The Term Structure & Interest Rate Dynamics Flashcards
(45 cards)
1
Q
What is formula for discount factor at maturity?
A
DFn = (1 / (1+ Zn)^n)
DFn = discount factor at maturity
Zn = yield to maturity of a single payment is called spot rate
- present value of $1 received at maturity (eg. This means that $1 received in 1 year is worth $0.95 today.)
2
Q
What does the spot rate represent?
A
- represents current annualized return on a zero-coupon bond that has no default risk and no embedded options
3
Q
What are forward rates?
A
- Forward rates are interest rates that can be determined today but apply to future time periods
- implied future interest rates between periods.
4
Q
What is term structure?
A
- interest rates of similar quality bonds at different maturities
5
Q
What does a forward rate for a deposit that will be made at time A and mature at time B be denoted as?
A
Fa,b-a
example, an investor who will make a 3-year deposit in two years will earn a rate of F2,3 and collect the proceeds five years from today.
6
Q
What is the forward pricing model?
A
- forward pricing model is based on the no-arbitrage principle, an investor who makes a 5-year risk-free deposit today should earn the same return as an investor who makes a one-year risk-free deposit today and then rolls the proceeds over at maturity into a 4-year risk-free deposit.
- forward pricing model is used to determine the price of a forward contract based on the spot price of the underlying asset and the cost of carrying it to a future date
7
Q
What are the 2 formulas that explain the relationship between discount factors and the forward rate formula?
A
DFb = DFa * Fa, b-a which is equivalent to Fa, b-a = (DFb / DFa)
DF @ time 2 = DF @ time 1 * Fa, b-a
Fa, b-a = (DF @ time 2 / DF @ time 1)
Fa, b-a = forward rate
8
Q
What is formula for forward price model using forward rate?
A
Fa, b-a = (1 / (1+fa, b-a)^ b-a)
Fa, b-a = forward price model
fa, b-a = forward rate model
9
Q
What is formula to find forward rate derived from the spot rate?
A
(1+ zb)^b = ((1+za)^a) * ((1+ fa, b-a)^b-a)
fa, b-a = forward rate
zb = spot rate at time B
za = spot rate at time A
10
Q
What is formula for the T - year spot rate?
A
((1+ zt)^t) = (1+z1) * (1+f1,1) * (1+f2,1) * (1+f3,1)
11
Q
When does the spot curve lie above the forward curve or below the forward curve?
A
- spot curve will lie above forward curve when spot curve is downward sloping
- spot curve will lie below forward curve when spot curve is upward sloping
12
Q
What is the par curve?
A
- par curve represents the yield to maturity on similar coupon-paying government bonds priced at par.
13
Q
What is yield to maturity and when will I be investor earn yield to maturity?
A
- YTM is rate of return that investors expect to earn from holding it if 3 conditions are met
- bond is held to maturity.
- all coupon and principal payments are made on time and in full.
- all cash flows are reinvested at the original YTM.
14
Q
What is riding the yield curve strategy (aka rolling down the yield curve)? What kind of yield curve does the riding the yield curve benefit from?
A
- a trading strategy that involves buying a long-term bond and selling it before it matures to profit from the declining yield and an increase in price of bond (yields and bonds have opposite relationship) that occurs over the life of a bond.
- benefits from an upward sloping yield curve.
15
Q
What is carry trade trading strategy vs maturity spread carry?
A
- carry trade: trading strategy that involves borrowing at a low-interest rate current and re-investing in a currency or financial product with a higher rate of return
- maturity spread: borrow short term investments to invest proceeds into long term investments. (Eg. Borrow short term rate at 3% and invest in long term rate at 4.5% and you earn 1.50%.
16
Q
What are swaps?
A
- Swaps: derivative contracts that typically exchange fixed-rate interest payments for floating-rate interest payments
17
Q
What is the swap rate and what is it denoted as?
A
- fixed-rate leg of an interest rate swap is called the swap rate and is denoted as sT
18
Q
At inception what is the swap rate set to?
A
- swap rate is set so the swap value is zero at inception
19
Q
What is the swap spread?
A
- swap spread is the swap rate less the on-the-run or most recently issued government security with the same maturity (aka government bond yield). It indicates credit spreads and liquidity spreads in a market.
20
Q
What is the I-spread?
A
- I-spread (interpolated spread): which measures the difference between a bond’s yield and the swap rate for the same maturity.
21
Q
What is the z spread?
A
- a constant basis point spread that is added to the implied spot yield curve in order to ensure that discounted future cash flows are equal to the current market price. more accurate measure of credit and liquidity
22
Q
What is the TED spread?
A
- TED spread (i.e., Treasury-Eurodollar spread): Libor minus the yield on a T-bill of matching maturity. indicator of perceived credit risk in the economy, an increase means increased risk of default on interbank loans
23
Q
What is the Libor-OIS spread?
A
- Libor-OIS spread is the difference between Libor and the overnight indexed swap (OIS) rate. indicates the risk and liquidity of money market securities.
