How to Calculate YTM of Bond?

Hi, it's William Jiamin here. In this video, we're going to talk about the two-year maturity of bonds. Sometimes, you might see it referred to as YT M, which is essentially the same thing. We briefly covered the concept of year-to-maturity when discussing spot rates.

Now, if you're dealing with a zero-coupon bond, let's say it was issued at time zero and has a maturity of time T, the two-year maturity refers to the spot rate of that particular bond. It's pretty straightforward because the bond doesn't pay any coupons, so any changes in price will reflect the spot rate.

Sometimes, I refer to the spot rate as the investment return or required return for investment. This works both ways, as when you invest in a bond, you expect a certain return, which is the spot rate.

But what about bonds that do have coupons? Since the spot rate is changing, if you have a bond with a term period, you'll have multiple coupon payments. So, how do you calculate that?

Here's a good way to calculate the yield to maturity (YTM) using a calculator. If you have a financial calculator, you can input the number of periods (n), the present value (PV), future value (FV), and the yearly interest rate (rate). You can also use Excel to calculate it.

In our previous example, we had the spot rate curve, the term structure spot rate, the bond, the cash flow, and we calculated the price at the present time. We can use the RATE function in Excel to calculate it. The RATE function takes inputs such as the number of periods, the payments (PMT), the present value (PV), the future value (FV), the type (Z or 1), and the guess (guess can be left blank).

When you enter the formula, you may encounter an error. This is because it can be confusing for the computer to understand that you receive some money at the beginning and some at the end, along with other cash flows. To resolve this, you need to add a minus sign before the present value, as from an investor's point of view, it's a cash outflow.

So, the present value becomes the cash outflow, while the future value represents the cash inflow. The coupons are treated as inflows. When you enter these values, you'll get the answer, which will be our YTM or yield to maturity. It's pretty amazing when you think about it because this amount is like the weighted average of the spot rate. You have three spot rates for this amount, and the spot rate with a greater weight is the one that corresponds to the larger future value.

Essentially, the YTM is a weighted average of the spot rates, with the third-year spot rate having the greatest weight. It's larger than the first and second-year spot rates, but smaller than the third-year spot rate. It's like an in-between value. This is how I remember it.

Of course, this calculation is skewed towards the final payment since most of the time, at the end of the bond's term, you receive the principal, which is a significant amount compared to the everyday coupon payments.

So, that's how you calculate the yield to maturity of bonds.