Second Half Semester

Question 1

Macaulay Duration Formula

Answer 1

sigma(time*PVcashflows)/PV of cashflows Value-weighted time average

Question 2

Modified Duration

Answer 2

Dmod = v_ -1/P (dP/di) = v (t1Rv^t1 + … + tnRv^tn)/(Rv^t1 + … + Rv^tn)

Question 3

Volatility

Answer 3

v_ = -1/P (dP/di) = d_ / (1 + i) = d_v

Question 4

Annuity equation for d bar

Answer 4

(Ia)n]i / an]i

Question 5

Duration for a zero coupon bond that pays in n years

Answer 5

d_ = n

Question 6

D bar as an equation for force of interest

Answer 6

(-1/P)(dP/d&) = d_

Question 7

Macaulay Convexity as force of interest

Answer 7

(1/P)(d^2P/d&^2) = d_

Question 8

Modified Convexity

Answer 8

(1/P)(d^2P/di^2) = v^2[Cmac + Dmac]

Question 9

Forward Rates

Answer 9

Spot rates: a(1) = 1.06, a(2) = (1.07^2), a(3) = (1.08^3)
f[1,2] = one forward rate deferred 1 year a(2)/a(1)

time 2 –> 3 a(3)/a(2) = 1 + f[2,3]
time 1 –> 3 a(3)/a(1) = (1 + f[1,3])^2

Question 10

Immunization (Full and Reddington)

Answer 10

PVassets = PVliabilities Dmacassets = Dmacliabilities

Question 11

Reddington Immunization

Answer 11

Asset convexity > liability convexity, asset convex has to be more curvy

Question 12

Variance/Convexity and Expected Value/Duration

Answer 12

Variance acts like convexity, and expected value acts like duration

Question 13

Higher convexity and Lower convexity

Answer 13

Bonds and lump sum

Question 14

Immunization overkill

Answer 14

Match cashflows assets + liabilities move together

Question 15

Basic Immunization

Answer 15

Match value at i, match duration

Question 16

Time weighted rate of return

Answer 16

History of a dollar, needs to beginning and end balances, needs multipliers