Bond Valuation Basics - Flashcard set - Mathematical Finance

Still learning

Convexity

A measure of the curvature in the relationship between bond prices and bond yields, indicating the extent to which the duration changes as the yield to maturity changes. The formula for convexity is complex and involves the sum of the present values of all future cash flows, multiplied by the time until receipt squared.

Coupon Rate

The annual coupon payment paid by the issuer relative to the bond's face or par value. The formula for the coupon rate is

\text{Coupon Rate} = \frac{\text{Annual Coupon Payment}}{\text{Face Value}}

Credit Risk

The risk that a bond issuer will default on its obligation to pay back the principal or make interest payments. Bonds are rated by credit rating agencies to help investors assess the likelihood of default.

Face Value

The nominal value of the bond, which the issuer agrees to pay back at maturity. This is also known as par value.

Macaulay Duration

A weighted average time to receive the bond's cash flows. It's calculated using the following formula:

D_{\text{Mac}} = \frac{\sum_{t=1}^{N} t \times \frac{C}{(1+r)^t} + N \times \frac{F}{(1+r)^N}}{P}

where

D_{\text{Mac}}

is the Macaulay Duration,

C

is the coupon payment,

r

is the YTM,

F

is the bond's face value,

N

is the number of periods, and

P

is the bond's price.

Coupon Payment

The periodic interest payment that the issuer makes to the bondholders during the life of the bond. The formula to calculate a coupon payment is

\text{Coupon Payment} = \text{Coupon Rate} \times \text{Face Value}

Discount Rate

The interest rate used in discounted cash flow (DCF) analysis to determine the present value of future cash flows. In the context of bonds, it may refer to the yield to maturity or the required rate of return.

Modified Duration

A measure of the price sensitivity of a bond to interest rate changes, calculated by dividing the Macaulay duration by one plus the yield to maturity per period. The formula for modified duration is

D_{\text{Mod}} = \frac{D_{\text{Mac}}}{1 + \frac{r}{m}}

where

D_{\text{Mod}}

is the Modified Duration,

D_{\text{Mac}}

is the Macaulay Duration,

r

is the YTM, and

m

is the number of compounding periods per year.

Current Yield

The annual coupon payment divided by the current market price of the bond. The formula for current yield is

\text{Current Yield} = \frac{\text{Annual Coupon Payment}}{\text{Current Market Price}}

Yield to Maturity (YTM)

The total return anticipated on a bond if the bond is held until it matures. YTM is considered a long-term bond yield expressed as an annual rate. Calculation involves solving for $r$ in the bond price present value formula:

P = \sum_{t=1}^{N}\frac{C}{(1+r)^t} + \frac{F}{(1+r)^N}

where

P

is the price of the bond,

C

is the coupon payment,

r

is the YTM,

F

is the bond's face value, and

N

is the number of periods until maturity.

Market Price of Bond

The current trading price of the bond in the secondary market, which can fluctuate based on changes in interest rates, credit quality of the issuer, and other factors.

Interest Rate Risk

The risk that a bond's price will decline due to rising interest rates. The longer the bond's duration, the more sensitive it is to this type of risk.

Callable Bond

A bond with a feature that allows the issuer to repurchase the bond at a predetermined price at certain times before maturity. The call price is usually above the face value to compensate the investors for this risk.

Zero-Coupon Bond

A bond that does not pay periodic coupon payments and is issued at a discount from its face value. The investor receives the face value of the bond at maturity. The formula to calculate the price of a zero-coupon bond is

P = \frac{F}{(1+r)^N}

where

P

is the price of the bond,

F

is the face value,

r

is the discount rate (YTM), and

N

is the number of periods until maturity.

Puttable Bond

A bond that gives the holder the right to force the issuer to buy back the bond at a specified price on certain dates before maturity. This feature protects investors against a decline in market interest rates.

Know

Discover published sets by community