Bonds effective yield

[Mattel]

Hi guys

I'm a student in need of a bit of guidance for an assignment and would greatly apprecite any help! I'm required to explain the difference between the nominal and effective yield to maturity on a bond. I understand the theory, that effective includes the compounding effect of reinvesting coupon payments. I have also found the following formula and understand what it is calculating.

(1 + i/n)^n - 1

Where n is the rate in a period and n is the number of periods in a year.

My question is, what stage would you use this formula, do you use it after calculting a YTM? Or, do you use it before in order to give a different cash flow amount to use in the YTM forumla?

As I've said, any help is greatly appreciated and you can consider it your good deed for the day!

 

[Mattel]

bump

 

[Rhody Trader]

I'm struggling to recall in my memory banks any difference between effective yield and YTM.

 

[A Dashing Blade]

From "NOMINAL YIELD" <HELP> in Bloomberg . . .
Nominal Yield. The percentage of a fixed-income security's par
value to its annual payout. Also known as the "coupon rate."

YTM assumes, as you rightly said, income is reinvested at the current price and the instrument is held to maturity.

 

[raysor]

Who would ever use a nominal yield? As you say it is the yield at par or the coupon. In a tradeable bond you would rarely get the nominal yield and even then it would be the same as the yield (flat or running?). If the coupon was 5% and the price 100 the 5% return would still be called the yield. It would be coincidently the same as the nominal yield or the coupon return! As I see it you only have two yields; flat and redemption.

 

[Rhody Trader]

Who would ever use a nominal yield? As you say it is the yield at par or the coupon. In a tradeable bond you would rarely get the nominal yield and even then it would be the same as the yield (flat or running?). If the coupon was 5% and the price 100 the 5% return would still be called the yield. It would be coincidently the same as the nominal yield or the coupon return! As I see it you only have two yields; flat and redemption.

Actually, nominal yield usually refers to the current coupon/price rate. For example, the nominal yield of a 9% coupon on a bond trading at 90 would be 10%. It is, I think, what you called "flat", while what you refer to as "redemption" is yield-to-maturity (YTM). There's also YTC, which is yield-to-call for those bonds that are callable.

 

[raysor]

Is that a US/UK translation thing? I always thought nominal meant "in name only". Why confuse the issue? A coupon is the coupon on the face of the bond and the yield is the rate of return dependent on the price paid or used for the calculation.
"YTM assumes income is reinvested at the current price...." That's not right is it? I thought it was the yield plus or minus the gain or loss of capital at redemption, sorry maturity. With a bit of discounting thrown in somewhere.

 

[Rhody Trader]

Since YTM (and YTC) is based on discounting the cashflows back (coupons and final par repayment), it does assume reinvestment.

 

[raysor]

Crikey, it's complicated isn't it?
Does that mean I should be unravelling the stated YTM if I knew a client wasn't going to reinvest the interest (maybe a cost aspect) in order to illustrate the YTM he would actually get?

 

[Mattel]

Just to confirm, you guys are on the right lines. Unversity has taught me something by the sounds of it, all the debt is worth it!

Back to my original question then, nobody has heard of effective YTM then? As I said before, its for including the effect of the extra interest on interest recieved is a coupon is paid semi annually rather than annually, I just need to check I'm calculating it correctly.

In the example I have a bond with a yield of 8.03% if paid annually, and I have worked out an effective YTM of 8.1912% if the same yield were to be recieved semi annually. The numbers obviously look right and would make sense, but am still unsure.

I'm worried that the formula shown in the first post should instead be used on the coupon payment recieved in order to give a new "semi annual" coupon.

 

[Rhody Trader]

Crikey, it's complicated isn't it?
Does that mean I should be unravelling the stated YTM if I knew a client wasn't going to reinvest the interest (maybe a cost aspect) in order to illustrate the YTM he would actually get?

If an investor will be living off the coupon or otherwise not reinvesting the interest, then YTM definitely isn't the measure for them. Coupon yield would probably suit just fine.

 

[Rhody Trader]

Back to my original question then, nobody has heard of effective YTM then? As I said before, its for including the effect of the extra interest on interest recieved is a coupon is paid semi annually rather than annually, I just need to check I'm calculating it correctly.

You can confirm your figures with Excel, but it does sound like you're on the right path.

 

[raysor]

If an investor will be living off the coupon or otherwise not reinvesting the interest, then YTM definitely isn't the measure for them. Coupon yield would probably suit just fine.

I just think that say you buy a 5 year bond at 120 and it gives you a flat yield of 5%. Then at redemption you lose the 20 points then that annual interest has been inflated at the expense of your capital. So you should really know what your actual return has been over the 5 years. And I would have thought this could be ascertained by knowing the redemption yield? Even if this is just for comparison reasons.
Presumably I have it all wrong, so what is the YTM used for? And how do you reinvest the interest? (say on £500 of Treasury stock)
In the UK the interest would be taxable but the capital gain ( if any) at redemption would not be so in a practical example that would need to be taken into account.

 

[A Dashing Blade]

. . .
Back to my original question then, nobody has heard of effective YTM then?

Nope

As I said before, its for including the effect of the extra interest on interest recieved is a coupon is paid semi annually rather than annually

You're still talking about YTM

In the example I have a bond with a yield of 8.03% if paid annually, and I have worked out an effective YTM of 8.1912% if the same yield were to be recieved semi annually. The numbers obviously look right and would make sense, but am still unsure.

You can express YTM in any time space (annual, semi, quarterly etc). However, given the same YTM, the implied semi annual coupon would be less than the implied annual coupon.

In your example, obviously 8.03% paid annually will yield less than if the same bond paid 4.015% semiannually bacause of the compounding effect.

Simple example illustrating compounding
10% paid annually over 10 years = (1+0.1)^10 = 2.5937
OR
10% paid semi over 10 years = (1 + 0.05)^20 = 2.6532

 

[A Dashing Blade]

so what is the YTM used for?

As a very simple way of ranking bonds of differing coupons. (These days the Z-Spread or the Asset Swap Spread is used)

And how do you reinvest the interest? (say on £500 of Treasury stock)

YTM is a theoretic measure, it ASSUMES you will be able, in the future, to reinvest gross coupon payments back into the bond at the current price

 

[A Dashing Blade]

Just to confirm, you guys are on the right lines. Unversity has taught me something by the sounds of it . . .

Thanks for that vote of confidence, nice to know my 23 years in the City hasn't been wasted.

 

[A Dashing Blade]

Crikey, it's complicated isn't it?

Er . . . no, this is about as simple as it gets in bond space. However, the point you should take from the exercise is that any and all financial instruments can be modelled as a series of expected cash flows, and that those cash flows, when discounted at the approriate rate(s) and summed, should be equivilant to the instrument's price in the market.

 

[gooseman]

Er . . . no, this is about as simple as it gets in bond space. However, the point you should take from the exercise is that any and all financial instruments can be modelled as a series of expected cash flows, and that those cash flows, when discounted at the approriate rate(s) and summed, should be equivilant to the instrument's price in the market.

if not arb the hell out of it

 

[raysor]

If you are discounting the future cash flow is this calculated using a predicted future interst rate, and if so don't you have to get that spot on? Otherwise the calculations are a nonsense.

 

[Rhody Trader]

If you are discounting the future cash flow is this calculated using a predicted future interst rate, and if so don't you have to get that spot on? Otherwise the calculations are a nonsense.

You don't use a future rate. The YTM is really just an IRR (internal rate of return). It's a matching of the current price of a bond to the yield which values the future cashflows to that price.