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CFA 22nd Nov 2024 > Fixed Income > Flashcards

Fixed Income Flashcards

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CFA flashcards
1
Q

What is the term structure of interest rates?

A

is how the interest rate evolves with time or what the interest rates are across different time maturities.

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2
Q

What is a Spot rate in interest rate term structure?

A

A spot rate is the interest rate on a security that makes a single payment at a future point in time.

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3
Q

What is the discount factor?

A

The price or the present value of a risk-free single unit payment after N periods is called the discount factor.

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4
Q

How to calculate discount factor?

A

It’s the PV, so DF = 1 / (1 + Zn)^N where Zn = spot rate (YTM).

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5
Q

What is the Discount Function?

A

It’s a combination of Discount factors (PV) for a range of maturities.

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6
Q

What is a spot curve?

A

It shows the annualized return on an ‘option-free’ and ‘default-risk-free’ zero-coupon bond with a single payment at maturity, for various maturities.

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7
Q

What is a Forward Rate?

A

An interest rate that is determined today for a loan that will be initiated in the future time period.
fa,b-a is how we write the forward rate. (small ‘f’ represents the rate)

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7
Q

How is a forward contract price represented?

A

Fa,b-a represents the forward contract price(PV) for a zero-coupon bond with unit principal which starts in the future (at time a and ends at time b).

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7
Q

What is the forward pricing model?

A

DFb = Fa,b-a * DFa to prevent any arbitrage opportunity.

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8
Q

What is the forward rate model?

A

Instead of calculating Forward prices, we calculate the forward rates.
Simple maths (expand the formula for Forward price!).

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9
Q

What are the implications of the Forward Rate model?

A

When the spot curve is upward sloping, the forward curve will lie above the spot curve & when the spot curve is downward sloping, the forward curve will lie below the spot curve.

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10
Q

What is a par curve?

A

Basically a par curve represents the YTM (like spot rates) of a government bond which pays coupons over a range of maturities, priced at par. (like discount function, it’d have a par function).

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11
Q

What is Bootstrapping?

A

A process which can be used to construct a spot curve from a par curve.

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12
Q

What is YTM?

A

YTM is the single discount rate when applied to the bond’s promised cash flows, equates those cash flows to the bond’s market price.

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13
Q

How is YTM related to spot rates?

A

YTM is the weighted average of spot rates used in the valuation of the bond.

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14
Q

How is YTM calculated?

A

Using spot rates and finding the discount factor, then with the DF we can come up with YTM.

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15
Q

Is YTM a good estimate of expected returns, yes or no? Why?

A

It’s not, it can be a poor estimate of expected return when -
Interest rates are volatile, so coupons can be reinvested in different rates.
Risk of default and also the bond can have embedded options(put, call or convert) in it.

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16
Q

What is the strategy Riding the yield curve or Rolling down the Yield curve?

A

You expect the spot rates to remain static! So, they don’t change when you bought a bond, then the price of the bond will be higher if you buy a bond with longer maturity!
The returns will be higher if the gap between the spot curve and forward curve is higher and also more returns the longer the maturity.

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17
Q

What is a swap rate?

A

is the interest rate for the fixed-rate leg of an interest rate swap. The floating rate can be a market reference rate like LIBOR.

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18
Q

What is swap rate curve?

A

Swap curve or swap rate curve is the yield curve of swap rates.

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19
Q

Why is the swap market highly liquid?

A

A) a swap doesn’t have multiple borrowers or lenders, only counterparties who exchange cash flows.
B) swaps provide one of the most efficient ways to hedge interest rate risk.

20
Q

When to use government spot rates for bond valuation and when to use swap rates? What factors affect the choice of which to use?

A

a major factor which contributes to which one to use is relative liquidity of both markets.
Organisations like wholesale banks frequently use swap curves for valuation, as they have many items on their balance sheet which they hedge with swaps.
Retail banks on the other hand have little exposure to the swap market and use government spot curve as a benchmark.
So it depends upon the organisation to decide which is the best curve to use for bond valuation.

21
Q

What is a swap price?

A

The swap price is the fixed rate of interest in the swap.

22
Q

How do we calculate a swap price?

A

We solve for a constant fixed rate that sets the PV of the fixed leg payments equal to the PV of the floating-leg payments over the life of the swap.

23
Q

What is the PV of a floater?*

A

If there is no change in credit risk, the PV of a floater at a reset point will be the par value (1 or 100).

24
Q

Are spot rates and swap rates mathematically linked?

A

YES!
the swap pricing formula shows the link.
The formula is [PV of all fixed leg payments over the period of the swap(total) + par value discounted back with spot rate] = 1 (Par value of a floater at a reset date)

25
Q

What is a swap spread?

A

The spread paid by the fixed-rate payer of an interest rate swap over the rate of the “on-the-run”(most recently issued) government security with the same maturity as the swap.

26
Q

Reasons for the swap market to be more popular than government spot market?

A

A) Swap market is unregulated, so swap rates are more comparable across different countries relative to government securities. (Cross border comparison)
B) Swap market has more maturities with which to construct a yield curve than do government bond markets.
C) Swap spread reflects the default risk of private entities at a rating of about A1/A+ (roughly the equivalent of commercial banks)

27
Q

What is the Z-spread?

