Fixed Income

Question 1

Convert Spots from Forwards

Answer 1

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

Question 2

Approximate Convexity

Approximate Effective Convexity (embedded options)

Answer 2

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

Question 3

Calc bond value using spot rates

Answer 3

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.

Question 4

Calculating the full price of a bond

Answer 4

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.

Question 5

Convert forward rate from spot rates

Answer 5

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)

Question 6

Approximate Modified Duration

and Effective Duration Formula (used for bonds with embedded options)

Answer 6

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.

Question 7

Modified Duration

Answer 7

Approximate % change in price of a 1% change in yield

ModDur = Macaulay Dur / (1 + YTM)

Question 8

Repo Rate vs Repo Margin (haircut)

Answer 8

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

Question 9

Calc bond price using forward rates

Answer 9

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)

Question 10

Macaulay duration and Macaulay duration of a non-callable perpetual bond

Answer 10

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

Question 11

Higher Duration results from -3 Ls or 3 things that make a bond price more sensitive

Answer 11

Longer maturity
Lower coupon
Lower YTM

Short term zero coupon bonds are the most sensitive

Question 12

G-spread

Answer 12

A yield spread over a government bond

Question 13

z-spread

Answer 13

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.

Question 14

Int Exp on a bond under IFRS

Answer 14

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

Question 15

Convexity characteristics of various bonds

Answer 15

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.

Question 16

using duration and convexity to approximate a change in price

Answer 16

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.

Question 17

Eurobond

Answer 17

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.

Question 18

Forward rate agreements are most likely used

Answer 18

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.

Question 19

Affirming Covenants

Answer 19

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.

Question 20

Negative Covenants

Answer 20

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,

Question 21

the bond exposed to the greatest level of reinvestment risk is most likely the one selling at:

Answer 21

A premium because it has a higher coupon rate and, all else being equal, bonds with higher coupon rates face higher reinvestment risk.

Question 22

Duration assumption

Answer 22

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.

Question 23

4 Cs of Credit Analysis

Answer 23

1. Capacity - Ability to service/ pay debt (industry structure (portor’s 5), fundamentals, management)
2. Collateral -
3. Covenants
4. Character - soundness of managements strategy, execution of strategy, aggressive accounting practices, history of shady shit,