Post on 14-Apr-2017
Duration slidesWhy does duration give us a measure of elasticity?
Peter Fraser
1(c) P Fraser 2010
Forget weighted averages?
Duration originally conceived as alternative to maturity.
More importantly used as sensitivity of price changes to interest rates.
Basic relationship:
(c) P Fraser 2010 2
*dP
MD Pdr
2
2...
1 1 1 1n n
C C NC N
r r r rD
P
Why? (mathematical interlude)
Price of a bond is discounted sum of cash
flows
(c) P Fraser 2010 3
2 3
1...
1 1 1 1 1n n
C C C CP
r r r r r
Differentiate to discover sensitivity to
rates dP
dr
Why? (cont…)
Use product and chain rule for each
term.
(c) P Fraser 2010 4
2 3 1 1
2...
1 1 1 1n n
dP C C NC N
dr r r r r
multiply both sides by
2
21 ...
1 1 1 1n n
dP C C NC Nr
dr r r r r
1 r
Why? (cont…)
(c) P Fraser 2010 5
1
1 *
*1
dPr
dr DP
dPr D P
dr
dP DP
dr r=-MD!
Right-hand side divided by price =
- duration. Divide both sides by price