============== Which of the following statements regarding yield spreads is least accurate? The: A. option cost in percentage terms can be computed by subtracting the OAS from the zero-volatility spread. B. nominal yield spread measures the difference between the YTM on a risky bond and the YTM on a Treasury bond of similar maturity. C. The zero volatility spread is the constant spread that is added to each Treasury spot rate to equate the present value of a bond’s cash flows to the price of an otherwise identical option-free bond. Answer: C. The zero volatility spread is the constant spread that is added to each Treasury spot rate to equate the present value of a bond’s cash flows to its actual market price. ============== A and B is correct, but I not able to understand the explantion for C. In the question where they state “…bond’s cash flows to the price of an otherwise identical option-free bond” - isn’t the PRICE assumed to be the market price here? What is the difference between this and the “…bond’s cash flows to its actual market price” as they have stated in the answer?
seems poorly worded, perhaps the part, “to the price of an otherwise identical option-free bond.” is part that is least accurate. where did this question come from? if it was on the exam, i would be pissed, because it serves only to be tricky with wording and not test the facts.
To be true, c would need to read: The zero volatility spread is the constant spread that is added to each Treasury spot rate to equate the present value of a bond’s cash flows to the market price of the bond.
Wait a minute - that’s what the answer says. The answer is correct and is different from the wording in the question.
I agree that the original wording of c may be quite clumsy, but it is actually theoretically correct, and explicitly clear. There is no Z-spread for an option-embedded bond. When one talks about Z-spread for an option-embedded bond, it implicitly means the z-spread for an identical bond with the option stripped out (thus matching the market price of this identical option-free bond, not the market price of the option-embedded bond)
Nope. The z-spread is a really simple calculation where you take Market price of bond = coupon1/(1 + r + z-spread)^t1 + … + couponk/(1 + r + z-spread)^tk + principal/(1 + r + z-spread)^tk The market price of a bond with an embedded option is different from a bond without an embedded option. Where you are getting messed up is that the z-spread is the spread over treasuries assuming that the bond is held to maturity. A high z-spread can be due to optionality, credit unworthiness, liquidity, taxation, etc…
I agree that I was wrong at last post. It should be market price of THAT bond, not equivalent option free. Z spread is the spread to compensate for the non-Treasury security’s credit risk, liquidity risk, and any option risk (i.e., the risks associated with any embedded options) in a static interest environment. PS: a small correction for your formula, to make it also 100% correct. Market price of bond = coupon1/(1 + r1 +z-spread)^t1 + … + couponk/(1 + rk + z-spread)^tk + principal/(1 + rk + z-spread)^tk i.e. z-spread is over the entire T spot rate curve. The way you wrote the formula originally can be interpreted as NOMINAL spread definition, i.e, spread on ONE point on the T yield curve (e.g., the r with similar duration as the bond). Hope you agree JoeyDVivre Wrote: ------------------------------------------------------- > Nope. The z-spread is a really simple calculation > where you take > > Market price of bond = coupon1/(1 + r + > z-spread)^t1 + … + couponk/(1 + r + > z-spread)^tk + principal/(1 + r + z-spread)^tk > > The market price of a bond with an embedded option > is different from a bond without an embedded > option. Where you are getting messed up is that > the z-spread is the spread over treasuries > assuming that the bond is held to maturity. A > high z-spread can be due to optionality, credit > unworthiness, liquidity, taxation, etc…
No, that’s why they were called r1, … ,rk. If they were going to be equal I would have called them all r. Would you have preferred if I wrote them with subscripts in HTML? Convince Chad to make the HTML-able and I’m there.
JoeyDVivre This was exactly what you wrote: you have called them all r. I copied what you wrote below: Market price of bond = coupon1/(1 + r + z-spread)^t1 + … + couponk/(1 + r + z-spread)^tk + principal/(1 + r + z-spread)^tk I corrected you by adding r1,…rk instead of just r.
Oops I did miss that. Yep different rates for sure.