Q47: Valuing Bonds with embedded option

CFA Level II Fixed Income
#1

Q47: Valuing Bonds with embedded option

Could someone go over the following 2 questions? Thank you!

Q1)

We use Treasury Market rates as benchmarks to evaluate a callable corporate bond. We know:

Z-spread: 190bps

OAS : 150bps

Given that an option-free bond with the same credit rating, liquidity, and maturity as the callable bond being evaluated is trading in the market at a z-spread of 180bps, the callable bond is most likely ____

Answer: Overvalued.

Thought Process)

Part I.

We should compare the OAS of a callable bond vs. z-spread of the option-free bond. Since it is a call, the “option cost” is greater than 0, as we receive compensation for writing the option to the issuer. This means we require more yield on the callable bond than for an option-free bond. Since OAS of 150 bps is < z-spread of 180bps, this means the callable bond is offering too low a yield. So, for callable bond, it should be such that OAS > Z spread for it to be either properly valued or undervalued?

Part II.

In addition, if this was a putable bond, then the putable bond is most likely undervalued?

Part III.

If it is such that the callable bond is overvalued in the case where OAS < Z Spread, is it partially relating to the fact that the cash flows will not be discounted at a high enough rate to compensate for the “prepayment” risk? In other words, since the issuer can call the bond, the OAS should be higher so that when we take the present value of spot rate + OAS, the current market value is lower (i.e. cheaper)?

Q2)

The following info is regarding a callable bond:

Z Spread = 45 bps

OAS = -35 bps

The bond is most likely ____

Answer: Overvalued.

Thought Process_

If the OAS of a callable bond (-35bps) is negative, then it indicates that it is relatively expensive? Not sure why, but I’m guessing that this will be answered based on the question above.

#2

I think you’re over complicated it a touch but i’m curious as to how other’s see it.

If the OAS spread is < 0, that means the spread to the benchmark is actually negative. Meaning, the rate you’re receiving on the bond is lower than the market rate, implying the issue is overvalued to the market of similar bonds.

If the OAS spread is > 0, that means the spread to the benchmark is positive. Meaning, the rate you’re reciving on the bond is higher than the market rate, implying the issuing is discounted to the market of similar bonds.

#3

Agree- think thats how the curriculum explains it

#4

For an option-free bond, z-spread = OAS. Thus, the OAS of the callable bond (150bps) < OAS of the comparable bond (180bps); the callable bond is (relatively) overpriced.

If the bond were putable, its OAS (150bps) is still less than the OAS for the comparable bond (180bps); it’s still (relatively) overpriced.

Yes.

Yes: a negative OAS says that its spread is too low; it’s overvalued.

#5

Thanks for everyone’s input.

Is it correct to say that since OAS reflects for credit risk and liquidity risk, OAS should be always greater than Z Spread for calls and puts? If OAS > Z Spread for a comparable bond, then it is either

  • correctly priced or undervalued.

If OAS < Z Spread, it is always relatively overpiced for both calls/puts.

Thanks again, especially to s2000 for going through each of my questions.

#6

OAS is always lower than the z-spread since the z-spread = OAS + Option cost

#7

I thought it depends on whether the option is a call or a put.

  • For a call, option cost is > 0. Thus, Z spread > OAS.
  • For a put, option cost is < 0. Thus, OAS < Z Spread.

If the above is correct, this makes sense to me. For example, since it is the spot rate + the spread, it makes sense that the spread is lower for a put. The put should be more expensive since the investor could “put” the bond once it drops below a certain amount.

Where I cannot make the connection is what spread to add to the spot rate when it is call option vs. put option. Since it is OAS = Z Spread - Option Cost, the OAS is higher for a put?? (since option cost is “negative”, z spread - “negative option cost” gets me a higher OAS. But higher OAS + spot rate gets me a higher discount rate, which in turn gets me a lower value of the bond? Lower value of the bond does NOT make sense to me since putable bond should be more expense.

Hopefully my logic process above is clear… haha. If I am completely off-base, feel free to slap and educate me haha.

#8

hmm perhaps you’re right!

#9

PassOrNothing knows whereof he speaks.

#10

Well, I don’t think credit risk enters into it anywhere.

For callable and putable bonds, OAS is not = Z-spread because of option cost, which would depend on multiple factors, one of which is default probability. But also liquidity, overall interest rate environment, whether Yellen has a cold, …

#11

I have a slightly related question:

Why is it that, the higher the assumed interest rate volatility, the lower the option adjusted spread for a callable bond?

I am trying to understand it this way: The higher the interest rate volatility, the higher the value of the call option and since the value of the call option is inversely related to the OAS, the lower the OAS.

Am i correct?

#12

Yes.

Increased volatility of the underlying increases the value of all options: puts and calls.

#13

This is an interesting point. Can you please elaborate why the OAS would be lower when vol goes up?

The way I think about it is, vol goes up —> option cost goes up —> spread between Z and OAS goes up. But then it gets a bit cloudy for me. I am having a hard time understanding the inverse relationship you guys are talking about and why it is like that.

#14

In a callable bond you’re long an option-free bond and short a call option. If the value of the option increases, the value of the callable bond decreases, so the difference between the Z-spread and the OAS increases. Either the Z-spread increases (most likely) or the OAS decreases (possible), or both.

#15

Using the formula based on the statement above, Z Spread = OAS + Option Cost, I’m wondering why you said the Z-Spread would “most likely” increase or the OAS would “possibly” decrease.

Since the option cost goes up, it appears that the Z spread would definitely go up and the OAS would definitely go down.

Question on another concept:

"For tranches trading at a premium (coupon rate exceeds market interest rates) a decrease in the prepayment would 1) increase the OAS and 2) increase the value of the security (if OAS is held constant). This is because the investor would receive higher coupon for a longer period. Further, slower prepayments would delay the capital loss (as it is the par value of the loan that is repaid) from prepayment. The longer the effective duration of the tranche, the more it benefits from a slowdown in prepayments."

Question 1)

Based on the explanation in italics, I am still unsure how a decrease in prepayments would 1) increase the OAS and 2) increase the value of the security if OAS is held constant. How is it that the investor would receive the higher coupon for a longer period because of a decrease in the prepayment rate?

Thank you.

#16

If A = B + C and C goes up, either A can go up and B remain constant; or B can go down and A remain constant; or A can go up and B can go down. Heck, A can even go down and B can go down even more and the equality will still hold.

A = Z-spread, B = OAS, C = option cost.

For the prepayment question, consider prepayments as exercising a call option where you are holding a bond worth $110 and it gets called at $100 (capital loss because the loan is repaid at par.)

Decrease in prepayments means less option exercise, less loss, less option cost, so if the Z-spread remains the same then OAS goes up. Or, OAS can remain the same and Z-spread can go down, in which case the security is selling at less of a spread to treasuries so it has become more valuable. Or both.