Chapter 10 -Finance

Front 1

Straight Bonds

Back 1

-An IOU that obligates the issuer to pay the bondholder a fixed sum of money at the bond’s maturity along with constant, payments during the life of the bond.
-Maturity= principle, par value, stated value, or face value.
-Interest payments= coupons.

Front 2

Bonds with special features

Back 2

-When a bond has a special feature, it no longer is a straight bond.
-Convertible bonds- Bondholders have the right to convert their bonds into shares of common stock of the issuing corporation.
-Putable bonds- Have a put feature that grants bondholders the right to sell their bonds back to the issuer at a special put price.
-Callable Bonds

Front 3

Two basic yield measures for a bond

Back 3

-When change in the bond’s price, the coupon rate remains constant.
-A bond’s current yield is inversely related to its price, changes when bond’s price changes.

Front 4

Straight Bond Prices

Back 4

Have two components:
1st- The present value of all the coupon payments
2nd- The present value of the principal payment at maturity.
-Calculating bond prices is mostly “plug and chug”

Front 5

Premium and Discount Bonds

Back 5

-Bonds are distinguished whether they are selling at par value or discount/premium to par value.
-Whether bond sells at premium/discount depends on relationship between its coupon rate and yield.
-Vertical axis measures bond prices, horizontal axis measures bond maturities.
-Overtime, the price of a premium bond declines and the price of a discount bond rises. At maturity, the price of each bond converges to its par value.
-The longer the term to maturity of the bond the greater is the discount from par value, and the same goes for premium bonds.

Front 6

Premium Bonds

Back 6

Bonds with a price greater than par value are said to be selling at a premium. The YTM of a premium bond is less than its coupon bond.

Front 7

Discount Bonds

Back 7

Bonds with a price less than par value are said to be selling at a discount. The YTM of a discount bond is greater than its coupon rate.

Front 8

Par Bonds

Back 8

Bonds with a price equal to par value are said to be selling at par. The YTM of a par bond is equal to its coupon rate.

Front 9

Relationships among yield measures

Back 9

-The 3 different bond rates/yield (coupon rate, current yield, and yield to maturity)
-Current yield is the relationship between the coupon rate and the yield to maturity
-When a premium bond and a discount bond both have the same YTM, the premium bond has a higher current yield than the discount bond.

Front 10

Yield measures model

Back 10

Premium bonds: Coupon rate> Current yield> Yield to Maturity
Discount bonds: Coupon rate<Current yield<Yield to Maturity
Par Value bonds: Coupon rate=Current yield=Yield to Maturity

Front 11

A Note on Bond Price Quotes

Back 11

-If you buy a bond between coupon payment dates, the price you pay will usually be more than the price you are quoted.
-Clean Price- The price you usually pay includes the accrued interest.
-Dirty Price- Full or invoice price.

Front 12

More on Yields

Back 12

-An investor will be bale to reinvest the coupon interest payments at a rate equal to the yield to maturity of the bond.
Calculating Yields
-The only way to calculate is by “trial and error”.

Front 13

Callable bonds

Back 13

The issuer can buy back outstanding bonds before the bonds mature.

Front 14

Call Price

Back 14

The price the issuer of a callable bond must pay to buy it back.

Front 15

Yield to Call

Back 15

Have assumed so far that a bond will have an actual maturity equal to its originally stated maturity.
-When a bond is called, the bondholder does not receive any more coupon payments.
-A call usually occurs after a fall in market interest rates.
-Outstanding bonds cannot be called until the end of a specified call protection period.
-If a bond is callable, its YTM may no longer be a useful number. The yield to call is more useful.
-It depends whether the YTM or the yield to call are better. If the bond is callable at par then for a premium bond, the yield to maturity is greater. For a discount bond, the reverse is true.

Front 16

Interest rate risk

Back 16

-Bond yields are like interest rates, they fluctuate through time.
-Hodlers of bonds face interest rate risk
-The yield actually earned or "realized" on a bond is called the realized yield.
-The reason a realized yield will always differ from a promised yield is that interest rates fluctuate.

Front 17

Interest Rate risk and Maturity

Back 17

-Some bonds are more sensitive to interest rate changes than others.
-Both bonds display the inverse relationship between bond prices and bond yields.
-Falling yields cause both bond prices to rise, but the larger maturity bond experiences a larger price increase than the shorter maturity bond.

