## Understanding Bond Metrics

Have a question about your personal investments? No matter how simple or complex, you can ask it here.
Topic Author
doneat53
Posts: 87
Joined: Tue Jul 04, 2017 1:23 pm

### Understanding Bond Metrics

I've been trying to understand Bonds and Bond funds recently. I've learned a lot here particularly from Kevin M. Sometimes it helps me to have some skin in the game and dive in to fully understand so I purchased a Treasury note on the secondary market at Fidelity. At the time of purchase the note had a maturity time of ~ 1.1 years. Here are the details.

CUISP 912828W97
par value 100
Coupon 1.25%
payments every 6 mo.
Date Purchased 2/20/2018
maturity date 3/31/2019
price paid 99.069
current 3rd party 99.117
YTM 2.239 (my calculation current, slightly different than fidelity (2.237%))
coupon date 03/31/2018
next coupon date 09/31/2018
my tax bracket 32%
TEY = 1.523% (YTM*(1-0.32)) (I don't pay any state tax)

I noticed I received a coupon payment equal to 1/2 * 1.25% * 1000 * #shares on 3/31/2018

So I received 0.625% interest for holding the bill for a little over a month. I should get another 0.625% on 9/30/2018 and another 0.625% 3/31/2019 plus the face value of 1000.

When I add the coupon payments and return of capital up (6.25 *3 payments) + 9.31 because I paid 99.069 (less than par value) for the bill but will receive par value at maturity, I get a return of 28.06 / bill or 28.06/990.69 = 2.832%. (probably a little higher given compounding but for the sake of this discussion close enough).

I have a couple of questions.

1. I would think if I plug in my purchase date to my Yield To Maturity (YTM) calculation I should get 2.832 or something close but I don't... I must not understand YTM correctly, isn't it the percentage yield on investment from the current time point to the maturity date considering the coupon rate and the price of the bill?

2. The 2.832% number (return on investment if held to maturity) is an important number to me because it allows me to compare this investment to other investment opportunities. Is there a bond metric that allows calculation of this number if it isn't yield to maturity (YTM)?

alex_686
Posts: 5097
Joined: Mon Feb 09, 2015 2:39 pm

### Re: Understanding Bond Metrics

"Yield to Maturity" is the standard number. Or maybe "Yield to Worse", which is the worse two different number - Yield to Maturity or Yield to Call.

You calculations are way off. You are going to need a financial calculator to run a NPV or IRR calculation.

The discount is amortized. If you want a annual yield you amortize the discount to get a constant yield. So not straight line. Yield calculations also assume that coupons are reinvested at the yield. In both cases this is the "Yield to Maturity"

If you are asking yourself how do you calculate these yields if the inputs require that you know the output before hand. Iterative approaches. Plug in one number, see if you are high or low, then plug in another number. There are some fancy curve fitting techniques to speed up the calculations.

Lastly, don't just consider yield. Also consider risk. More importantly, consider how adding a perspective investment affects your portfolio's return and risk. This is ultimately what you care about. Adding a low correlation low return low risk asset can often increase a portfolio's return and decrease its risk.

Topic Author
doneat53
Posts: 87
Joined: Tue Jul 04, 2017 1:23 pm

### Re: Understanding Bond Metrics

Thanks for the quick reply alex_686
You calculations are way off. You are going to need a financial calculator to run a NPV or IRR calculation.
Which calculation is off? The YTM calculation is within a 1/1000 of fidelity's value.

The 2.832 number is reality (3 coupon payments of \$6.25 and return of the \$1000 par value for the note)/amt invested.

I'm clearly overlooking something but I'm pretty confident when all is said and done I'll earn 2.832% on my investment.

patrick013
Posts: 2757
Joined: Mon Jul 13, 2015 7:49 pm

### Re: Understanding Bond Metrics

doneat53 wrote:
Fri May 04, 2018 2:04 pm

So I received 0.625% interest for holding the bill for a little over a month. I should get another 0.625% on 9/30/2018 and another 0.625% 3/31/2019 plus the face value of 1000.
How much was accrued interest on the purchase ? You paid
for that as part of the purchase price.

alex_686
Posts: 5097
Joined: Mon Feb 09, 2015 2:39 pm

### Re: Understanding Bond Metrics

doneat53 wrote:
Fri May 04, 2018 2:49 pm
Thanks for the quick reply alex_686
You calculations are way off. You are going to need a financial calculator to run a NPV or IRR calculation.
Which calculation is off? The YTM calculation is within a 1/1000 of fidelity's value.

The 2.832 number is reality (3 coupon payments of \$6.25 and return of the \$1000 par value for the note)/amt invested.

I'm clearly overlooking something but I'm pretty confident when all is said and done I'll earn 2.832% on my investment.
I think I misinterpreted your question. I was focused on how you did your calculations, which are way off. It got you the 2.832% yield instead of the 2.239%? Was that not your question? If not, what was it?

