# How is the yield of this particular bond calculated?

I am looking at this particular bond of coinbase company via Interactive Brokers website. Coinbase Bond ISIN : USU19328AA89

The rate of the bond is 3.4 so at the ask price of the bond at 62 the yield should have been (3.4/62)*100% = 5.66%. How is the yield of the bond at 62 showing 13.280%? How has it been calculated mathematically?

Additional info on the corporate bond

Yield is always calculated as the discount rate that makes the present value of the coupons and final redemption equal to the market price. (If you aren't familiar with the concepts of discounting and present value, that's the first place to start) As the market price goes down, the cash flows are fixed, and must be discounted at a higher rate to get the present value down to the market price. The actual calculation for a bond with 11 coupons remaining is too long to show here (and must be solved iteratively anyway) but it can easily be done in excel with the XIRR function (which is the same concept mathematically). There are plenty of tutorials online to calculate Yield to Maturity (YTM).

A simple example with just two coupons - one in 6 months and one in 12 months (at final redemption):

``````c = coupon rate
y = yield

pv = (c/2)*(1+y/2)^(-1) + (c/2)*(1+y/2)^(-2) + (100)*(1+y/2)^(-2)
|----------------|   |----------------|   |----------------|
first coupon        second coupon          face value
``````

The first coupon is discounted by 6 months (`y/2` or one period), the second and the face value are discounted by 12 months (`y/2` for 2 periods). Find the value of `y` that makes the present value match the market price.

Excel's IRR and XIRR do the same thing, except the market price is treated as a cash outflow at the beginning. Excel does it iteratively by trying different values of `y` until the retsult (effectively `PV - market price`) is 0,

What you are calculating is the current yield, which is how much return do you get on your investment just from the next coupon. The yield to maturity is a more complicated calculation, and is an annualized return. You would get closer to that annualized yield if you doubled the current yield since coupons are paid twice a year.

• is it not that there are 11 coupons left? how is that there are 17 coupons remaining? Mar 15 at 15:23
• You're right- for some reason I was thinking there were 8 years left instead of 5. I probably had 2028 in my head and just did the quick math wrong Mar 15 at 15:40
• could you show the calculation here, hypothetically assuming that there were just 2 coupons left? or even one would be enough. Mar 16 at 15:04

Simplified, you can expect (no default, no call as this bond is callable etc) that the bond pays back 100 at the end but is only worth 62 now. Therefore, over the next 5 years until maturity, you gain (100-62)/5 = 7.6% per year.

Add this to your current yield of 5.66% and you get 13.26% which is close to the shown yield of 13.28%.

To do it properly, you would need exact daycount and all cashflows spread out over time. The YTM is the discount rate applied to all cashflows that makes the computed value of the bond match the quoted market price.