24
Q
What is the unbiased expectations theory (aka pure expectations theory)?
A
-unbiased expectations theory states that if there are two investors, one invests in two consecutive one-year bonds and the other invests in a single two-year bond, in the end, the return will be the same for both investors.
25
What is the local expectations theory?
- Local Expectations Theory: theory that suggests that the returns of bonds with different maturities should be the same over the short-term investment horizon
- similar to pure expectations theory: you should earn same rate if you buy 5 1 year bonds as someone who buys 1 5 year bond, however, local expectations allows for risk premium for longer periods.
26
What is the liquidity preference theory?
- liquidity preference theory: assumes that investors expect additional compensation for the interest rate risk associated with lending over longer periods.
27
What is the segmented markets theory?
- segmented markets theory: assumes that the shape of the yield curve is influenced by the preferences of lenders and borrowers. The yield curve is a function of supply and demand at different maturities. If demand is particularly high for bonds with a certain range of maturities, yields in that segment of the curve will be lower.
28
What is the preferred habitat theory?
- preferred habitat theory: investors generally prefer short-term bonds but may opt for long-term ones if they offer higher yields and suitable risk premiums.
- preferred habitat theory allows for the possibility that investors can be induced to leave their preferred segment of the market if the compensation is sufficient.
29
What is shaping risk?
- Shaping risk: sensitivity of a bond’s price to the changing shape of the yield curve
30
What are 3 factors affecting the shape of a yield curve? LSC
- Levelness
- Steepness
- Curvature
31
What is yield curve risk?
- bond portfolio exposure to shifts in the yield curve
32
Describe the 3 factors affecting the shape of a yield curve?
- Level: parallel up or down shift in yield curve (eg. level coefficient of -0.5 indicates that the bond's price will fall by 0.5% in response to an increase of one standard deviation in the level of the yield curve.)
- Steepness: non parallel shift in yield curve (e.g., short-term rates increase by more than long-term rates)
- Curvature: twists in the yield curve (e.g., short-term rates increase while long-term rates fall)
33
Why is the volatility curve for bonds with embedded options usually downward slopping?
- downward sloping because short-term rates tend to be more volatile while longer-term rates are relatively stable.
34
What is the difference between effective duration and key rate duration?
- effective duration: measure bond price sensitivity to small parallel shift in benchmark yield curve
- key rate duration: measure sensitivity of a security or value of portfolio to a 1% change in yield for a given maturity
35
What is formula for change in value of portfolio that accounts for change in 3 factors of a yield curve?
change in value of portfolio = (-Dl * r) - (-Ds * r) - (-Dc * r)
Dl = levelness
Ds = steepness
Dc = curvature
r = yield change
36
What rates are primarily influenced by monetary policy and what rates are primarily influenced by inflation?
- short term/ intermediate term rates are primarily influenced by monetary policy
- long term rates are primarily influenced by inflation
37
How does fiscal policy, maturity structure, and investor demand impact bond yields?
- fiscal policy: yields rise as governments issue more debt to finance their budget deficits. restrictive fiscal policy will reduce the supply of new government debt, causing investors to lower their required returns
- maturity structure: relative increase in the supply of longer-dated government bonds increases yields and excess returns in this segment of the market
- investor demand: greater demand will put downward pressure on yields, driving up bond prices.
38
What is the bond risk premium?
- bond risk premium: yield required to hold a long-term default-free bond in excess of the short-term risk-free rate.
39
What is a bullish steepening?
- bullish steepening: (eg. short-term rates falling faster than long-term rates) is typically observed when a central bank loosens monetary policy in an effort to stimulate an economy that is operating below its potential
- fall in short term rates and rise in long term rates.
40
What is the difference between bearish flattening and bullish flattening?
- bearish flattening: short-term rates increasing faster than long-term rates
- bullish flattening: also called flight to quality indicates that long term interest rates are falling, while short term interest rates remain stable. implying lower inflation in the future, which is good for the economy
41
What is the difference between bullet portfolio and barbell portfolio?
- bullet portfolio: concentrated on single maturity
- barbell portfolio: combination of short and long dated bonds
42
If yield curve is expected to steepen what should a manager do with duration for their portfolio, and if the yield curve is expected to no steepen and interest rates are expected to fall what should a manager do with duration for their portfolio?
- yield curve steepening: reduce portfolio duration relative to benchmark they’re tracking.
- falling interest rates: increase portfolio duration relative to benchmark they’re tracking.
- reducing duration means shifting towards shorter-term bonds, which are less sensitive to interest rate changes.
43
What is the formula to convert spot rates to spot prices?
spot price = (1/1+ spot rate ^n)
44
What is SOFR?
- secured overnight finance rate (SOFR) cash borrowing rate collateralized by US treasuries.
45
What type of curve is a swap rate curve and how is the swap rate curve derived?
- swap rate curve is a type of par curve
- derived from using short-term lending rates
