Question

Setup B: George, a bond portfolio manager, owns the following four bonds with a combined market value of $20 million. The bond portfolio’s yield to maturity is 7.00 percent. When the government releases new economic numbers tomorrow, George believes yield to maturities will increase 100 basis points as there will be a parallel shift in yield curve.

Bond	Market Value	Duration (Years)
A	$2 million	2.0
B	$5 million	3.0
C	$6 million	4.0
D	$7 million	5.0
Total	$20 million	?

What is the duration of a bond portfolio?

Assume George is correct and yield to maturities increase 100 basis points (there is a parallel shift in the yield curve). What will happen to the market value of the bond portfolio … bond portfolio’s market value is currently at $20 million so would it increase/decrease, by how much, and what would be the new market value for the bond portfolio?

Answer 1

a)	Duration of a Portfolio is the weighted average duration of all bonds in the Portfolio.
	Bond	Market Value	Weight Formula	Weight	Duration	Weight*Duration
	A	$2	= Market Value / Total = $2/$20	0.10	2.0	0.20
	B	$5	= Market Value / Total = $5/$20	0.25	3.0	0.75
	C	$6	= Market Value / Total = $6/$20	0.30	4.0	1.20
	D	$7	= Market Value / Total = $7/$20	0.35	5.0	1.75
		$20		1.00		3.90
	So Duration of a Portfolio = 3.90 Years
b)	If yield to maturity increases to 100 basis points.
	100 basis points means 1%, as to convert basis points in % divide it by 100.
	The Price of Bond Portfolio is inversely related to the Yield to maturity.
	So if yield to maurity increases then price of a bond portfolio will be decreases.
	We first need to calculate, Modified Durahtion
	Modified Duration
	= Macaulay's Duration / (1+YTM)
	= 3.90 years / (1+7%)
	= 3.90 years / (1.07)
	= 3.64486
	Percentage change in price
	= (-Modified Duration) * Change in Yield
	= (-3.64486)*(1%)
	= -3.64486%
	So,
	New Market Value of Bond Portfolio
	= Current Market Value + Current Market Value * Percentage Change in Price
	= $20 million + $20 million*(-3.64486%)
	= $20 million - $0.728972 million
	= $19.271028 million
	= $19.27 million