Ch 05-15 Build a Model Solution								2/26/2001
Chapter 5. Solution for Ch 05-15 Build a Model
a. Suppose you are considering two possible investment opportunities, a 12-year Treasury bond and a 7-year,
A-rated corporate bond. The current real risk-free rate is 4%. Inflation is expected to be 2% for the next two
years, 3% for the following four years, and 4% thereafter. The maturity risk premium is estimated by this
formula:MRP = 0.1% ( t-1) %. The liquidity premium for the corporate bond is estimated to be 0.7%. Finally,
you may determine the default risk premium, given the company’s bond rating, from the default risk premium
table in the text. What yield would you predict for each of these two investments?
Treasury Bond
Risk-free rate =						4.00%
Maturity:		12
Expected inflation:		for the next	2	years =		2%
Expected inflation:		for the next	4	years =		3%
Expected inflation:		for the next	6	years =		4%
			12
Inflation premium:		=((G17*D17)+(G18*D18)+(G19*D19))/D20 =				3.33%
Maturity risk premium =				=0.1*(C16-1)% =		1.1%
12-year Treasury yield=						Risk free rate plus the premiums. 8.43%
7-year corporate bond
Rating :	A
Risk-free rate =						4%
Maturity:		7
Expected inflation:		for the next	2	years =		2%
Expected inflation:		for the next	4	years =		3%
Expected inflation:		for the next	1	years =		4%	Default Risk from
			7				text table:
Inflation premium:		=((G33*D33)+(G34*D34)+(G35*D35))/D36 =				2.86%	Rating	DRP
							AAA	1.0%
Maturity risk premium:		=0.1*(C32-1)% =				0.60%	AA	1.2%
Liquidity premium:						0.7%	A	1.5%
Default risk premium:		=IF(B28=H38,I38,IF(B28=H39,I39,IF(ETC.) =				1.5%	BBB	1.9%
		(see screen to right for an alternative way to find the					BB+	3.7%		The default premium could also be determined using the VLOOKUP function. To use
		default risk premium.)
7 year Corporate yield=						Risk free rate plus the coporate premiums 9.66%				the data in the table as shown below:
											Rating	DRP
		Yield Spread = Corporate - Treasury =				1.224%					BB+	3.7%
		R:econciliation:		Default premium		1.500%					BBB	1.9%
				Liquidity premium		0.700%					A	1.5%
				Inflation premium		-0.476%					AA	1.2%
				Maturity premium		-0.500%					AAA	1.0%
						1.224%
										VLOOKUP VALUE:		1.50%
b. Given the following Treasury bond yield information from the May 27, 2000, Federal Reserve Statistical Release,
construct a graph of the yield curve as of that date.										With the data in ascending order, click the function wizard, fx, select "Lookup & Reference,"
	Maturity									then VLOOKUP, and then fill in the menu items as shown in the picture below:
	Periods	Years	Yield
	3 month	0.25	5.89%							Add VLOOKUP picture
	6 month	0.50	6.40%
	1 year	1.00	6.32%
	2 year	2.00	6.86%
	3 year	3.00	6.80%
	5 year	5.00	6.71%
	10 year	10.00	6.51%
	20 year	20.00	6.64%
	30 year	30.00	6.22%
Now we can use Excel's chart wizard to construct a yield curve.
c. Based on the information about the corporate bond that was given in Part a, calculate yields and then construct a
new graph that shows both the Treasury and the corporate bonds.
The real risk-free rate would be the same for the corporate and treasury bonds. Similarly, without information to the
contrary, we would assume that the maturity and inflation premiums would be the same for bonds with the same
maturities. However, the corporate bond would have a liquidity premium and a default premium. If we assume that
these premiums are constant across maturities, then we can use the LP and DRP premiums as determined above and
add them to the T-bond yields to find the corporate yields. This procedure was used in the table below.
	Years	Treasury	A-Corporate	Spread		LP	DRP
	0.25	5.89%	8.09%	2.20%		0.7%	1.5%
	0.50	6.40%	8.60%	2.20%		0.7%	1.5%
	1.00	6.32%	8.52%	2.20%		0.7%	1.5%
	2.00	6.86%	9.06%	2.20%		0.7%	1.5%
	3.00	6.80%	9.00%	2.20%		0.7%	1.5%
	5.00	6.71%	8.91%	2.20%		0.7%	1.5%
	10.00	6.51%	8.71%	2.20%		0.7%	1.5%
	20.00	6.64%	8.84%	2.20%		0.7%	1.5%
	30.00	6.22%	8.42%	2.20%		0.7%	1.5%
Now we can graph the data in the first 3 columns of the above table to get the Treasury and corporate (A-rated) yield
curves:
Note that if we constructed yield curves for corporate bonds with other ratings, the higher the rating, the lower the
curves would be. Note too that the DRP for different ratings can change over time as investors' (1) risk aversion and
(2) perceptions of risk change, and this can lead to different yield spreads and curve positions. Expectations for
inflation can also change, and this will lead to upward or downward shifts in all the yield curves.
d. Using the Treasury yield information above, calculate the following forward rates:
	(1) The 1-year rate, one year from now.				1r1
	(2) The 5-year rate, five years from now.				5r5
	(3) The 10-year rate, ten years from now.				10r10
	(4) The 10-year rate, twenty years from now.				20r10
	Maturity	Maturity	Yield
		in years
	1 year	1	5.37%
	2 year	2	5.47%
	3 year	3	5.65%
	5 year	5	5.64%
	10 year	10	5.75%
	20 year	20	6.13%
	30 year	30	5.99%
	(1) The 1-year rate, one year from now.
	r2	= (	r1	+	1r1	) /	2
	5.47%	= (	5.37%	+	1r1	) /	2
	5.57%	=	1r1
	(2) The 5-year rate, five years from now.
	r10	= (	r5	+	5r5	) /	2
	5.75%	= (	5.64%	+	5r5	) /	2
	5.86%	=	5r5
	(3) The 10-year rate, ten years from now.
	r20	= (	r10	+	10r10	) /	2
	6.13%	= (	5.75%	+	10r10	) /	2
	6.51%	=	5r5
	(4) The 10-year rate, twenty years from now.
	r30	= (	2 x r20	+	20r10	) /	3
	5.99%	= (	12.26%	+	20r10	) /	3
	5.71%	=	20r10