interest rates decline, and the yield-to-maturity on the bond falls to 7%. With 20 years remaining to maturity, the price of the bond will be 100/1.0720, or $25.84. Even though the yield-to-maturity for the remaining life of the bond is just 7%, and the yield-to-maturity bargained for when the bond was purchased was only 10%, the return earned over the first 10 years is 16.25%. This can be found by evaluating (1+i) from the equation (1+i)10 = (25.842/5.731), giving 1.1625.
Over the remaining 20 years of the bond, the annual rate earned is not 16.25%, but rather 7%. This can be found by evaluating (1+i) from the equation (1+i)20 = 100/25.84, giving 1.07. Over the entire 30 year holding period, the original $5.73 invested increased to $100, so 10% per annum was earned, irrespective of any interest rate changes in between.
Here is another example:
You buy ABC Company bond which matures in 1 year and has a 5% interest rate (coupon) and has a par value of $100. You pay $90 for the bond.
The current yield
Current yield
The current yield, interest yield, income yield, flat yield or running yield is a financial term used in reference to bonds and other fixed-interest securities such as gilts...
is 5.56% ((5/90)*100).
If you hold the bond until maturity, ABC Company will pay you $5 as interest and $100 par value for the matured bond.
Now for your $90 investment, you get $105, so your yield to maturity is 16.67% [= (105/90)-1] or [=(105-90)/90].
See also
- Bond Valuation — Yield To Maturity
- I-spreadI-spreadThe Interpolated Spread or I-spread or ISPRD is the difference between the yield to maturity of the bond and the linearly interpolated yield to the same maturity on an appropriate reference curve....
- Dividend yieldDividend yieldThe dividend yield or the dividend-price ratio on a company stock is the company's total annual dividend payments divided by its market capitalization, or the dividend per share, divided by the price per share. It is often expressed as a percentage...
- Bond durationBond durationIn finance, the duration of a financial asset that consists of fixed cash flows, for example a bond, is the weighted average of the times until those fixed cash flows are received....
- Coupon rate
- Yield to Maturity on Wikinvest