Fixed Income Flashcards
What is the effective duration equation?
PV- - PV+ / 2 x Δcurve x PVo
What is the effective convexity equation?
PV- + PV+ - 2PVo / Δcurve^2 x PVo
What is the equation for the return of a portfolio with leverage?
Ri(Ve+Vb) - (VbxRb) / Ve
What are type 1 liabilities and one example
Known cash outlay and timing. Standard bond.
What are type 2 liabilities and one example
Known cash outlay and unknown timing. Callable/putable bonds.
What are type 3 liabilities and one example
Unknown cash outlay and known timing. FLN and ILS.
What are type 4 liabilities and one example
Unknown cash outlay and timing. Property and casualty insurance.
What are the three criteria to immunising a single liability?
Assets equal or more than liabilities, Macaulay duration = liability horizon date, and minimise convexity.
What is the portfolio convexity statistic equation?
(MacDur^2 + MacDur + dispersion) / (1+cashflow yield)^2
What are the three criteria to immunising multiple liabilities?
Assets equal or more than liabilities, asset BPV = liability BPV, asset convexity is slightly higher than liability convexity.
What are two advantages to a laddered portfolio?
Yield curve diversification (of price and reinvestment risk) and high liquidity.
What are two challenges of managing a bond portfolio in line with a bond index?
Illiquidity of some bonds mean there is a lack of observable prices. Universe of bond markets is large making is costly to fully replicate.
What is roll return in words?
The change in price of a bond over time but with the same YTM.
What is the expected change in price from an expected change in benchmark yields, in words?
The change in the price of a bond for a change in yields with the same maturity.
What is the butterfly spread equation and what shape of the curve indicates the spread is getting more positive?
-ST yield + 2 x MT yields - LT yield.
More humped.
What is a positive butterfly?
Belly down and wings up. Buy the middle and sell the wings.
What are three yield curve strategies with a static upward sloping yield curve?
Buy and hold, rolling down the yield curve, and a repo carry trade.
Macaulay duration is equal to?
Maturity on zero coupon bonds.
Modified duration is equal to?
Macaulay duration / 1+r
Identify the stage of corporate leverage, defaults, credit spread levels, and credit spreads slope (IG and HY) for an early expansion
Falling, peak, stable, IG stable and HY inverted.
Identify the stage of corporate leverage, defaults, credit spread levels, and credit spreads slope (IG and HY) for an late expansion
Stable, falling, falling, IG and HY upward sloping.
Identify the stage of corporate leverage, defaults, credit spread levels, and credit spreads slope (IG and HY) for a peak
Rising, stable, rising, IG and HY upward sloping.
Identify the stage of corporate leverage, defaults, credit spread levels, and credit spreads slope (IG and HY) for a contraction
Peak, rising, peak, IG stable and HY inverted.
What is and name and one pro and one con of the yield spread as a fixed-rate credit spread measure
Corporate bond yield - closest maturity OTR government BM. Simple to calculate. Might not have a comparable maturity OTR bond.
What is and name and one pro and one con of the G-spread as a fixed-rate credit spread measure
Corporate bond yield - interpolated yield of OTR BM. Matches maturity through interpolation. Subject to changes in government bond demand.
What is and name and one pro and one con of the I-spread as a fixed-rate credit spread measure
Corporate bond yield - interpolated yield of fixed swap rates. Yields available for many points on the curve. Limited to option free bonds and not truly risk-free (carries bank risk).
What is and name and one pro and one con of the asset swap as a fixed-rate credit spread measure
Fixed coupon on a par corporate bond - interpolated yield of fixed rate swap. Limited to option free bonds.
What is and name and one pro and one con of the Z-spread as a fixed-rate credit spread measure
A trial and error method to find the single fixed spread that when added to the BM yield discounts the bonds cash flows back to its current MV. Captures term structure of government rates. Complex and limited to option free bonds.
What is and name and one pro and one con of the OAS as a fixed-rate credit spread measure
Can compare option free bonds with bonds with embedded options. Complex calculation based on volatility and prepayment assumptions.
What is quoted margin and con?
Fixed spread above MRR for assuming credit risk. Fixed so does not capture changes in credit quality.
What is discounted margin and one con?
Represents changes in credit conditions. Assumes a flat BM curve.
What is zero discounted margin and one con?
Fix of DM that incorporates the term structure of interest rates. Complex to calculate.
When is DM > Z-DM?
Upward sloping yield curve
What is the expected excess spread equation?
spread/m - (modified duration × Δspread) - (POD/m × LGD).
LGD = exposure × loss severity.
What is the instantaneous expected excess spread equation?
duration × Δspread
What is a reduced form model and an example model?
A bottom-up credit strategy approach that solves for default intensity using company-specific factors. Examples are the Z-score.
What is a structural form model and an example model?
A bottom-up credit strategy approach that uses market-based variables to estimate the MV of an issuers assets and the volatility of assets, with the likelihood of default being the chance of the L>A. Example is the DRSK model.
What party pays when CDS spread > fixed coupon and is the CDD trading at a discount or premium?
Buyer pays upfront fee and CDS is trading at a discount.
What is the equation for CDS price?
1 + (fixed coupon - CDS spread) × effective spread
What is the equation for immediate change in the CDS price from a change in spreads?
-ΔCDS spread × effective spread
A CDS seller is _____ credit risk?
Long
What is empirical duration?
Evidence that HY bonds are less sensitive than IG bonds to interest rates but more sensitive to credit spreads, suggesting that HY bonds have a lower duration than IG bonds.
Why is a portfolio with a slightly higher convexity compared to the liability chosen for immunising multiple liabilities?
Because it will minimise the effect of non-parallel shifts in the yield curve (structural risk).
What is the equation for bond portfolio VaR?
MV ⨯ ( -modified duration ⨯ yield volatility ⨯ SQRT(days) ⨯ stdevs)
What is the BPV of a swap?
BPV receiving - BPV paying
These are usually quoted as BPV per 100 notional so divide by 100.
What is the impact on different CDO tranches from an increase in default correlations?
Lower traches increase in value relative to higher tranches.
What are the two risk components that make up spreads?
Credit and liquidity risk.
What are the two risk components that make up credit spread?
POD and LGD.
What are the value ranges and meanings for outputs of the Z-score?
More than 3 is low chance of default.
Between 1.8 and 3 is some risk.
Below 1.8 is high risk of defaults.
What is the equation used to find the weight of the longer maturity bond when interpolating bond yields?
M-S / L-S
What is an asset swap?
Where an investor owns a corporate bond and enters into a pay fixed swap and receives the MRR. Net inflow in a spread between bond coupon and fixed leg + MRR.
When finding the value of a FRN, what is the coupon and YTM equal to?
Coupon = MRR + QM. YTM = MRR + DM.
What has the highest reinvestment risk and convexity for a bullet, barbell, and laddered portfolio?
BB > L > bullet.
What does the spread curve do in an economic recovery/expansion?
Narrows and steepens. HY spreads narrow by more than IG.
What are two explanations of why a hedge can fail?
Based on MD:
- MD only works for small changes in rates.
- MD assumes parallel shifts in the yield curve only.
What is the equation for what a short bond futures position receives at settlement?
futures settlement price /100 x CF x 100,000.
Compare this to the price of the CTD bond the short bought from the market to deliver to the long.
