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# P2.T6.306. Credit spreads and spread '01 (DVCS; Malz section 7.1)

#### Fran

AIMs: Define the different ways of representing spreads. Compare and differentiate between the different spread conventions and compute one spread given others when possible. Define and compute the Spread ‘01.

Questions:

306.1. The following curves are applicable to a risky 2-year bond that pays 6.0% semi-annual coupon:

The bond's market price of $103.73 can be computed by discounting its cash flows continuously at 4.0% per annum, which is represented by the flat yellow line. Specifically:$3.00*exp(-4%*0.5) + $3.00*exp(-4%*1.0) +$3.00*exp(-4%*1.5) + $103.00*exp(-4%*2.0) =$103.73. The bond's same market price of $104.73 can also be derived by discounting the same cash flows according to the continuous discount rates given by the the steep blue line. The lower steep line, which shows a rate of 0.40% at six months, is actually two nearby curves: a swap rate curve and nearby spot rate curve. Both start at 0.40% but, as the spot rate curve is slightly steeper, by year 2.0, the spot rate is 1.61% while the swap rate is 1.60%. For this purpose, we assume both the spot and are risk-free curves; e.g., US Treasury. Each of the following is true about this bond EXCEPT which is false? a. The bond's yield-to-maturity is 4.0% b. The yield spread, represented by the solid red vertical arrow, is the difference between 4.0% (yellow line) and 0.40% (spot rate at six months) c. If the price of the bond decreased due solely to perceived credit risk of bond (without any change in market risk), the upper curves (yellow and blue) would shift up d. The z-spread, represented by the dashed red vertical arrow, is the difference between the (upper steep) blue line and the (lower steep) spot rate; e.g., 2.42% = 4.03% - 1.61% 306.2. The risk-free spot rate curve is (unrealistically) steep and given by the following: 1.0% at 0.5 years, 2.0% at 1.0 year, and 3.0% at 1.5 years, with continuously compounded rates (this question being sourced in Malz). (Source: Allan Malz, Financial Risk Management: Models, History, and Institutions (Hoboken, NJ: John Wiley & Sons, 2011)) A 1.5 year bond that pays a 10.0% semi-annual coupon has a price of$105.62 such that its z-spread happens be a round 3.00%. Specifically, $105.62 =$5.00*exp[-(1.0%+3.0%)*0.5] + $5.00*exp[-(2.0%+3.0%)*1.0] +$105.00*exp[-(3.0%+3.0%)*1.5].

Which is nearest to the bond's Spread '01 (aka, DVCS) per $1,000,000 of par value? a.$0.14
b. $36.09 c.$151.16

#### ashanks

##### New Member
Great questions, especially .1 and .2. Thanks for posting.

However, there are typos in the descriptions of both questions:
In .1, $103.00*exp(-4%*0.5) should read as$103.00*exp(-4%*2.0)
In .2, $5.00*exp[-(2.0%+3.0%)*1.5] should instead be$5.00*exp[-(2.0%+3.0%)*1.0]

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi ashanks, yes, absolutely, THANK YOU for spotting these typos. Corrected above!
Suzanne Evans: we need to revise the PDF, thanks.

#### Pflik

##### Active Member
mistake is still in the pdf. Also i'm noticing that the calculation doesn't seem to be correct either. (i.e. i'm getting 150.31) just a small difference.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Pflik thanks, we missed the revision (this thread is not the source).

Re: Also i'm noticing that the calculation doesn't seem to be correct either. (i.e. i'm getting 150.31) just a small difference.

##### New Member
I am struggling with a very basic concept related to 306.1:

The bond's YTM is 4%. Ok sounds good, but if a check it with my calculator:

PV = -100 FV= 103,75 PMT = 3 N =4 this is: YTM = 3,88 which is different from 4

where is my big mistake? thanks

#### QuantMan2318

##### Well-Known Member
Subscriber
I am struggling with a very basic concept related to 306.1:

The bond's YTM is 4%. Ok sounds good, but if a check it with my calculator:

PV = -100 FV= 103,75 PMT = 3 N =4 this is: YTM = 3,88 which is different from 4

where is my big mistake? thanks

The Market value of the Bond is higher than the Face value which suggests that the Coupon (6%) should be greater than the YTM. Here the FV should be 100 as you are redeeming it at par. And the PV should be -103.75. So, PV = -103.75; FV = 100; PMT = 3; N = 4
which gives the YTM as 4% if you use semi annual compounding on your calculator

P.S And if you use semi annual compounding in your calculator, you should directly get the YTM which is 7.76% in your example which is a way of verifying your calculations

Hope this helps

Thanks