Fixed Income Formulas

Question 1

Conversion Value

Answer 1

stock price * conversion ratio

Question 2

Market conversion price

Answer 2

Bond price / conversion ratio

Question 3

Market conversion premium per share

Answer 3

market conversion price - stock price

Question 4

market conversion premium ratio

Answer 4

market conversion premium per share / stock price

Question 5

Premium over straight value

Answer 5

(market price of convertable bond / straight value) - 1

Question 6

Zero Coupon Bond Price

Answer 6

Pt = 1 / (1 + St)^T

Question 7

Forward Pricing Model (zero-coupon)

Answer 7

Based on arbitrage-free pricing; basically says that the same timeframe yields the same

Step One: Calculate discount factors for each
1 / (1 + r)^t

Step Two: Calculate Forward Price
F = Discount(long) / Discount(short)

Question 8

Fixed Income: Implied Forward Rate

Answer 8

[(Rlong * t) - (Rshort * t)] / timplied

Example: S2 = 4%, S5 = 6%, calculate 3 year implied

Long: 6 * 5 = 30 Short: 4 * 2 = 8

30 - 8 = 22

22 / 3 = 7.33

Question 9

Calculate the PV of expected loss

Answer 9

Formula: Coupon * log^ minus time * rate

Example:

25 * e^ -.5 * 0.0112 = 24.86

25 = coupon

-.5 is 6 months

.0112 is the rate (1.12%)

Question 10

Bootstrapping

Answer 10

Purpose: Build up method for interest rates

Formula: 100 = Coupon / (1 + r) + (Par + coupon) / (1 + x)²

Think: Solve for X to get the bond to 100

Question 11

Calculate the forward rates based on spot rates

Answer 11

[(1 + Slong)^t / (1 + Sshort)^t] - 1

Question 12

Calculate Swap Fixed Rates

Answer 12

Formula: (1 - P3) / (P1 + P2 + P3)

Question 13

Calculate Forward Interest Rate

Answer 13

[(1 + Rlong)^t / (1 + Rshort)^t] - 1

Example:

Forward rate starts in 2 years, and last 1 year

[1 + r(3)]³ / [1 + r(2)]² - 1