Fixed Income Flashcards
What is definition of bootstrapping on spot rate?
It allows investors to determine zero coupon rate using the par yield curve. The par curve shows the yield to maturity on government bonds with coupon payments, priced at par over a range of maturities.
What is par yield?
Sequence of yields to maturity such that each bond is priced at par value.
on the run: coupon equal yield, where price = par (eg 100 today).
Forward > Spot > par yield
Relationship of forward, spot and YTM under upward slop yield curves?
Forward > Spot > YTM
Can YTM be used to value a bond?
Only price using YTM when the coupon of the bond match par yield.
What is the definition of the riding the yield curve?
If the curve does not change and is upward sloping, then buying a bond with a longer maturity then the holding period will earn the investor a higher return than the initial one year spot rate.
If you believe that upward sloping yield curve will not change its level nor shape over an investment horizon then buying longer dated bonds will provide a higher return.
How do you price a swap?
Eg for a for a 2 year bonds
Coupon * Discount factor y1 + Coupon * Discount factor y2 + PAR * discount factor y2 = PAR at yr 0
Coupon = (PAR - PV of PAR) / sum of discount factors
Coupon is the fixed % swap
Why use a swap curve rather than govt bonds as benchmark?
Liquidity if the swap market is more liquid than the govemment bond market
If a client uses swap to hedge interest rate risk, then for hedging purpose to value the asset using swap curve.
The swap curve is a bank product, and the bank is risker than government, therefore the investors would expect the swap curve higher than the govt curve.
What is a TED spread?
TED is the treasury Eurodollar rate.
The difference between the interest rates on the 3 months LIBOR and treasury bills.
It is an indicator of credit risk of interbank loans. Treasury bill is considered risk free and LIBOR reflects the credit risk of lending to commercial banks.
What is the LIBOR-OIS spread?
Is the difference between LIBOR and OIS rates. It is a measure of risk and liquidity in the money markets . A higher spread indicated a higher risk.
What is a swap spread?
Is the difference between the fixed rate on an interest rate swap and yield on the government bonds at the same maturity.
What is a Z spread?
It uses the zero coupon yield curve.
It is a constant spread value if added to each government spot rate, would make the present value of each cashflow equal to the bond price.
It is the constant basis point that would need to be added to the spot yield curve such that the discounted cashflow is equal to it’s current market price.
What is a swap rate?
It is the interest rate for the fixed rate of an interest rate swap with value zero at inception.
What is the relationship between an upper and lower node in Binomial Interest Rate Tree?
upper (1)= down(1) * e^(2*volatility)
The higher rate for time 1 will be the lower rate multiplied by e(2 x σ); at time 2 this relationship becomes lower rate x e(4 x σ) i.e. the higher rate depends upon the lower rate for any given time period. The higher the lower rate, the higher the upper rate and the wider the gap between the two. Also note the binomial tree assumes risk-neutral probabilities are fixed at 50%.
Difference between Vasicek model and the CIR model.
The drift term allows for the mean-reverting element of rates. Both of these models have the same drift term, but they differ in the stochastic term. The CIR model assumes the stochastic term is a function of interest rates (not time) whereas the Vasicek model uses a simpler stochastic term.
The Vasicek and CIR models are very similar in many respects. Both have the same drift element and both have short-term interest rates following a mean reversion. However, the Vasicek model is slightly simplified with respect to interest rate volatility, which is assumed to remain constant. Interest rate volatility follows a normal distribution in the CIR model.
The interest rates are calculated in the Vasicek model assuming that volatility remains constant. This assumption is not made for the CIR model.
Define pure expectations theory, Liquidity theory, and Segmented market theory.
Pure (unbiased) expectations theory:
The forward rate is an unbiased predictor of the future spot rate.
Risk neutral, assume the risk premiums do not exist.
Bonds of any maturity can substitutes each other.
The yield curve is dependent on expectations and could be of any shape.
Local expectation theory assumes that risk premiums do not exist for very short holding period but can exist long term investments.
Liquidity preference theory:
Liquidity premium insrease with maturity.
Can only explain upward sloping curve.
Segmented market theory:
Investors are only willing to invest in bonds with preferred maturity.
Yield reflects demand and supply.
Preferred habitat theory says investors have preferred maturity but are willing to move to other maturities if the return is higher.
