Question

The following table contains the Treasury Spot Rates.

Treasury Spot Rates
Mat	Rate
0.5	2.13%
1	2.47%
1.5	2.95%
2	3.21%
2.5	3.49%
3	3.93%
3.5	4.18%
4	4.55%
4.5	4.89%
5	5.12%

a) What is the Nominal Spread:

b) What is the Z-Spread of a 7% semiannual 2.5-Year corporate bond if it is selling for $1060.86. The Par = 1000. (Hint: Use Solver)

Answer 1

Solution Nominal Spvead A nominal spreced measures the difference between the yield oy a bond and yield to matowity of a Similar matovity treasury bond. Fou encample: • Non treusovy bond hawing a yeild - 7.54] 5 year • Tveu sony bond having a yield oy = 5% d Bond. Nominal spuead: Yield oy non trecruny Yield oy frecisory bond Bonds 7.5 - 5 = 2.5-1.. The diference between 2 bonds us 250 basis points. A non treasury bond will gnouide a higher yil yield when compared to the treasury bond because it inauolues credit risk, li quickily niske, and addition al siste involved. · Nomincel spread can never be below zero, ie. it cannot be -ve. Nominal spread is not a appropricele measure oy corusideration as it ignoves spot rates you different maturities and effect of embedded options * embedded option - a special condition is attached to a security. It movides the bond holder or the issues to take some action against the other party ATO

B)

Face Value of the Bond			1000
Market Value			1060.86
Cupon Rate			7%
Effective Cupon rate			3.50%	Since the intrest rest is semi annual the given cupon rate will be half
Time			2.5
Effective Time			5	The time will get twice to calculate semiannually
Time	1	2	3	4	5
Cash Flows	1000*3.5%	1000*3.5%	1000*3.5%	1000*3.5%	(1000*3.5%)+1000
=	35	35	35	35	1035
Treasury Spotrate	2.13%	2.47%	2.95%	3.21%	3.49%
Discounted Cashflow	35/(1+2.13%)^1	35/(1+2.47%)^2	35/(1+2.95%)^3	35/(1+3.21%)^4	35/(1+3.49%)^5
=	34.27	33.33	32.08	30.84	871.86
Total Cash flow	1002.39
Since the market price of the bond is 1060.86 and the cssh flow comes out to be 1002.39
Now the Z spread is the % that should be added/subtracted to the treasury spot rates to get the exact market price of1060.86
Let the Z spread Be	-1.2%
So if we reduce 1.2% from each treasury spot rate well get a value as follows
Time	1	2	3	4	5
Cash Flows	1000*3.5%	1000*3.5%	1000*3.5%	1000*3.5%	(1000*3.5%)+1000
=	35	35	35	35	1035
Treasury Spotrate	2.13%-1.2%	2.47%-1.2%	2.95%-1.2%	3.21%-1.2%	3.49%-1.2%
Discounted Cashflow	34.68	34.13	33.22	32.32	924.22
Total Cash flow	1058.57
Let the Z spread Be	-1.3%
So if we reduce 1.2% from each treasury spot rate well get a value as follows
Time	1	2	3	4	5
Cash Flows	1000*3.5%	1000*3.5%	1000*3.5%	1000*3.5%	(1000*3.5%)+1000
=	35	35	35	35	1035
Treasury Spotrate	2.13%-1.3%	2.47%-1.3%	2.95%-1.3%	3.21%-1.3%	3.49%-1.3%
Discounted Cashflow	34.71	34.20	33.32	32.45	928.75
Total Cash flow	1063.43
The market value is 1060.86 which means that the value of z spread falls between -ve 1.3% to 1.2%
On solving the value comes out to
	Val at 1.3	1063.43
	Val at 1.2	1058.57
	Diff	4.86
	Diff in rate	0.01
	So rate =	0.0486
	Z rate	1.2486	Appx
By using the rate of -1.2486 we'll get		1060.93
This means we are earning 1.2486% less that the treasury bonds