|
Yield To Maturity (YTM)
The total return anticipated on a bond if the bond is held until the end of its lifetime. Yield to maturity is considered a long-term bond yield, but is expressed as an annual rate. In other words, it is the internal rate of return of an investment in a bond if the investor holds the bond until maturity and if all payments are made as scheduled.
Calculating 'Yield To Maturity (YTM)'
Calculations of yield to maturity assume that all coupon payments are reinvested at the same rate as the bond’s current yield, and take into account the bond’s current market price, par value, coupon interest rate and term to maturity. YTM is a complex but accurate calculation of a bond’s return that can help investors compare bonds with different maturities and coupons.
Because of the complex means of determining yield to maturity, it is often difficult to calculate a precise YTM value. Instead, one can approximate YTM by using a bond yield table. Because of the price value of a basis point, yields decrease as a bond’s price increases, and vice versa. For this reason, yield to maturity may only be calculated through trial-and-error, by using a business or financial calculator or by using other software.
Though yield to maturity represents an annualized rate of return on a bond, coupon payments are often made on a semiannual basis, so YTM is often calculated on a six-month basis as well.
Yield to maturity is also often known as “book yield” or “redemption yield.”
Yield to maturity is very similar to current yield, which divides annual cash inflows from holding a bond by the market price of that bond, to determine how much money one would make by buying a bond and holding it for one year. Yet, unlike current yield, YTM accounts for the present value of a bond’s future coupon payments. In other words, it factors in the time value of money, whereas a simple current yield calculation does not. As such, it is often considered a more thorough means of calculating the return from a bond.
Because yield to maturity is the interest rate an investor would earn by reinvesting every coupon payment from the bond at a constant interest rate until the bond’s maturity date, the present value of all of these future cash flows equals the bond’s market price.
Bonds can be priced at a discount, at par and at a premium. When the bond is priced at par, the bond’s interest rate is equal to its coupon rate. A bond priced above par (called a premium bond) has a coupon rate higher than the interest rate, and a bond priced below par (called a discount bond) has a coupon rate lower than the interest rate. So if an investor were calculating YTM on a bond priced below par, he or she would solve the equation by plugging in various annual interest rates that were higher than the coupon rate until finding a bond price close to the price of the bond in question.
Calculating Yield to Maturity
Imagine you are interested in buying a bond, at a market price that's different from the bond's par value. There are three numbers commonly used to measure the annual rate of return you are getting on your investment:
Coupon Rate : Annual payout as a percentage of the bond's par value
Current Yield : Annual payout as a percentage of the current market price you'll actually pay
Yield-to-Maturity : Composite rate of return off all payouts, coupon and capital gain (or loss)
(The capital gain or loss is the difference between par value and the price you actually pay.)
The yield-to-maturity is the best measure of the return rate, since it includes all aspects of your investment. To calculate it, we need to satisfy the same condition as with all composite payouts:
Whatever r is, if you use it to calculate the present values of all payouts and then add up these present values, the sum will equal your initial investment.
In an equation,
c(1 + r)-1 + c(1 + r)-2 + . . . + c(1 + r)-Y + B(1 + r)-Y = P, where
c = annual coupon payment (in dollars, not a percent)
Y = number of years to maturity
B = par value
P = purchase price
You should try to form a mental picture of what this equation is saying. The left side representsY+1 different compound interest curves, all starting out now, and each one ending at the moment that the payout it corresponds to takes place. Most of these curves will lie pretty low to the axis, because they only grow to a value of c, the coupon payment. The very last curve will be a lot taller, and end up at the par value B. And if you add up the present values of all these curves (that's the left side of the equation), the sum will exactly equal the purchase price of the bond (that's the right side).
As with most composite payout problems, equation 1 can't be solved exactly, in general. The nice part is that all yield-to-maturity problems have basically the same form, so people have been able to create programmable calculators and computer programs (and even tables back in the old days) to help you find r.
YTM Examples :
Suppose your bond is selling for 950, and has a coupon rate of 7%; it matures in 4 years, and the par value is 1000. What is the YTM?
The coupon payment is 70 (that's 7% of 1000), so the equation to satisfy is
70(1 + r)-1 + 70(1 + r)-2 + 70(1 + r)-3 + 70(1 + r)-4 + 1000(1 + r)-4 = 950
Of course you aren't really going to solve this, so you just use any calculator instead, and find that r is 8.53%. If you want, you can plug this number back into equation, just to make sure it checks out.
