Revised Fixed Income Flashcards
(113 cards)
1
Q
Why would you hold fixed income in a portfolio?
A
- Less volatility
- Regular Cash flows
- Inflation Hedging Potential
- Diversification
2
Q
Explain the level of inflation protection that nominal, floating, and TIPs provide
A
Nominal bonds provide no inflation protection
Floaters provide no principal protection but interest rates typically increase with inflation, therefore protecting coupons from inflation
Inflation linked bonds protect both, as the principal is adjusted according to inflation.
3
Q
What is the basic premise of a liability based mandate?
A
The purpose of the portfolio is to manage or match cash inflows with cash outflows.
4
Q
What are the two main approaches to liability based mandates?
A
- Cash flow matching
2. Duration matching
5
Q
What are the benefits and drawbacks of cash flow matching?
A
Benefits: 1. Very little reinvestment risk 2. Rebalancing may not be necessary Cons: 1. Perfect matching is nearly impossible 2. Default and optionality 3. May be overlooked cost savings
6
Q
What is the primary drawback of duration matching strategies?
A
It only protects against parallel shifts in the yield curve.
7
Q
What are the two basic requirements of a duration matching liability based mandate?
A
- Duration is matched
2. PV of assets is equal to or greater than liabilities
8
Q
What is contingent immunization?
A
This combines classical immunization plus active bond management. You will grow the portfolio, but if it drops to a certain threshold, you will go into full immunization.
9
Q
What is horizon matching?
A
This strategy uses cash flow matching for short term liabilities, but duration matching for long term liabilities.
10
Q
What effect would a one time parallel shift in the yield curve have on a cash flow matching and duration matching strategy?
A
There will be no effect. CF matching does not matter. Duration matching will protect from the one time parallel shift.
11
Q
Which is more liquid, sovereign or corporates bonds?
A
Sovereigns
12
Q
Which is more liquid, higher quality or low quality bonds?
A
Higher quality typically has higher inventory with dealers, more dealers willing to purchase
13
Q
What are the primary effects of fixed income liquidity on portfolio management?
A
- Pricing - issues often have stale prices, estimate prices
- Yield vs Liquidity payoff - lower liquidity generally means higher yields, although bigger bid ask spreads.
- General increased costs of trading
- Use of derivatives will increase as fixed income becomes less liquid
14
Q
How can you decompose the returns of fixed income?
A
Expected Return =
Yield Income +
Rolldown Yield +
Projected price change from yield curve shifts -
Expected credit losses (pro of default*Loss given default)
Expected currency gains/losses
15
Q
How do you calculate rolling yield?
A
Rolling yield = Yield Income + Rolldown Return
Rolldown Return = Price change as a %
16
Q
How do you calculate the change in bond prices using duration and convexity?
A
-ModDurationchange in yield + 1/2Convexity*Change in Yield ^2
17
Q
How do you calculate return on equity when leverage is used?
A
= Return + Loan/Equity * (Return - Cost
18
Q
What are the basic ways to achieve leverage?
A
- Futures
- Swaps
- Structured notes
- Repo agreements
- Securities lending
19
Q
How does a futures position use leverage?
A
A futures position allows you to get exposure to an underlying with only a margin deposit.
20
Q
What is the leverage factor on a futures contract?
A
Leverage Factor = Notional Value - Margin/Margin
21
Q
What are type 1-4 liabilities?
A
- Known amount, timing known
- Known amount, timing unknown
- unknown amount, timing known
- Both unknown
22
Q
How is Macaulay Duration related to bond prices and reinvestment risk?
A
Mac Duration is the time measurement showing the time in which reinvestment and price changes offset each other given a one time parallel shift.
23
Q
What are the three conditions to set up an immunization of a single liability?
A
- Duration of the portfolio is = investment horizon (liability duration)
- Initial PV of portfolio >= PV of liability
- Minimize convexity subject to first 2
24
Q
What is a zero replication strategy?
