Term Structure and IR Dynamics Flashcards
Forward Rate
A forward rate is the implied future interest rate between two dates, derived from the spot curve.
Z(1,3) notation implies what?
The forward rate starting in 1 year and lasting for 3 further years.
Where A = 1 and B = 4
So,
DF(4) = DF1(1) x F(1,3)
What is the relationship between forward rates and spot rates?
Forward rates will be above spot rates if the curve is upwards sloping. If the curve is downward sloping, then forward rates will be below spot rates.
A further out maturity will be even further from the spot rate.
Suppose f7,1 is 3%. Under the principal of no arbitrage, what does this imply?
This is a 1 year bond, starting in 7 years from now.
The 3% is the reinvestment rate that would make an investor indifferent between holding an 8 year ZCB or a 7 year ZCB and reinvesting the proceeds for 1 year.
What is the formula to calculate different zero coupon bonds with differing maturities?
F(a,b)
(1+Za+b)^a+b = (1+Za)^a * (1+Fa,b)^b
So,
F(2,1)
(1+z3)^3 = (1+z2)^2 * (1+F2,1)^1
What is the relationship between implied forward rates and spot rates?
Implied forward rates are generally the best available and most accessible proxy for future spot rates.
What is the YTM of a default-risk free bond?
This can be viewed as the weighted average of the spot rates applying to its cash flows.
What is the definition of a Par curve?
A Par curve represents the relationship between the yield and the term to maturity of bonds that are priced at par. The par curve can be used to construct a zero-coupon yield curve.
Broadly speaking, what is the YTM of a bond?
The expected rate of return for a bond held to maturity. The IRR of the bond.
In what scenarios can the YTM be a poor predictor of estimated return?
If IR are volatile
If the yield curve is sloped upward or downwards
There is significant default risk
If the bond has embedded options.
Calculate the price of a 2 year bond assuming a 6% coupon and a FV of 1000. Z1 = 9% and Z2 = 10%
Price = 60 / (1+0.09)^1 + 1060/(1+1.1)^2
Price = 931.08
YTM can then be computed using the calculator.
A trader expects the future spot rate to be below what is being predicted by the prevailing forward rate. What should he do?
The forward contract value is expected to increase and therefore he should buy the contract.
What is the forward pricing model solved for forward price?
Fa,b-a = DFb / DFa
Spot rates can be derived from par rates using a method called?
Bootstrapping
Talk about inverted yield curves
This is a preceding factor for a recession. It is the expectation of a recession with lower real rates plus expectation of lower inflation.
Explain the strategy of rolling down the yield curve
If our spot curve is upward sloping, the expected return we get on the bond will be higher than the yield to maturity because the reinvestment rate will be done at the forward rates not the YTM and the forward rate lies above the spot rate.
A bond with a longer maturity is purchased but then sold prior to maturity at the end of the investment horizon. If the yield curve is upwards sloping and the yields don’t change the bond’s total return with exceed that of a bond whose maturity is equal to the horizon.
What 2 conditions must be met in order for the rolling down the yield curve strategy to work?
The yield curve must be upwards sloping
The expected future spot rate < current forward rates
If the expected future spot rate is greater than the current forward rate, then the bond will be overvalued.
What is the E(R) of a bond?
E(R) = coupons + reinvestment of coupon +/- capital gains/loss on sale
What is the swap rate?
It is the rate for the fixed leg of an IRS. It is analogous to the YTM on a government bond. The difference being that it is derived using short term lending rates.
For countries where private sector > public sector the swap curve is a more relevant measure of time value.
