Learning spreadsheet P2.T6 Malz ch7

[Linghan]

Hi @David Harper CFA FRM, I am a little confused with the first tab on excel. How did you calculate the z spread to get 1.71%? It's not linked with formula so I'm guessing you prob use solver?

 

[David Harper CFA FRM]

Hi @Linghan The XLS could be clearer, sorry. See screenshot below. I only needed Goak Seek: solving for bond price ("Set cell") equal to 98.8 by changing the z-spread. You can see that Row 19 discounts the bond's cash flows by multiplying by 1/(1+(S+Z)/2)^(T*2); in this way, the z-spread is the value that, when added to the risk-free spot rate (given by S), will produced a discounted value equal to the "observed" price of $98.00. To my knowledge, this requires an iterative (goal seek, solver) type solution .... I hope that clarifies, thanks for looking at it!

 

[Linghan]

@David Harper CFA FRM Thanks for clearify that!

 

[trigg989]

Hi @David Harper CFA FRM , wanted to clarify (this is a dumb question). Are we expected to calculate the z-spread w/ our calculator on the Part II exam?

 

[David Harper CFA FRM]

Hi @trigg989 I was thinking about this because Tuesday we publish a quiz (part of a new interactive credit quiz series) and i allocated a question to z-spread (because it is a Malz concept and it is an important spread concept) . So my upcoming 710.3 does ask for a z-spread approximation by using duration (that is, duration is a single factor approximation such that it can be used to approximate the z-spread, I realized and my simulations did confirmed; but it makes intuitive sense because duration assumes a parallel shift in the yield curve). I mention that because, to your question, I could not find or generate a "fair" z-spread question that could be somewhat easily answered without excel (given that it requires an iteration to solve). However, there is one obvious exception and, therefore, one obvious exam-worthy candidate: if the assumption is given that the risk-free zero (aka, spot) rate curve is flat, then it's easy to imagine a fair question. For example,

• [and this is the one I almost wrote Tuesday, and will eventually include in the new credit set] If the zero (aka, spot) rate curve is flat at 2.0% per annum with semi-annual compounding, what is the z-spread on a five-year $100.00 fair value bond that pays a semi-annual coupon of 3.0% when its price is $97.00. Answer: this bond's yield is given by N = 10, PV = -97, PMT = 1.5, FV = 100 and CPT I/Y = 1.831 * 2= 3.66%; and only in this special case where the risk-free curve is flat can we simply deduct 2.0% to retrieve the z-spread of 1.66%. This is the only realistic example that i can think of. So, i think the answer to your question is: no, you would not be expected to find a z-spread except where the risk-free curve is flat (because if the Rf curve is flat, then the z-spread equals "nominal yield spread" or what Malz simply calls the "yield spread"). I hope that helps!

 

[trigg989]

Very helpful @David Harper CFA FRM , thank you!