A
A zero replication strategy is the idea of replicating a zero coupon bond to immunize interest rate risk
25
What are the structural risks of immunization strategies?
Non parallel yield curve shifts
26
How is the dispersion of bond maturities/durations related to convexity?
The more dispersed (greater variance) of cash flows around the duration, the higher convexity. Convexity benefits from interest rate movements. In general, immunization strategies seek to minimize convexity subject to other constraints.
27
What are the pros and cons of using a cash flow matching strategy to meet multiple liabilities?
Pros:
1. Can improve credit rating
2. Defeasance (remove liabilities from BS)
Cons:
1. Very complex for a lot of liabilities
2. Cash in advance constraint - maturity mismatches lead to large cash holdings
28
What are the differences between a duration matching strategy for a single liability and multiple liabilities?
Single liabilities mean matching and rebalancing to match MacDuration. You cannot do this as simply for multiple liabilities
29
What are the conditions for duration matching with multiple liabilities?
1. PV assets >= liabilities
2. Dollar Duration of A = Liabilities
3. Dispersion of assets must be higher than liabilities (Convexity) - we need to benefit from interest rates more than our liabilities would increase
You must have assets maturing/duration before and after first and last liabilities.
4. After these conditions are met, convexity should be minimized
30
How do interest rate contracts alter duration?
Long interest rate futures increase duration. If rates go up, futures prices go down (you end up overpaying). This is similar to bonds.
31
How do you find the BPV of a futures contract?
BPV of cheapest to deliver/Conversion Factor
32
How do you find the notional number of futures contracts to adjust duration?
N = BPV Liabilities - BPV Assets/BPV Futures
| This means you buy futures to extend BPV out to liabilities.
33
What is the formula for BPV?
This is the ModDuration * Value * 0.0001.
34
How can you use interest rate swaps to adjust duration?
A pay floating, received fix is essentially a long fixed short floating. Duration of floating is near zero, so net duration is higher. The opposite would be true to reduce duration.
35
How do you find the notional amount of interest rate swaps you need to adjust duration?
The same as normal, just multiply by 100.
| NA = BPVL - BPVA/BPVswap * 100
36
What is a receiver swaption?
This is an option to enter into a receive fixed, pay floating. You pay a premium and will exercise is the swap rate is below the exercise rate. This is a net positive duration instrument as you benefit when swap rate decrease. This is essentially a call option
37
What is a payer swaption?
This is an option to enter into an interest rate swap where you pay fixed, receive floating. If rates go up, you can exercise and you will be paying a lower than market rate. this makes this a negative duration instrument as it benefits from increases in rates.
38
What are the basic options/strategies to pursue if you expect rates to decrease?
In general, you want to increase duration. This can be done via...
1. Long bonds
2. Buying Bond futures
3. Receive fixed, pay floating swaps or swaptions
4. Long interest rate options
If the BPV of your assets is higher than liabilities, then you don't really need to do anything.
39
What are the basic options/strategies to pursue if you expect rates to increase?
in general, you want to decrease duration. This can be done via...
1. Short Bonds
2. Selling Bond Futures
3. Receive floating, pay fixed swaps or swaptions
4. Sell interest rate options
40
Draw and explain the features of a swaption collar (received and pay)
Draw
41
How do you know how much to hedge in a liability matching strategy?
You never do, but consider the following....
When BPV of assets is greater than liabilities, no sense in hedging down rates, but would want to hedge up rates. The opposite is true if BPV L > BPV A
42
What is the fundamental equation governing duration matching hedging?
BPV A * Change in Asset Yield + BPV N * Change in yield Hedge = BPV L * Change in Yield L
43
What are the primary risks to liability driven strategies?
1. Model risks
2. Measurement errors - duration, BPV, etc
3. Implicit assumption that yield changes are consistent across assets, liabilities, and hedges.
4. Spread risk - IG yields are less volatile than treasury yields, therefore greater spread volatility between corps and treasuries than corps and swaps
5. Counterparty risk - non collateralized OTCs
6. Collateralization risk
7. Liquidity - if contingent immunization fails
44
What are the primary challenges of benchmarking fixed income portfolios?
