Market Value ($1000s) Market Value ($1000s) Market Value ($1000s) Bond Sector PO
ID: 2774122 • Letter: M
Question
Market Value
($1000s)
Market Value
($1000s)
Market Value
($1000s)
Bond Sector
PORTFOLIO A
PORTFOLIO B
PORTFOLIO C
Modified Duration
Cash
$0
$0
$0
0.00
2-YR
$400
$400
$0
1.90
5-YR
$300
$600
$600
4.65
10-YR
$300
$0
$400
8.50
Portfolio
$1000
$100
$1000
Consider the three portfolios, A, B and C above as alternative ways to invest $1,000,000.
Suppose that yields on bonds of all maturities rose by 100 basis points. Which of the three portfolios would give the manager the best investment performance should this happen? (A, B or C?)
Market Value
($1000s)
Market Value
($1000s)
Market Value
($1000s)
Bond Sector
PORTFOLIO A
PORTFOLIO B
PORTFOLIO C
Modified Duration
Cash
$0
$0
$0
0.00
2-YR
$400
$400
$0
1.90
5-YR
$300
$600
$600
4.65
10-YR
$300
$0
$400
8.50
Portfolio
$1000
$100
$1000
Explanation / Answer
Portfolio durationA = 0.4 * 1.90 + 0.3 * 4.65 + 0.3 * 8.50
= 4.705
Portfolio durationB = 0.4 * 1.90 + 0.6 * 4.65 + 0.0 * 8.50
= 3.550
Portfolio durationC = 0.0 * 1.90 + 0.6 * 4.65 + 0.4 * 8.50
= 6.190
Lower the duration, lower is the sensitivity of the bonds to yield change. If the yield increases by 100 basis points, then the bond price declines and so lower the price sensitivity is better for investment performance. As such portfolio B is the better investment as it has the lowest protfolio duration.
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