One thing to notice is that the YTM is greater than the current yield, which in turn is greater than the coupon rate. (Current yield is 70/950 = 7.37%). This will always be true for a bond selling at a discount. In fact, you will always have this:
One more basic formula for calculating yield to maturity looks like this:
Approximate YTM=(C+(F-P)/n)/((F+P)/2)
Where...
YTM = Yield to Maturity
C = Coupon/Interest Payment
F = Face Value
P = Price
n = Years to maturity
This calculation can only approximate what the yield or actual interest rate will be because prices change in the actual bond market on a daily basis.
If a bond has a face value of 100 at 8% interest with a 15 year maturity and the coupon or interest payment each year is 8 (8% x 100). The yield for the bond at its current price is 92.
The equation to find the yield looks like this:
Approximate YTM=(8+(100-92)/15)/((100+92)/2)
This looks like a lot of complex math but it's not as difficult as it may seem. We can break it down into parts and solve it.
= 8+(100-92)/15
= 8+8/15
= 8+0.533
= 8.533
= (100+92)/2
= 192/2
= 96
= 8.533/96
= 0.088
= 8.8%
Yield to Maturity Calculation
Remember this is still only an approximation as the yield will change as the price of the bond changes. The bonds interest rate (8%) is less than its yield to maturity (8.8%) so it is selling at a discount.
Bond Selling At ... Satisfies This Condition
Discount Coupon Rate < Current Yield < YTM
Premium Coupon Rate > Current Yield > YTM
Par Value Coupon Rate = Current Yield = YTM
Bond Yields and Prices
Once a bond has been issued and it's trading in the bond market, all of its future payouts are determined, and the only thing that varies is its asking price. If you buy such a bond the yield to maturity you'll get on your investment naturally increases if you can buy it at a lower price: as they say, bond prices and yields "move" in opposite directions. That can be confusing since people aren't always consistent in the way they talk about bond performance. If somebody says "10 year treasuries were down today", they probably mean that the asking price was down (so it was a bad day for bond holders); but they sometimes mean that the yield to maturity was down because the asking price was up (a good day for bond holders).
Uses of Yield to Maturity (YTM)
Yield to maturity can be quite useful for estimating whether or not buying a bond is a good investment. An investor will often determine a required yield, or the return on a bond that will make the bond worthwhile, which may vary from investor to investor. Once an investor has determined the YTM of a bond he or she is considering buying, the investor can compare the YTM with the required yield to determine if the bond is a good buy.
Yet, yield to maturity has other applications as well. Because YTM is expressed as an annual rate regardless of the bond’s term to maturity, it can be used to compare bonds that have different maturities and coupons since YTM expresses the value of different bonds on the same terms.
Variations of Yield to Maturity (YTM)
Yield to maturity has a few common variations that are important to know before doing research on the subject.
One such variation is Yield to call (YTC), which assumes that the bond will be “called” (repurchased by issuer before it reaches maturity) and thus has a shorter cash flow period.
Another variation is Yield to put (YTP). YTP is similar to YTC, except for the fact that the holder of a put bond can choose to sell back the bond with a fixed price and on a particular date.
A third variation on YTM is Yield to worst (YTW). YTW bonds can be called, put or exchanged, and YTW bonds generally have the lowest yields out of YTM and its variants.
Limitations of Yield to Maturity (YTM)
Like any calculation that attempts to determine whether or not an investment is a good idea, yield to maturity comes with a few important limitations that any investor seeking to use it would do well to consider.
One limitation of YTM is that YTM calculations usually do not account for taxes that an investor pays on the bond. In this case YTM is known as the “gross redemption yield.” YTM calculations also do not account for purchasing or selling costs.
Another important limitation of both YTM and current yield is that these calculations are meant as estimates and are not necessarily reliable. Actual returns depend on the price of the bond when it is sold, and bond prices are determined by the market and can fluctuate substantially. Though this limitation generally has a more noticeable effect on current yield, because it is for a period of only one year, these fluctuations can affect YTM significantly as well.
……………………………………………………………………………………………………………………………………………
|
