# Help me with Fixed Income please!

Hi, guys,

I am a bit confused with callable and putable bonds concepts.

From practice questions:

1)“When interest rates rise, the option embedded in a callable bond will most likely…”

But why? I thought that as interest rates rise the price of the bonds will fall and the issuer can redeem bonds at lower price…(so the option must increase in value)

2)“At high yield levels as interest rates further increase, the value of a putable bond will most likely…”

Answer is: Decreases at a decreasing rate

3)“At high yield levels as interest rates further increase, the value of a put option…”

Answer is: Increases at an increasing rate

Could you clarify it for me please?

Nzhukov,

callable and putable bonds are combination of option free bond and derivative options.

Since callable bond is beneficial to issuer as the market interest rates decrease the issuer can call his high yield bond from the holder so the value of callable bond= option-free bond - call option.

since putable bonds are beneficial to the holder of bond and is exactle vice versa to callable bond, so the price of putable bond=option-free bond + put option. As far as your problems are concerned let me answer it separatly.

1, as the interest rates in market increases, it makes no sense that a callable bond issuer will call his bonds from the market as already his issue is giving less coupon payment then market so the issue is in advantage position. No call option will be excersed and callable bond at higher market yield will ac as an option-free bond.

2, as i have explained that putable bond is beneficial to the holder, as the interest rates in market increases, the holder of putable bond is in advantage as he can put the exsisting bond and replace it with higher yield bonds, so taking this fact into consideration the market value decreases at a decreasing rate as compared to option-free bond. Putable bond shows a greater positive convexity that is decrease in price is less than an increase in price. See putable bonds graph in notes. Remember putable bond=opt free bond + put option

3, your third query is linked with your second question. Suppose at day one, @ 5% market rate value of opt free bond= 100 and putable bond =102 (\$2 put price) at day two @6% market rate the price of opt free bond=98 and putable bond 101(\$3 put price, as at higher yield the holder of putable bond can replace his bonds with high yield bonds) as the rate increases put option price will increase ! Again see the positive convexity graph in schweser notes.

Another point i would like to add is that as volitility increases, the price of both call option and put option increases. But as the equ says callable bond= opt free bond - call option so the price of callable bond decreases as volitility is increasing and the price of putable bond that is putable bond= opt free bond + put option,the price will increase.

hope you will grasp all this explanation.

be well

Howdy!

You’re not alone in that respect.

The issuer can call the bond at \$1,020. Is that worth more when interest rates are low (and the market price of the bond is \$1,040), or when interest rates are high (and the market price of the bond is \$980)?

(Yes, I know that if there’s a call option at \$1,020 the market price won’t exceed that value; I chose the numbers above to highlight the situation.)

The price of bonds will fall, and the issuer can purchase them cheaply on the open market. Therefore, they will not exercise an option that requires them to pay more.

The floor value of an option-free bond is \$0. The floor value of a putable bond is the put price. Thus, as interest rates increase the value of the putable bond will decrease (as bonds do), but not as much as the value of an option-free bond.

I agree that the value of the put option increases – it’s analogous to the case of a call option when yields are low and decreasing – but whether the rate of increase is increasing or decreasing is more problematic. After some point, the rate of increase has to be decreasing. I think that this is a bad answer.

You’re welcome in arrears.

Thanks a lot!

Could you also clarify please a couple of more items

1. The issuer of what securities benefits from a DECREASE in interest rates:

Inverse floater

Fixed rate corporate bond

2.1 “If the bonds required to meet the terms of a SINKING FUND PROVISION are trading below par, it would be more cost effective to deliver bonds to the trustee”.

Why? Wnen do we deliver bonds and when do we pay cash? Struggling to catch this sinking fund provision concept.

2.2"Under regular redemptions bonds are called ABOVE par"

Is it because the investors will not let us redeem bonds at par?

No problemo

Could you also clarify please a couple of more items

1. The issuer of what securities benefits from a DECREASE in interest rates:

Inverse floater

Fixed rate corporate bond

[/quote]

thats right. suppose if ur fixed coupon issuer who issued bonds at 10% per anum coupon and market interest rates of the bonds are 8% then you are definitly losing !! so cross fixed coupon out.

