Chapter 9 Flashcards
Duration definition
Weighted average time to maturity
Where weights are the relative present values of the CFs
It is a measure of the % change in the price of a bond for a given % change in YTM (interest elasticity)
Duration of a zero-coupon bond
= maturity since there are no intervening CFs btw issue and maturity
For all other bonds: D < M
Consol bond definition + M and D
Bond that pays a fixed coupon each year indefinitely
M = inf
D = 1 + 1/R
Relationship btw D and M
D increases with M but at a decreasing rate
Relationship btw D and yield
D decreases as yield increases
Relationship btw D and coupon interest
D decreases as coupon interest increases
Duration equation
[DeltaP/P] / [DeltaR/(1+R)] = -D
-> DeltaP = -D * [DeltaR/(1+R)] * P = -MD * DeltaR * P
Where MD = modified duration
OR
D = Sum { PV(CF_t)/TPV(CF) * t }
Dollar duration: definition + eq
Dollar value change in the price of a security to a 1% change in the return on the security
Dollar duration = MD * P
Duration eq of semi-annual coupon bond
[DeltaP/P] / [DeltaR/(1+R/2)] = -D
Change in net worth (Delta MVE) given changes in interest rates + 3 factors
Delta MVE = -DGAP * A * DeltaR/(1+R)
1) leveraged adjusted duration gap
2) size of the FI
3) interest rate shock
Where k=L/A
Immunization if target is Delta(E/A)=0 and if DeltaE=0
Delta(E/A)=0: D_A = D_L
DeltaE=0: D_A = k*D_L
Convexity definition
Degree of curvature of the price-yield curve around some interest rate level
Marking to market
Process by which changes in the economic value of assets and liabilities are accounted
Leverage adjusted duration gap (DGAP) + meaning if positive
DGAP = D_A - k*D_L
where k = L/A
Positive: increase in interest rate lead to a decrease in MV(Equity)
DeltaR/(1+R) meaning
Shift in the yield curve
