Yield to Put

CFA Level I Fixed Income
#1

The YTP will likely be higher than the YTM. Why is it so?

If the bond is putable, shouldn’t the yield on that bond be lower as compared to a vanilla bond because the investor is at an advantage here?

#2

You get your money back sooner when you exercise the put. There are a lot of factors that determine whether the YTP will be higher that the YTM, but getting your money back sooner (especially for a bond selling at a discount) is a biggie.

#3

If I get my money back sooner, why should the YTP be higher? If we are referring to the discounting math in general here, then how do we account for YTC oh and as I type it, I see it that the investor will only exercise the put option if he has a profit to earn. Apples with Apples. Great!

S2000Magician, see this is what happens when you hobnob with the finest on the forum.

#4

If you buy it at 950 and put it at 970 you make a profit. If you make that profit in 2 years your annual yield is higher than if you make that profit in 10 years, and the yield for putting it at 970 in 2 years may be higher than getting 1,000 in 10 years.

I didn’t realize that you’re the finest on the forum, but now that I know that I’m all the happier to hobnob with you.

wink

#5

Put option is an advantage for bondholder, It provides you right to sell the bond back to the issuer at some specified time but before maturity. Hereby in putable bond your put price amount is insured and if you are using put option it means you are recieving your put price amount sooner than others who are not having such options that’s why YTP is greater than YTM.

#6

But if the market price is between the put price and par, then YTP will be less than YTM.

Suppose that you have a 10-year, semi-annual pay, 6% coupon, $1,000 par bond puttable after 5 years at 97, selling at $980. The YTM is 6.272%, the YTP is 6.122%: YTP is less than YTM. The reason the YTP is lower is that at maturity the bond has a built-in gain, whereas at the put it has a built-in loss.

Please think these answers through.

#7

Yes it depends on PV calculation if you are getting $50 less but the maturity time(maturity value=$500) is very near (6 months) in this case abosolutely YTP is lesser than YTM.

But nobody use put option if it is the situation.

#8

No fight guys… :slight_smile: Bond holder will exercise the put option when the market yield goes up (Bond price goes down), so that the bond holder can take advantage of the market rates with the money s/he will get from the issuer after putting the bond at the puttable price (usually lower than par). So, when the bond is trading at discount YTP comes into play which is usually higher than your coupon rate. But if the bond is trading at premium, which means YTM is lower (definitely lower than YTP) there is no use of YTP as bond holder will not excercise his or her option

Hope it helps… and now start fight again :slight_smile:

#9

None of these yields – yield to call, yield to put, yield to first call, yield to second put, yield to conversion, yield to worst – is predicated on whether it would be smart to exercise the option. They’re calculations based on the presumption that the option is exercised at the earliest opportunity, whether it’s smart to do so, or stupid to do so.

Whether to exercise the option is a separate question from how to calculate YTC or YTP or whatever. Please don’t complicate the answer to a simple question with information that isn’t relevant to that question.

#10

Its your turn Edupristine :slight_smile:

#11

You, sir, are a charmer! _/_

#12

Thanks for explaining. What is put price amount?

#13

Boo-yah!

#14

By advantage do you mean that the investor will have more money compared to what he could have if t was a vanilla bond? So, more money buys you at better rates now? Am I right? I don’t understand one thing. The price at which the bond is trading when the market rates go up is only temporary, right? Then why do we compare YTP to YTM based on that? Also, my understanding is YTM accounts for capital loss on the bonds as well (even if the vanilla bond was trading at premium at the time the investor bought it), though I never really understood the core reason behind this.

Why would YTP be higher than CR?

Why would YTM be lower if a bond is trading at premium? Why will YTP be definitely lower?