1. Fixed income markets are larger and broader, much more heterogenous
2. Fi market is a dealer market - not very much volume, stale prices, matric pricing
3. Limited size of issues
4. Index constitution changes very frequently
45
What are the primary risk factors of a fixed income index based strategy that must be matched to the benchmark?
1. Duration - Effective, option adjusted, convexity
2. Key rate duration - could also just match CF's
3. Sector and quality %
4. Sector and quality spread duration
5. Sector/coupon/maturity cell weights
6. Issuer exposures
46
What are the different strategies for enhanced fixed income index investing?
1. Lower cost enhancement - lower transactions costs compared to full replication
2. Issue selection enhancement - find undervalued bonds or possible credit changes
3. Yield curve enhancements - overweight undervalued areas of the curve.
4. Sector and quality enhancements - go across sector and credit quality based on outlook
5. Underweight callable bonds (no convexity, no upside on rate drops)
47
How can you use a total return swap to gain fixed income exposure?
Total return swaps involve paying LIBOR plus a spread (including default and depreciation losses) in exchange for total returns of the underlying. This involves a cash outlay. The issue with this is that they are short term in nature and must be rolled over. Subject to counterparty risk
48
What are the criteria for selecting a FI benchmark?
1. Unambiguous (transparent)
2. Investable
3. Measurable
49
What are the benefits of laddered bond portfolios?
1. Better protection from twists and shifts
2. Diversification of CF across time
3. Consistent duration
4. Liquidity stream
50
What is the butterfly yield and what does it measure?
Butterfly yield = - (SR + LR) + 2* mid rate
| This measures yield curvature
51
How do we measure yield curve slope (in practice)?
30 - 2 yields. Wider would mean steeper.
52
How do upward or downward shifts typically effect yield curve shape?
Rates are set at the short end. Therefore, when short rates increase there is typically a flattening. The opposite is true.
53
Describe Mac, Mod, Eff, and Money duration:
MacDuration is the time to when reinvestment offsets gains in a parallel yield curve shift.
ModDuration is a measure of % sensitivity of the value of a bond to YTM changes.
EffDuration is a measure of % of sensitivity of the value of a bond to yield curve shifts
Money Duration is the dollar change in price - Mod Duration * Price of bond
54
How does convexity related to rate shifts?
Positive convexity creates greater prices increases on rate drops, and lower price drops when rates increase. Due to this benefit, yields are lower.
55
When should we seek out greater convexity in our portfolios?
1. Rates increasing
| 2. Rate volatility
56
What drives the convexity of a bond or bond portfolio?
1. Higher duration generally means higher convexity. Duration is roughly duration ^2
2. For equal durations, convexity will be lower when coupons/payments are higher.
57
Draw the effect of convexity on a bond
Draw
58
What are the major strategies we can use when we expect the yield curve to be stable?
1. Buy and hold
2. Ride Curve
3. Sell convexity
4. Carry trades
59
Explain a buy and hold strategy for bonds and the ideal circumstance for it to be used in active management
Buy and hold strategies involve buying at the long end of the curve. This involves lengthen duration and diverging from the benchmark to pick up extra yield. This works well in stable yield curve environments.
60
Explain a yield curve riding strategy for bonds and the ideal circumstance for it to be used in active management?
A riding strategy involves holding longer bonds and letting the yield decline over time (price increase). This strategy is based on the idea that curves are stable and will not evolve into the forward curve.
61
What does it mean when we say that the spot curve will not evolve into the forward curve?
The forward curve is an extrapolation based on spot curve such that a one yield holding period for every length of bond should be the same. An upward sloping yield curve will have a forward curve higher than it. For example, Spot curve of 1.5, 2, 2.5 will have a forward curve of 2.5025 as that is the rate in which the one year bond would have to be reinvested in to acheive a 2 year yield equal to the current 2 year spot rate. This must hold due to arbitrage conditions.
