"The rate of return anticipated on a bond if held until the end of its lifetime. YTM is considered a long-term bond yield expressed as an annual rate. The YTM calculation takes into account the bond’s current market price, par value, coupon interest rate and time to maturity. It is also assumed that all coupon payments are reinvested at the same rate as the bond’s current yield. YTM is a complex but accurate calculation of a bond’s return that helps investors compare bonds with different maturities and coupons."
Unfortunately, there aren't really "simple numerical examples" to use in calculating/explaining YTM, especially if you don't understand the time value of money. But I'll try.
The simplest example is a bond that bought at par, and interest rates don't change (or aren't expected to change) over the life of the bond. Since the YTM assumes you've invested the coupons you receive at the YTM rate, you must account for that. So, let's say you have a $1,000 bond that pays coupons annually and the coupon rate and the market rate are both 5%. We'll use a two year maturity to keep the math short.
Each coupon = $1,000 * 0.05 = $50 < you receive one each year, for two years
You pay $1000 for the bond, at maturity you receive your $1,000 back.
At the end of the first year, you receive the first coupon: $50. Since there is one year left to maturity, you must assume this is invested at the YTM for one year. So the future value of that $50 is: $50(1.05) = $52.50.
The next year, at the end of the year, you receive the second $50 coupon and par $1000 = $1,050.
Your total "value" at the end of two years is then: $52.50 + $1,050 = $1,102.50
Your two year return Holding Period Return "HPR" is: (1,102.50 / 1,000) - 1 = 0.10250, or 10.25%
Your geometric mean return, e.g. geometric average annual return is: where n = the number of years
= [(1 + HPR)^1/n] - 1
= -1.1025^1/2]- 1
= [1.1025^0.50] - 1
= 0.05, or 5%
Note that if you don't reinvest the coupon at the same rate, you wouldn't actually "realize" the YTM.
YTMs get more complicated when the coupon rate does not equal the market rate. This occurs for a variety of reasons, e.g. "riskiness" of the bond, changes in market interest rates, etc.
You will often hear that if you buy at par and hold your bond until maturity you will receive a YTM equal to the coupon rate. This is not so, because in order to "realize" that YTM, the coupons must be reinvested at the YTM, i.e.coupon rate, until the maturity date of the bond. FYI, YTMs are actually special forms of IRRs, Internal Rates of Return. Since most bonds pay coupons semi-annually, the YTM is actually a "Bond Equivalent Yield" equal to two times the 6 month periodic IRR. Now I'm starting to get into the weeds, so I'll shut up.
A bond normally has a fixed coupon. That is the rate of interest paid. So a bond with a 5% coupon pays ￡5 for every ￡100 of nominal stock (face value).
Now bonds are usually tradeable so the price of ￡100 of nominal might not be ￡100.
To make it is easy let's say you could buy this bond at ￡50. What would your return, or yield, be? Well you would still receive ￡5 interest but the yield would not be 5%, would it? The yield would be ￡5/￡50 x100=10%
Likewise if you paid ￡200 for ￡100 nominal you would still receive ￡5 interest but then the yield would be ￡5/￡200 x 100=2.5%
The yield is inversely proportional to the price (price goes up, yeild comes down and vice versa. So that is flat yield or running yield.
But we have another thing to consider. A bond usually has a fixed redemption date when the nominal value is repaid. Maybe it is is 5 years time (2019). So in 2019 the borrower will repay the bondholder ￡100 for every ￡100 nominal. But wait. You may have paid only ￡50 for your ￡100 nominal yet you still get back ￡100! You have a gain of ￡50. This ￡50 gain in 2019 can be calculated, or added to the flat yield an in this case would increase the yield. It would be more than 10%, wouldn't it. A simple way would be to say that the ￡50 gain could be divided by 5(number of years) to give ￡10 extra interest each year. So your effective interest would be ￡5 + ￡10=￡15 per annum or ￡15/50 x100=30%
Conversely, if you paid ￡200 your redemption yield would be a lot less than 5% as you wouldhave to take into account the loss of ￡100 at redemption. Of course this is not accurate because the gain (or loss) is not just divided by 5 (years). It has to be discounted.
Note that if the bond is bought at par (￡100 for ￡100 nominal) then the redemption yield is the same as the flat yield
Yield to maturity is a term used for bonds. Just to make sure, bonds are financial instruments where I loan money to you, and you promise to pay me small amounts of money several times a year, and then at the maturity date (the set date when the bond ends) you repay me the original amount of money I paid you. Yield to maturity is the rate of interest I receive if I own the bond from the time it is made to the time it ends/matures. Of course, bonds can be bought and sold like stocks, but YTM refers to a single person owning the bond for its whole life.
For example, I purchase a bond from you for $1,000, and you promise to pay me 5% interest once a year, and after ten years you will repay the original $1,000 that I gave you to buy the bond. The 5% is the yield to maturity. You will get 5% interest (0.05*$1,000=$50) once a year. This means your interest rate or the percentage return is 5% each year. The yield to maturity is very important and widely discussed even though bonds are rarely held by one person for their entire life, since they are sold in financial markets like stocks. The reason YTM is so important is that it helps determine the price of the bond to sell in the bond markets. When the market interest rate changes (as a result of the central bank's decision, perhaps), the YTM may be lower or higher than the market rate. As a result, the bond price will change so it returns a fair rate of interest to the owner.
Let me explain this more precisely. Using the same 5% semiannual bonds discussed earlier. When the bonds were issued, 5% was the market rate of interest. However, one month later, the central bank raises interest rates to 6%. Because I could buy a bond from another company that would offer a 6% YTM, I don't want to buy 5% bonds at the same price, since I'd get less money in my annual payment. So, the price of the 5% bonds will fall so that I receive the same 6% return that I could get with another bond. Instead of being $1,000, the 5% bond would fall in price to, let's say $900, so that the buyer of the bond still receives 6% at maturity, when the company pays $1,000 for the bond that I bought for $900. This $100 difference allows me to make up the difference between the market rate of interest and the rate on the bond, and makes the bond desirable and fair.
Let me know if anything's unclear or not explained simply enough. I'll fix it up so you understand everything well! Have a great day! I'd appreciate best answer very much!
There are 5bajillion places on teh web where YTM is defined correctly starting with Wikipedia. Every last one uses the word "discount" in there somewhere. Bill's answer is idiotic and mostly wrong. The YTM is the discount rate applied to all the cash flows that equate the discounted cash flow valuation to the market price. If you don't understand that, go read Wiki or something
Bill - if you don;t know an asnwer STFU.
I'm not an accountant, but I think that means the total amount of money you would get when the loan or bond has finished its term. I don't know whether 'yield' refers to your profit or the entire amount of money the loan would be worth.
Hi.Can someone explain me what is yield to maturity in simple words with a simple numerical example? My english isn't great and the definition given with this financial terminiology makes me confused .