I would also point out that Patrick013 has a very good point. Pull your original trade ticket and see if you had to pay some pre-paid interest.

Topic Author
doneat53
Posts: 87
Joined: Tue Jul 04, 2017 1:23 pm

### Re: Understanding Bond Metrics

CUISP 912828W97
par value 100
Coupon 1.25%
payments every 6 mo.
Date Purchased 2/20/2018
maturity date 3/31/2019
price paid 99.069
current 3rd party 99.117
YTM 2.239 (my calculation current, slightly different than fidelity (2.237%))
coupon date 03/31/2018
next coupon date 09/31/2018
my tax bracket 32%
TEY = 1.523% (YTM*(1-0.32)) (I don't pay any state tax)

I noticed I received a coupon payment equal to 1/2 * 1.25% * 1000 * #shares on 3/31/2018

So I received 0.625% interest for holding the bill for a little over a month. I should get another 0.625% on 9/30/2018 and another 0.625% 3/31/2019 plus the face value of 1000.

When I add the coupon payments and return of capital up (6.25 *3 payments) + 9.31 because I paid 99.069 (less than par value) for the bill but will receive par value at maturity, I get a return of 28.06 / bill or 28.06/990.69 = 2.832%. (probably a little higher given compounding but for the sake of this discussion close enough).

I have a couple of questions.

1. I would think if I plug in my purchase date to my Yield To Maturity (YTM) calculation I should get 2.832 or something close but I don't... I must not understand YTM correctly, isn't it the percentage yield on investment from the current time point to the maturity date considering the coupon rate and the price of the bill?
thank you patrick013!

Yes I have an interest payment at the time of purchase of the TNote.

This effectively reduces the coupon payment I received on 3/31/2018 to 1.305 / note

so... 1.305+6.25+6.25+9.31 = 23.115/note
23.115/99.069 = 2.33% which is much closer to the current YTM of 2.239% and likely different by the fact that the 2.239 is a "current YTM" and the 2.33% would have been the YTM at the time of purchase.

It's all making more sense now, thanks for pointing out that I might have an interest payment at the time of purchase.

Valuethinker
Posts: 39047
Joined: Fri May 11, 2007 11:07 am

### Re: Understanding Bond Metrics

doneat53 wrote:
Fri May 04, 2018 2:04 pm
I've been trying to understand Bonds and Bond funds recently. I've learned a lot here particularly from Kevin M. Sometimes it helps me to have some skin in the game and dive in to fully understand so I purchased a Treasury note on the secondary market at Fidelity. At the time of purchase the note had a maturity time of ~ 1.1 years. Here are the details.

CUISP 912828W97
par value 100
Coupon 1.25%
payments every 6 mo.
Date Purchased 2/20/2018
maturity date 3/31/2019
price paid 99.069
current 3rd party 99.117
YTM 2.239 (my calculation current, slightly different than fidelity (2.237%))
coupon date 03/31/2018
next coupon date 09/31/2018
my tax bracket 32%
TEY = 1.523% (YTM*(1-0.32)) (I don't pay any state tax)

I noticed I received a coupon payment equal to 1/2 * 1.25% * 1000 * #shares on 3/31/2018

So I received 0.625% interest for holding the bill for a little over a month. I should get another 0.625% on 9/30/2018 and another 0.625% 3/31/2019 plus the face value of 1000.

When I add the coupon payments and return of capital up (6.25 *3 payments) + 9.31 because I paid 99.069 (less than par value) for the bill but will receive par value at maturity, I get a return of 28.06 / bill or 28.06/990.69 = 2.832%. (probably a little higher given compounding but for the sake of this discussion close enough).

I have a couple of questions.

1. I would think if I plug in my purchase date to my Yield To Maturity (YTM) calculation I should get 2.832 or something close but I don't... I must not understand YTM correctly, isn't it the percentage yield on investment from the current time point to the maturity date considering the coupon rate and the price of the bill?
It is the Internal Rate of Return of the cash flows from owning the bond including the cash outflow of the purchase price.

Your calculation appears not to take into account the timing of the cash flows ie the time value of money.

2. The 2.832% number (return on investment if held to maturity) is an important number to me because it allows me to compare this investment to other investment opportunities. Is there a bond metric that allows calculation of this number if it isn't yield to maturity (YTM)?
Ish. YTM assumes coupons are reinvested at the same YTM. That's never true. Except in the case of a zero coupon bond.

Callable bonds are usually prices on yield to call.

patrick013
Posts: 2757
Joined: Mon Jul 13, 2015 7:49 pm

### Re: Understanding Bond Metrics

doneat53 wrote:
Fri May 04, 2018 8:16 pm
It's all making more sense now, thanks for pointing out that I might have an interest payment at the time of purchase.
Bond Yield to Maturity Calculator

I tried to verify the calc on a 2 year TRSY at Fidelity with a May 7, 2018
settlement date. Both answer were identical. However, the calc did
not include accrued but not paid interest. So the total cash would be
higher than just the purchase price.