FinToolBox - Yield to Maturity

Yield to Maturity

Different from the mortgage loan you got from the bank, which is tied between only two parties — you and the bank — corporate bond can be traded on the market. That is to say, a bond can be traded like a used car on ebay, regardless of its face value and coupon payments. In the market, the only thing that can drive the price of the bond is the supply and demand.

Because price of the bond is decided by the trade between investors, as any traded financial security, its price fluctuates up and down all the time. The figure on the left is price of one of Boeing bonds between 2017 and 2020. As you can tell, the market price of the bond is not always the same — as a matter of fact it is NEVER the same. It fell below 80% of its face value in early 2018, and spoke at 140% of the face value in early 2019. If you buy low and sell high of the bond, you will make money, and this profit is irrelevant to the coupon payment and final principal payment as we discussed in last section. This profit is purely made from trading.

Despite its fixed face value, we call this fluctuating spot price of the bond traded in the market the Present Value of the bond.

Yield to Maturity

Now we know that the present value of the bond changes all the time, which probably makes you wonder how do you compare the prices across different bonds, since some bonds' par value is 1000, some are not.

Using the percentage points of the par value is a good idea, as in the figure above of the Boeing bond. But the most frequent way in the finance world is the Yield To Maturity (YTM).

What is YTM? YTM is the nominal interest rate that one can infer from the present value and all the future cash flows from the bond. In other words, if you discount all the future cash flows using YTM to today, you will get the present value of the bond.

One extremely important point is, the reason we say YTM is a nominal interest rate is because it is actually an APR — it is not the real interest rate per year. I will show you what do I mean in the following example.

Learning by Example: Present Value of Bond

Avocado, Inc. just issued a 10-year semi-annual coupon bond. The face value of the bond is $1000, and its lucrative coupon rate is 6%. If the Yield to Maturity of the bond is currently marked at 2% by the Wall Street traders who are obviously fans of Avocado, what should be the market price of this bond?

To begin with, the formula of present value of a bond is:

where PV is the present value of the bond, FV is the face value of the bond, c is the coupon payment for each period, r is the real return rate of the bond per period, and T is the total number of periods (which is the number of coupon payments) of the bond.

Notice that this is a semi-annual coupon bond, hereby the trick is each year the annual coupon payment is split into halves and paid twice. With this being said, we have the following inputs for the equation:

Now you see why I say YTM is an APR. To get the real interest rate, we divide YTM into halves, because YTM is the real discount rate of the bond per period times the number of periods. Remember:

APR = (return per period) × (number of periods within in a year)

So, for our case, the bond pays every 6 months, so YTM tells us that the real interest rate that the market use to discount all the future cash flows of the bond is 1% per 6 months. This is the real interest rate you can rely on.

Furthermore, let's take a look at the formula itself: the first part is obviously the present value of an annuity with 20 equal payment of coupon ($30) coming every 6 months, and the second part is the present value of the lump-sum payment of $1000 principal coming by the end of the 20th period.

Now knowing all our inputs and plugging them into the equation of the present value of the bond, we have:

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