62
Explain the no arbitrage pricing conditions that explain the forward curve
This determines that an investment in a two year bond must return the same as a one year bond, reinvested at the 1 year forward rate. Lets say that the forward rate is too low. You want $100 in proceeds at the end of year 2. You can invest at the higher 2 year spot. You get a loan at the 1 year spot and lock in a loan at the 1,1 forward. The total proceeds owed would be less than the proceeds you receive at 2 years.
63
What does it mean to sell convexity? Why would you do this? How?
Selling convexity is reducing exposure to convexity, either by selling convexity you currently own or shorting high convexity instruments. The purpose of this strategy is to capitalize on a stable yield curve. High convexity instruments benefit from interest rate volatility, but returns drag from lower yields during periods of stability. We can sell convexity by writing calls on portfolio assets we own, or selling puts on assets we would like to own. Callable bonds and MBS have negative convexity and high yields, so you could buy those.
64
What are the three basic intramarket carry trades?
1. Buy a bond and finance in the repo market
2. Enter an interest rate swap (receive fixed, pay floating)
3. Long bond futures contract - this works because you would "earn" accrued interest on the bond, but cost of position would be financing
65
Buying a domestic bond and financing it in the repo market is what type of trade? Walk through how it is executed, the purpose, and the risks
This is an intramarket carry trade aimed to finance a high yield asset at a low yield. First, you would purchase your long(er) term bond. You would then enter a repo agreement where you received cash. The cost of this agreement is the repo rate, which is low when collateral quality is high. This strategy should be used when interest rates are not expected to change. If they were to change, this could involve the bond depreciation offsetting the carry trade income.
66
How is taking a long bond futures contract a carry trade?
This is an intramarket carry trade. The futures price will reflect the current price, plus the cost of financing it risk free, less any yield you miss out on. The futures price will converge to the spot price over time. You will have paid the financing cost as part of the futures price, but receive accrued interest as it pulls towards market value.
67
What are the three basic intermarket carry trade strategies?
1. Borrow from a bank in a lower rate country, invest in a higher rate country bond (FX risk)
2. Currency Swap - this will hedge out FX risk
3. Borrow in a high rate currency, buy security there, convert financing position to a lower rate country - this can be done using forwards
68
Explain the mechanics of a currency swap and why you would execute one. Draw an example using the following information:
US company wants to finance 1M Euro project
Spot is $/Euro = $1.30, therefore need company to borrow $1.3M
US company costs $8%, 7% Euro
French Company costs $9%, 6% Euro
A currency swap is when two parties give each other offsetting loans for different currencies. At the end of the payment, they will repay based on a set exchange rate. This may be attractive when you want to finance in FX but do not want FX risk.
69
Explain how the following intermarket carry trade would be executed:
You are in Country A with rates of 5%
Country B with rates of 4%
You want to use forwards to hedge FX risk
S(B/A) = 2
1. You purchase a bond in your country which will be worth Pb(1+rh)
2. You sell in the repo market to get Pb - this will cost you at most rh, fully offsetting position
3. You buy your country's currency forward and you will pay S(L/H)*Pb*(1+rh) and receive Pb(1+rh).
In the end you are just exposed to interest rate risk.
70
```
How can we exploit the slopes in two different yield curves? Draw and example using the following information:
USA market (steep)
Swap rate = 2.89, floating short rate = 2.03
CAD market:
Swap rate = 7.24, floating short rate = 7.19
```
We can carry out an interest rate swap in the steep curve where we receive long fixed and pay floating. This only involves one currency.
We can then carry out the opposite in the shallow market, where we pay long and receive short.
How does this work?
At the short end, we would be receiving 7.19 and only paying 2.03 in USD, netting 5.16 with FX risk
At the long end, we are receiving 2.89 and paying 7.24, netting -4.35. The net gain is 81 bps with no currency risk assuming yield curve shapes hold.