A

A more accurate measure of credit and liquidity risk is called the Zero spread(Z-spread).
It’s the constant basis point spread that would need to be added to a government (or interest rate swap) spot curve so that the discounted cash flows of a bond are equal to its current market price.

28
Q

What is the TED Spread?

A

It’s an indicator of perceived credit risk in the general economy.
Difference between LIBOR and the yield on a T-Bill of matching maturity.
An increase in the TED spread indicates a greater perceived credit and liquidity risk.

29
Q

What is LIBOR-OIS spread?

A

It’s difference of LIBOR and OIS (overnight indexed swap) rate. OIS is a swap in which the floating rate is the geometric average of an overnight index rate (typically the rate for overnight unsecured lending between banks - the federal rate for US dollars).
LIBOR-OIS spread is considered an indicator of the risk and liquidity of money market securities.

30
Q

What is SOFR?

A

Secured overnight financing rate (SOFR) is the overnight cash borrowing rate collateralized by US treasuries and will replace LIBOR in the future.

31
Q

What do the traditional theories of the term structure try to explain?

A

They try to explain the shape of the yield curve.

32
Q

What is the unbiased expectations theory?

A

It’s pure expectations theory.
Forward rate is an unbiased predictor of the future spot rate.
Can be used to explain any shape of the yield curve.
Does not consider risk. -> Investors are risk neutral.

33
Q

What is the local expectations theory?

A

More rigorous than the unbiased expectations theory.
Expected return for every bond over short time periods is the risk-free rate.
Bond pricing doesn’t allow for traders to earn arbitrage profits.
No risk premium for short time periods.
However, accommodates risk premium for long time periods.

34
Q

What is the liquidity preference theory?

A

asserts that liquidity premiums exist to compensate investors for the added interest rate risk they face when lending long term and these premiums increase with maturity.
expectation of unchanging short-term spot rates, liquidity preference theory predicts an upward-sloping yield curve.
Forward rate provides an estimate of the expected spot rate that is biased upward by the amount of the liquidity premium.
implies that the yield curve will typically be upward sloping.

35
Q

What is the segmented markets theory?

A

Assumes that the market is segmented where each maturity sector is considered a ‘market segment’.
Different credit categories such as investment grade vs high-yield can also be considered market segments.
Thus, yields are solely a function of the supply and demand for bonds in a particular ‘market segment’.

36
Q

What is the preferred habitat theory?

A

Similar to the segmented markets theory in proposing that many borrowers and lenders have strong preferences for particular maturities but it states yields at different maturities are determined independently of each other.
if expected additional returns to be gained are large enough, then institutions will be willing to deviate from their preferred maturities or habitats.
Agents and institutions will accept additional risk in return for additional expected returns.

37
Q

What is shaping risk?

A

The shape of the yield curve changes continually and yield curve shifts are rarely parallel.
Shaping risk is defined as the sensitivity of a bond’s price to the changing shape of the yield curve.
Shaping risk also affects the value of many options, which is very important because many fixed-income instruments have embedded options.

38
Q

How are yield curve movements described?

A

by a combination of three independent movements:
A) Level
B) Steepness
C) Curvature

39
Q

What is yield volatility?

A

The term structure of interest rate volatilities is a representation of the yield volatility of a zero-coupon bond for different maturities.

40
Q

How do we measure yield curve risk?

A

The volatility curve or volatility term structure measures yield curve risk.

41
Q

Why is it important to measure yield curve risk?

A

A) Most fixed-income instruments and derivatives have embedded options
B) Fixed-income interest rate risk management.

42
Q

Imp points about yield curve volatility?

A

Short term rates are more volatile than long-term rates (Due to changes/effects of monetary policies)

43
Q

How do we manage yield curve risks?

A

We do that using a measure called Duration.

44
Q

What is Effective Duration vs Key Rate Duration?

A

Effective Duration measures the sensitivity of a bond’s price to a small parallel shift in a benchmark yield curve.
Key Rate Duration measures a bond’s sensitivity to a small change in a benchmark yield curve at a specific maturity segment.

45
Q

How to calculate KeyRate Duration to measure yield curve risk?

A

KeyDurFULL = -KeyDur1z1 - KeyDur5z5 - KeyDur10*z10

46
Q

What is Bond risk premium?

A

Expected excess return of a default-free long-term bond (T-bill 10 years) less the expected excess return of an equivalent short-term bond (1 year T-bill) or the one-period risk-free rate.
It is a forward-looking expectation and must be estimated.

47
Q

Which factors explain short term and intermediate term bond yield?

A

Inflation explains about 2/3rds and rest is explained by economic growth factors & monetary policy.
For long term bonds, Monetary policy explains 2/3rds and remaining 1/3rd is explained by inflation.

48
Q

Which other factors influence the bond risk premium?

A

A) Fiscal Policy
B) Maturity structure of Debt
c) Investor Demand.

49
Q
A

CFA 22nd Nov 2024 (3 decks)

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