Fixed Income Flashcards
Convert Spots from Forwards
Use geometric mean
1-year spot rate is 2%, the 1-year forward rate one year from today (1y1y) is 3%, and the 1-year forward rate two years from today (2y1y) is 4%, what is the 3-year spot rate
{(1.021.031.04)^(1/3)] - 1
Approximate Convexity
Approximate Effective Convexity (embedded options)
Approximate Convexity = (New Increased Price + New Decrease Price - 2*current price) / Change in YTM^2 * current price
Approximate Effective Convexity = (New Increased Price + New Decrease Price - 2*current price) / Change in yield curve^2 * current price
Calc bond value using spot rates
The question will give you the spot rates
i.e.
1-year: 3%
2-year: 4%
3-year: 5%
you need to discount the payment using the spot rate and take the sum.
50/1.03 + 50/1.04^2 + 1050/1.05^3
NOTE: if the rates are presented on a semi annual basis, you have to devide the coupon and the int rate by 2.
Calculating the full price of a bond
First calc the value of the bond like you normally would using YTM as I/Y
Next Adjust for the number of days since the last coupon payment:
Semi - Days between June 15 and December 15 = 183 days.
Days between June 15 and settlement on August 21 = 67 days.
Full price = 1,019.04 × (1.02)67/183 = 1,026.46.
Convert forward rate from spot rates
The 2-period spot rate, S2, is 8%, and the 1-period spot rate, S1, is 4%. Calculate the forward rate for one period, one period from now, 1y1y.
=1.08^2 / 1.04 = 12.154% –> think of it as the later rate divided by the earlier rate. each rate is raised to the power of the year. (i.e. a 2 year would be ^2 a 3 year would be ^3).
NOTE: if you’re given semi annual rates you would (1.08/2)^2 / (1.04/2)
Approximate Modified Duration
and Effective Duration Formula (used for bonds with embedded options)
Approximate Modified Duration = New Increased Price - New Decreased Price / 2 * Current Price * Change in YTM
Effective Duration = New Increased Price - New Decrease Price / 2 * Current Price * Change in Yield Curve.
Modified Duration
Approximate % change in price of a 1% change in yield
ModDur = Macaulay Dur / (1 + YTM)
Repo Rate vs Repo Margin (haircut)
Repo rate is between what you sell for and what you buy back for.
Repo margin haircut is difference between what you sell for and the value of collateral
Calc bond price using forward rates
The question will give you the forward rates
i.e.
1-year: 3%
2-year: 4%
3-year: 5%
50/1.03 + 50/(1.031.04)+ 1050/(1.031.04*1.05)
Macaulay duration and Macaulay duration of a non-callable perpetual bond
Weighted average of PV of CF (PV of CF for period/total PV CF) * year of payment
Macaulay duration of a non-callable perpetual bond
(1 + r) / r
Higher Duration results from -3 Ls or 3 things that make a bond price more sensitive
Longer maturity
Lower coupon
Lower YTM
Short term zero coupon bonds are the most sensitive
G-spread
A yield spread over a government bond
z-spread
zero-volatility spread or Z-spread is the percent spread that must be added to each spot rate on the benchmark yield curve to make the present value of a bond equal to its price.
Int Exp on a bond under IFRS
IFRS requires the effective interest method for the amortization of bond discounts/premiums.
Interest expense = Value of bond (Liability value) × YTM (Market rate at issuance )= 0.05 × €46.140 = €2.307
Convexity characteristics of various bonds
A callable bond exhibits negative convexity at low yield levels and positive convexity at high yield levels.
an option-free bond always exhibits positive convexity.
a putable bond always exhibits positive convexity, higher than an option-free bond.
using duration and convexity to approximate a change in price
Change in price = -ModDur * (change in YTM) + 1/2 * ApproxConvexity * (change in YTM)^2
Note: you will need to convert 25 bps to .0025
Note: these tricky bastards . . . if the yield decreases, you enter the change in yield as a negative. if it increases, you enter it as a positive.
Eurobond
A Eurobond is an international bond issued outside the jurisdiction of any one country and not denominated in the currency of the country where it is issued.
Forward rate agreements are most likely used
to hedge interest rate exposure present in the money market. In a forward rate agreement, the underlying is the interest rate.
Forward rate agreements are forward contracts that conceptually allow lenders to lock in a fixed payment on a future investment by making variable payments and receiving a fixed payment.
Affirming Covenants
Think of this as making the issuer do something. Affirmative covenants do not typically restrict the operating decisions of the issuer. Common affirmative covenants are to make timely interest and principal payments to bondholders, to insure and maintain assets, and to comply with applicable laws and regulations.
Negative Covenants
Negative covenants are frequently costly and do materially constrain the issuer’s potential business decisions. The purpose of negative covenants is to protect bondholders from such problems as the dilution of their claims, asset withdrawals or substitutions,
the bond exposed to the greatest level of reinvestment risk is most likely the one selling at:
A premium because it has a higher coupon rate and, all else being equal, bonds with higher coupon rates face higher reinvestment risk.
Duration assumption
Duration measures the change in the price of a portfolio of bonds if the yields for all maturities change by the same amount; that is, it assumes the slope of the yield curve stays the same.
4 Cs of Credit Analysis
- Capacity - Ability to service/ pay debt (industry structure (portor’s 5), fundamentals, management)
- Collateral -
- Covenants
- Character - soundness of managements strategy, execution of strategy, aggressive accounting practices, history of shady shit,