71
What strategies could we follow when we expect changes in level, slope, or curvature of the yield curve?
1. Duration Management
2. Buy convexity at portfolio duration
3. Bullets and barbells
72
How does adding leverage increase duration? How do we know how much duration it is adding?
The relationship between leverage and duration can be described by MVp/MVe * Duration = effective duration. This is simply a function of leverage magnifying directional moves.
This is the same as determining how many bonds to buy to increase duration, regardless of leverage. PVBP/Duration of bonds in question = MV of bonds to add
73
Why would you use swaps over futures or leverage to alter leverage? Why wouldn't you?
Swaps are not as liquid as futures, or as flexible as leverage, but swaps can be created for any maturity so they are customizable.
74
How do you determine the notional value of a swap you need to extend duration?
Net effective PVBP/100 par = effective receive - effective fixed
Therefore, the notional amount = PVBP needed/PVBP swap in question
75
How do you determine the duration of an option?
Duration = Price of underlying/Price of option (leverage) * Duration of underlying * Delta
Deeper OTM = higher leverage, but lower delta
Deeper ITM = lower leverage, but higher delta
76
Under what situation would you use bullets and barbells?
Bullets are used for steepening curves, Barbells for the opposite
77
At a given maturity, if your forecasted rate is higher than the current futures curve, what does that say about returns?
If the forecasted rates come to fruition, then those bonds will appreciate, as the rates are lower than what was implied previously. Specifically, the 1 year return will be greater than the previous 1 year rate.
78
What is the equation to choose the best bond to purchase given a shift in the yield curve? How do you calculate the total return?
Maximize: (Forward Yield - Forecast Yield) * Duration at end of horizon.
The difference between the forward and forecast yield represents the yield curve shift that we anticipate happening in one year. This is scaled by the duration of the given bond at that point. The total return is the YTM at the beginning of the period plus price change due to duration. Essentially, this is the top equation plus expected YTM.
79
What should make you cautious to increase convexity (duration staying the same) when you expect rates to move but are uncertain when?
Convexity must outweigh the yield drag, which is more likely over short time horizons.
80
How do you construct a butterfly strategy in a fixed income portfolio? Why would you do this?
A butterfly strategy consists of a long short portfolio of bullets and barbells. A long barbell and short bullet would be a long convexity butterfly, and a long bullet and short barbell would be a short convexity. You would want a pos. convexity butterfly when you expect rates to move, and/or you expect a flattening of the curve. The opposite is true for a neg. convexity butterfly.
81
How do you construct a duration neutral butterfly?
A duration neutral butterfly involves having each leg of the trade equal in duration and equal in market value. This does not mean each wing will be the same size.
82
How do you construct a 50/50 butterfly?
You will short the body and use the proceeds such that half of the money duration is allocated to each wing. This is used when the body is seen as too expensive vs wings but do not know how it will be resolved.
83
Draw the two variation of a butterfly and explain the bets they are making and when they make money
Draw
84
Draw two variations of a condor and explain the bet they are making and when they make money
Draw
85
Why are MBS negative convexity?
When rates go up, there will be less prepayments which increases duration and interest rate sensitivity. If rates and duration are positively correlated, then convexity is negative. When rates go down, lots of prepayments, duration gets lower. This means duration and rates are positively correlated again.
86
What is spread duration and what does it measure?
Spread duration measures the sensitivity of a bond to changes in credit spreads.
87
Why is spread duration more relevant for floating rate bonds than fixed?
Floating rate bonds have very short durations. However, they are sensitive to changes in credit spreads. Fixed bonds typically have spread durations equal to modduration.
88
What is the relationship between credit spreads and risk free rates?
They are typically negatively correlated as credit spreads are countercyclical.
89
What factors compose credit risk?
1. Default risk
| 2. Loss severity
90
What is the benchmark spread? How is it different than the G spread?