For simplicity we know that floating bond rate= floating rate + margin rate so it is similar case as that of fixed coupon bond supose LIBOR is 5% and margin rate is 2% then floating rate is giving 2% more than LIBOR rate that is coupon of 7% so cross this out too.

Mortgage securities are beneficial to issuer as issuer can call/redeem/refund bonds as the market rate increases. It is the kind of features embedded in mortgage securities !! so if interest rate decreases the issuer can redeem his securities.

2.1 “If the bonds required to meet the terms of a SINKING FUND PROVISION are trading below par, it would be more cost effective to deliver bonds to the trustee”.

Why? Wnen do we deliver bonds and when do we pay cash? Struggling to catch this sinking fund provision concept.

2.2"Under regular redemptions bonds are called ABOVE par"

Is it because the investors will not let us redeem bonds at par?

[/quote]

My concept regarding this is, below par means coupon rate is lower than market rates then we can say that thorugh sinking funds provision it is fasible to issue a lower coupon bond relacing higher coupon exsisting bonds. above par means at premium that is coupon payments are greater than market rates so it is beneficial to give cash and redeem bond instead of issuing another high coupon bond. THIS IS MY CONCEPT OF UNDERSTANDING.

Be well

My pleasure.

With pleasure.

Inverse floater: when interest rates decrease, the coupon increases. Bad for issuers.

Mortgage: when interest rates decrease, prepayments increase, so the fee that the issuer receives increases. Good for issuers. (However, future fees decrease, which is bad for issuers. The net effect is unclear.)

Fixed rate corporate bond: when interest rates decrease, they pay the same coupon, and if they want to retire the bonds they have to do so at a premium. Bad (or indifferent) for issuers

When an issuer delivers the bonds to the trustee, they are redeemed at par. When the bonds are trading below par, the issuer is better off buying them on the open market at a lower price and retiring them.

Again, if the bonds are trading below par, the issuer would rather purchase them on the open market at a discount, rather than call them (at par).

Yup,and in another words, issuer avoid buying them on the open market when price is above par. All they need to call them back at par value. Because of these issue, you have to be aware of convexity of such provisions

You have to be aware of _ negative _ convexity of such provisions.

lol

no ending huh… heehee

Good evening everyone!

I have a minor question on the calculation side…

So, suppose we have 1,000 par value 4 year bond which offers coupon = 9%. Market yield is 10%. So, what we do know for sure is that the bond is issued at discount.

The question is: if market yield is up by 35 b.p (0.35%) at the end of year 3 what is the value of the bond? Why do wee enter N=2 (not 6) in the calculator?

there is 1 year left on the bond - 2 coupon payments

hi nzhukov

the bond is trading at a discount, not issued

at the end of year 3, there is only 2 coupon payment left to maturity (therefore N = 2)

we will only use N=6 if you are interested to know the price of the bond 1 year after issued => total bond coupon payment = 8 as this is a 4 year bond

Does this solve your question nzhukov?

Yes, pretty easy. Thanks a lot!

As you work through bond valuation problems, it’s good to remember 3 rules:

1. Bonds are solved on a “periodic” basis - i.e. if the bond pays coupons on a semiannual basis (the most likely case), think in terms of 6 months as a period. Then “N” will be the # of 6-month periods and I/Y will be the interest rate over 6 months.

2. When solving for the yield or remaining maturity, you solve on a periodic basis but express your answer in annual terms (i.e. interest rate per year and # years)

3. The value of the bond at any point in time will be the present value of the remaining payments (and the par value) at that point in time and at the discount rate or yield to maturity in effect at thte time you are valuing

A fourth rule that sometimes becomes useful is that when the coupon rate > YTM (or “market rate”) the bond sells at a premium, when coupon = YTM it sells at par and when Coupon < YTM it sells at a discount. If YTM doesn;t change, bonds move closer to par as time passes.