Front 18

Malkiel's Theorems

Back 18

1-Bond prices and yields move in opposite directions.
2-Longer term bonds are more sensitive to changes in yields than shorter term bonds.
3-A bond’s sensitivity to interest rate changes increase as its maturity grows, but at a diminishing rate.
4-Lower coupon bonds are more sensitive to changes in yields than higher coupon bonds.
5-The loss you would suffer from, say, 1 percent increase in yields in less than the gain you would enjoy from a 1 percent decrease in yield.
-Bond maturity is an important factor determining the sensitivity of a bond’s price to changes in interest rates.

Front 19

Duration and Macaulay Duration.

Back 19

DURATION: Difference in interest rate risk across bonds with different coupon rates.
Macaulay Duration
-Shows relationship between percentage changes in bond prices and changes in bond yields.
-Two bonds with the same durations, but not necessarily the same maturity, have approx. the same price sensitivity to a change in bond yields.
-This approx. is quite accurate for relative small changes in yields, but it becomes less accurate when large changes are considered.

Front 20

Calculating Macaulay Duration

Back 20

-Duration values are conventionally stated in years.
-Duration of a zero coupon bond is equal to its maturity.
-A pure discount instrument (U.S. Treasury STRIPS), no calculation is needed.
-The duration of a coupon bond is a weighted average of individual maturities of all the bond’s separate cash flows.
-The weights attached to the maturity of each cash flow are proportional to the PV’s of each cash flow.

Front 21

Properties of Duration

Back 21

-The duration on a bond with coupons is always less than its maturity.
1- The longer a bond’s maturity, the longer is its duration.
2- A bond’s duration increases at a decreasing rate as maturity lengthens.
3- The higher a bond’s coupon, the shorter is its duration.
4- A higher yield to maturity implies a shorter duration, and a lower yield to maturity implies a longer duration.
-The duration on a bond with coupons is always less than its maturity.

Front 22

Bond Risk measures based on duration

Back 22

Dollar Value of an 01
-A popular measure of interest rate risk among bond professionals.

Yield Value of a 32nd
-Used by bond professionals as an additional or alternative measure of interest rate risk.

Front 23

Dedicated Portfolio

Back 23

-Preparing to meet a future liability or other cash outlay.
Ex: Pension funds
-The date the payment is due is commonly called the portfolio's target date.

Front 24

Reinvestment Risk

Back 24

-Yields at which coupons can be reinvested are uncertain, and a target date surplus or shortfall is therefore likely to occur.
-The uncertain portfolio value on the target date represents reinvestment risk.
-More distant target dates entail greater uncertainty and reinvestment risk.
-A simple solution for reinvestment risk is to purchase zero coupon bonds that pay a fixed principal at a maturity chosen to match a dedicated portfolio’s target date.
-No coupons to reinvest = no reinvestment risk.
-U.S. Treasury STRIPS are the only zero coupon bonds issued in sufficient to satisfy dedicated portfolio needs.

Front 25

Immunization: Price Risk versus Reinvestment Rate Risk

Back 25

-Price risk and reinvestment rate risk- tend to offset each other (for a dedicated portfolio, interest rate changes have two effects):
1-Interest rate increases act to decrease bond prices (price risk) but increase the future value of reinvested coupons (reinvestment rate risk).
2- Interest rate decreases act to increase bond values but decrease the future value of reinvested coupons.

Front 26

Immunization by duration matching

Back 26

-Key to immunizing a dedicated portfolio is to match its duration to its target date.
-Immunization is often referred to as duration matching.
-Left vertical axis measures bond portfolio values
-Horizontal axis measures the passage of time from initial investment to bond maturity.

Front 27

Dynamic Immunization

Back 27

-Bond yields change constantly, therefore successful immunization requires that a dedicated portfolio be rebalanced frequently to maintain a portfolio duration equal to the portfolios target date.

Front 28

Advantage and Drawback of dynamic immunization.

Back 28

ADV.-Is that reinvestment risk caused by continually changing bond yields is greatly reduced.
DRAW-Is that each portfolio rebalancing incurs management and transaction costs.
Conclusion-Portfolios should not be rebalanced too frequently. Rebalancing each quarter is good.