The benchmark spread is the Yield on the security less the yield on a risk free security (typically a government bond). If the benchmark security is a government bond, this is called the G spread.
91
What are the pros and cons of a the G Spread?
Pros:
Simplicity and ease of calculation
Cons:
Does not work for optionality
92
What is the I spread? Why would you use it?
The I spread is the interpolated spread, very similar ot the G spread, but uses swap rates. This is beneficial as swap curves tend to have more availability of prices (smoother).
93
What is the issue with using I spread or G spread when hedging out benchmark interest rate risk?
You must know what you're hedging. If you're selling government bonds you want to hedge g spreads, if you're using swaps you want I spreads.
94
What is the difference between the Z spread and OAS? Why would you use them?
The Z spread and OAS are essentially the same. The Z spread is the constant add to the spot curve, whereas OAS is constant add to the forward curve. The OAS will accommodate optionality. OAS is most appropriate for a bond portfolio as a whole.
95
What is the main downside of using OAS?
It is very dependent on assumptions of interest rate volatility and is theoretical.
96
How do you approximate the excess return expected on a credit?
XR = (s*t) - (deltaS * SD) - (t*p*L)
s is the beginning spread (amount earned), t is the holding period, SD is the spread duration. P is the probability of default, and L is the loss given default
97
What is a bottom up credit strategy?
This is a strategy that involves selecting individual bonds or issuers with the best relative value. The key to this strategy is weighting the compensation for credit risk against the magnitude of credit risks such as liquidity, default, spread, and migration risk.
98
What are the factors focused on in a top down credit strategy?
1. Economic Growth
2. Corporate Profitability
3. Default rates
4. Risk appetite
5. Volatility
6. Spread changes
7. Rates
8. Industries
9. Currency
Top down managers will typically group sectors together
99
What are the two key components of deciding the credit quality for a top down investor?
1. Credit Cycle
| 2. Credit Spread change
100
How do you measure the credit quality of a top down approach?
1. Average credit rating
2. Average OAS
3. Average Spread Duration
101
What are the advantages and disadvantages of bottom up vs top down credit management?
Bottom up is easier to gain informational advantages. Top down is good because a sizable portion of returns is due to macro factors rather than security level.
102
What are some typical measures of credit liquidity?
1. Trading Volume
2. Spread sensitivity to outflows
3. Bid ask spreads
103
How can you measure tail risk in credit portfolios?
1. Scenario analysis to measure performance under specific circumstances
104
How can you manage tail risk in credit portfolios?
1. Diversification
2. CDS
3. Options
105
What are key considerations in EM credit vs DM?
1. Concentration in commodities and banking
2. Government ownership
3. Credit quality
4. Transparency and liquidity
5. Legal risk
106
What advantages do MBS have over corporate bonds?
1. Liquidity
2. Real Estate exposure
3. Negative convexity
4. Expression of credit cycles
107
How does the correlation of defaults affect the value of a CDO?
If correlation between senior and sub tranches of a CDO increase, the equity value will increase relative to the senior tranche. The equity pays a higher premium, which is all that matters if they have the same chance of default.
108
What are the general benefits of structured credits?
1. higher returns
2. More targeted exposure
3. Diversification
109
What are the pros and cons of cash flow matching?
Pros:
This is a simple solution that does not involve rebalancing, simply just setting up a cash flow schedule to match your needs
Cons:
You are subject to the cash in advance constrain where you hold large cash balances between payments, which introduces reinvestment risk.
110
What are the pros and cons of duration matching?
Pros:
Upward and downward shifts are matched
Cons:
Structural risks associated with twists in the curve and non-matched key rate durations or convexity
111
What are the pros and cons of a derivatives overlay matching?
Pros:
Cost effective way of "rebalancing" a FI portfolio towards target duration.
Cons:
Rounded contracts
112
How do you find the BPV of an FI future?
Futures BPV/CF
113
What are the pros and cons of contingent immunization
Pros:
Allow for ability to outperform
Cons:
Must have a surplus going into it
