VRM10 - Interest Rates

Question 1

Calculate and interpret the impact of different compounding frequencies on a bonds value

Answer 1

More frequent compounding means more valuable bond

Question 2

Define spot rate and compute discount factors given spot rates

Answer 2

d(t) = (1 + r(t)/m)) ^ (-mt), m is how many times per year compounded

Question 3

Interpret forward rates and compute forward rates given spot rates

Answer 3

Forward rates are the future spot rates implied by today’s spot rates

F = (1 + R2 / m) ^(T2 + m) / (1 + R1/m) ^(T1)

Question 4

Define par rate and describe the equation for the par rate of a bond

Answer 4

Par rate is the coupon rate where the value of a bond equals is face value

p/2 * d(0.5) + p/2 * d(1) + … + p/2 * d(T) + 100 * d(T) = 100

Question 5

Interpret the relationship between sport, forward, and par rates

Answer 5

When future rates are compounded, you get the spot rate

If term structure flat, all par rates and future rates equal the spot rate

If upward sloping, p < S < F
If downward sloping, F < p < S

Question 6

Assess the impact of maturity on the price of a bond and returns generated by bonds

Answer 6

Value of a bond will rise or fall depending on whether the forward rate for the last period is greater or less than the coupon

Question 7

Define the flattening or steepening of rate curves and describe a trade to reflect expectations that a curve will flatten or steepen

Answer 7

Flattening is where both long and short maturity rates move down but long move by down more than short OR both up but short more than long

Steepening is where both down but short more than long OR both up by long more than short

If thinks upward sloping will steepen, short longer maturity bonds and long shorter-maturity bonds

Question 8

Define overnight index swaps (OIS) and distinguish between OIS rates and LIBOR swap rates

Answer 8

OIS is geometric average of overnight rates