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#15

Yield and Bond Price have negative relationship. As the yield goes up, Bond price goes down and vice versa. Lets take an example to see why we have this relationship: Lets say you buy a bond with coupon 7%, now after 3 months the market yield (interest rate for similar bond) is 10% (Yield goes up). Now think market prefers 10% or 7%… Yes you got it right they prefer 10%. So, as the new coupon rate (equal to the new market rate) is 10% everyone will go for 10% bond and not for 7% bond. So, the demand for your bond goes down so does the price. Similarly, when the yield goes down the bond price goes up.

Because of this reason, YTM (yield) will be lower if a bond is trading at premium (Higher bond price).

Now, lets understand what is YTP. YTP is the yield at which you will put the bond back with issure. Basically sell back to the issuer. Usually it is done at the puttable price which is decided at the start of the bond contract.

Now, think when a bond holder will be happy to sell back to the issuer at a predefined rate? Yes you are right when the bond holder is getting something extra. Lets take the same example: your bond has a coupon rate of 7%. Now, if you sell back to issuer, it means you will have money with you which you can reinvest in the market. So, it will be good if you reinvest at a higher rate in the market. Yes you are thinking it right, as an example market yield is 10%, so your bond price is going down. So, it is decided that you will put the bond back only when market rate goes up.

How we think what will be puttable price (at which the bond will be put back) or YTP? Lets say you bought the bond in previous example issued at PAR (Bond price = 100, YTM = CR = 7%). Now, tell me one thing will the issuer gives you a right to put it back at a price above 100 or below or equal to 100. If the issuer is smart like you (unlike me ) then I think he will gives you a right to put it back below 100, lets say 90. Now, if we calculate the YTP with bond price 90 (which is lower) than YTP will be higher as compared to CR which is equal to YTM at the bond price = 100

Hope this make sense. If I left something… let me know

#16

Exotic hedge: I really appreciate your help here. I do understand the inverse relationship. Spent two sleepless nights on that :slight_smile: What I wanted to convey was YTM is a measure for the whole life of the bond i.e. from issue date to maturity date.

YTP, however, is till the date mentioned in the bond covenant (I assume it’s there only) i.e. putable date.

So, how can we compare YTM to YTP. Also, by temporary I meant market rate is justa fluctuation and the bond price will fluctuate accordingly at that point in time; however, it might happen that at a later date market rates may fall and the bond is trading at premium. Similarily, when the bond expires the bond might e trading at par. Who knows? Also, I have an understanding that YTM takes into a/c all the cash flows, even what you reinvest, but that is based on the predicted rates at the time of issue, right? I mean I think they must be using short term fwd rates to calcuLATE the rate at which an investor might reinvest his/her csh flows. So, how can you take into a/c (into YTM) the fluctuations that will be there at the time the investor “puts” his bond back to the issuer?

Thank You :slight_smile:

#17

  1. Although the yield measures are based on cash flows over different time periods, they are both expressed as ANNUAL yields. That’'s why they are comparable. It’s similar to how we can use IRR to compare projects over different time frames.

  2. As for the “temporary” fluctuations, the bond prices at the put/call dates and at maturity are fixed by the characteristics of the bond.

  3. YTC, YTP, and YTM all assume that interest rates are level over the term of whatever period you are looking at - essentially that the term structure is perfectly flat.

There is a measure that you’ll see in L2 called “Total return” that has you make explicit assumptions about reinvestment rates. In that sense, it’s basically the same as the Modified Internal Rate of Return (MIRR) measure as applied to a bond. While not typically used in the context of a putable bond, you could easily adapt it. Essentially, you would take all cash flows (coupons, put proceeds, etc…) and calculate their Future values as of the end of your investment horizon. You’d calculate your FV using whatever forward rates you assume. You then sum all the individual future values (from each cash flow) and find the rate that equates this to the current proce (basically, a Future/present value of a lump sum problem). That would be the retun on an annualized basis.

#18

Thanks. I got it. I was thinking that YTP is calc at a later point in time, but still this is weird. I mean the flat term structure assumption. However, I do know that these yield meaures are all hogwash in real world. Why are we even learning them? Do we build on these at L2 and L3?

#19

Work done… :slight_smile: