fin 3050 chapter 10

zero coupon bonds

"pure discount instruments", more than a year to maturity, have a single payment of face value at maturity with no other payments until then

actual rate of return

( FV / PV ) ^ (1/n) - 1

humped yield curve

*change in slope* short term yields decline more than long term yields going up

liquidity preference theory

- Forward rates are good predictors of future rates. - Investors prefer short-term bonds to long-term bonds. - Investors will hold long-term bonds in exchange for a liquidity premium. - If this theory is correct, the yield curve will slope upward (forward rate will be higher than the spot rate)

pure expectations theory

- Forward rates are unbiased estimates of expected future spot rates. - Investors indifferent between various combinations of maturities that add up to the same term - Investors choose the highest returning combination. - Changes in slope are important. Slope of curveless steep says investors expect smaller magnitudes for future interest rate changes

market segmentation theory

- Forward rates have no relationship with future spot rates. - Some investors prefer short-term bonds and some prefer long-term bonds - Spot rates are determined by supply and demand within maturity categories. - The shape and slope of the yield curve reveal nothing about the future direction of interest rates.

Properties of Duration

- all else the same, longer maturity = longer duration - all else the same, a bonds duration increases at a decreasing rate as maturity lengthens - all else the same, Higher coupon = shorter duration - all else the same a higher YTM = shorter duration - for zero coupon bond, duration = maturity - duration of a coupon bond < maturity

flat yield curve

- interest rates stay the same - short term yields are equal to long term yields change in slope (flat): - short term rise more than long term yields decreasing - hold long term bonds

inverted yield curve

- interest rates will decline - short term yields are higher than long term yields

longer duration characteristics

- lower coupon - longer maturity - lower YTM

percentage change in bond price

- modified duration x change in YTM

theories of yield curve

- pure expectations theory - liquidity preference theory - market segmentation theory

parallel shift

- slope remains unchanged - yields rise or fall over all maturities

classic upward slop

- strategy: hold short term bonds - interest rates will go up - short term yields are lower than long term yields

List the six principles associated with bond-pricing relationships (theorems)

1. Bond prices and interest rates are inversely related. 2. Prices of long-term bonds are more sensitive to a change in yields to maturity than short-term bonds. 3. Bond price sensitivity increases at a decreasing rate as maturity increases. 4. Bond prices are more sensitive to a decline in market yield to maturity than to a rise in market yield to maturity. 5. Prices of low coupon bonds are more sensitive to a change in yields to maturity than high coupon bonds. 6. Bond prices are more sensitive when yields to maturity are low than when yields to maturity are high.

1 basis point

1/100 % or 0.01%

identify the bond that has the longest duration.

15 year maturity with a 0% coupon (lowest coupon rate, medium years)

which bond has the longest duration?

15 year maturity, 6% coupon (lowest coupon, longest years)

Which one of the following bonds has the shortest duration?

8% coupon, 10 year maturity (highest coupon, lowest years)

% price change =

= - mod. duration x yield change

coupon rate

= annual coupon / par value

what is the difference between a bond's promised yield and its realized yield? which is more relevant? when we calculate a bond's yield to maturity, which of these are we calculating?

A bond's promised yield is an indicator of what an investor can expect to earn if (1) all of the bond's promised payments are made and (2) market conditions do not change. This second condition implies that coupon payments are reinvested at the promised yield (i.e., YTM) and the bond is sold or redeemed at its expected value. The realized yield is the actual, after-the-fact return the investor receives. The realized yield is more relevant, of course, but it is not knowable ahead of time. A bond's calculated yield to maturity is the promised yield.

for callable bonds, the financial press generally reports either the yield to maturity or yield to call. often yield to call is reported for premium bonds, and yield to maturity is reported for discount bonds. what is the reasoning behind this convention?

A premium bond is one with a relatively high coupon, and, in particular, a coupon that is higher than current market yields. These are precisely the bonds that the issuer would like to call, so a yield to call is probably a better indicator of what is likely to happen than the yield to maturity (the opposite is true for discount bonds). It is also the case that the yield to call is likely to be lower than the yield to maturity for a premium bond, but this can depend on the call price. A better convention would be to report the yield to maturity or yield to call, whichever is smaller.

modified duration

Approximate % change in price for a given change in yield to maturity - always less than duration - as modified duration goes down, maturity goes down

what is the relationship between the price of a bond and its YTM?

Bond price is the present value term when valuing the cash flows from a bond; YTM is the interest rate used in valuing the cash flows from a bond. They have an inverse relationship.

what is the relationship between the current yield and YTM for premium bonds? for discount bonds? for bonds selling at par value?

Current yield is defined as the annual coupon payment divided by the current bond price. For premium bonds, the current yield exceeds the YTM; for discount bonds the current yield is less than the YTM; and for bonds selling at par value, the current yield is equal to the YTM. In all cases, the current yield plus the expected one-period capital gains yield of the bond must be equal to the required return.

Explain the benefits derived from investing in deep discount bonds.

Deep discount bonds have almost no change of being called away even if prices go up because the value is already far removed from par. Secondly, deep discount bonds offer the opportunity for higher price increases than high coupon bonds if interest rates decline.

As market rates of interest become higher, what impact does this have on duration?

Duration becomes shorter. Duration and interest rates are inversely related.

define duration

Duration is based on the present value of the individual cash flows relative to the present value of the total cash flow. Duration measure interest rate risk

Why are the maturity date and duration the same for a zero-coupon bond?

Duration of a zero coupon bond is the same as the maturity date. There are no coupon payments prior to maturity for a zero-coupon bond.

For a premium bond, which is greater, the coupon rate or the yield to maturity? Why? For a discount bond? Why?

For a premium bond, the coupon rate is higher than the yield. The reason is that the bond sells at a premium because it offers a coupon rate that is high relative to current market required yields. The reverse is true for a discount bond: it sells at a discount because its coupon rate is too low.

Should an investor who thinks interest rates are going down seek low or high coupon rate bonds? Relate your answer to duration and price sensitivity.

He or she should seek low coupon rate bonds, which have a longer duration than high coupon rate bonds.

What is the significance of the yield-to-call calculation?

If a bond is callable, the yield to call calculation shows what the yield for that time period would be as compared to yield to maturity (which you may never get to) or some other length of time.

explain why some bonds sell at a premium to par value and other bonds sell at a discount. what do you know about the relationship between the coupon rate and the YTM for premium bonds? what about discount bonds? for bonds selling at par value?

If the coupon rate is higher than the required return on a bond, the bond will sell at a premium since it provides periodic income in the form of coupon payments in excess of that required by investors on other similar bonds. If the coupon rate is lower than the required return on a bond, the bond will sell at a discount, since it provides insufficient coupon payments compared to that required by investors on other similar bonds. For premium bonds, the coupon rate exceeds the YTM; and for discount bonds, the YTM exceeds the coupon rate. For bonds selling at par, the YTM is equal to the coupon rate

what is interest rate risk? what are the roles of a bond's coupon and maturity in determining its level of interest rate risk?

Interest rate risk refers to the fact that bond prices fluctuate as interest rateschange. Lower coupon and longer maturity bonds have greater interest rate risk.

How can duration be used to determine a rough measure of the percentage change in the price of a bond as a result of interest rate changes?

Multiply duration times the change in interest rates and reverse the sign. An exact measure is given by using modified duration.

what are premium, discount and par bonds?

Premium bonds are bonds that sell for more than (the same as, less than) their face or par value. Par bonds are bonds that sell the same as their face or par value. Discount bonds are bonds that sell for less than their face or par value.

bond ladder

Purchase an equal amount of bonds over a range of maturities from shortest to longest

suppose you buy a 9% coupon, 15-year bond today when it is first issued. if interest rates suddenly rise to 15%, what happens to the value of your bond? why?

Since the yield increased, the price of the bond will decrease. This can be explained in two ways. First, any new bonds will have a 15% coupon rate in order to sell at par since that is the market interest rate. Investors will pay less for a 9% coupon bond since they can buy a bond with a 15% coupon rate. Second, the decrease in price is a function of the time value of money. The price of the bond is the present value of the coupon payments plus the present value of the principal. In any present value calculation, the present value declines when the interest rate increases.

"It is possible that a bond with a shorter maturity than another bond may actually have a longer duration and be more price sensitive to interest rate changes." Explain why a bond with a shorter maturity than another bond could have a longer duration.

The bond with the shorter maturity may have lower coupon payments and possibly a longer duration. As indicated in the chapter, an eight percent 20 year bond has a longer duration then a twelve percent 25 year bond (based on a 12 percent market rate of interest).

what are coupon rate and current yield on a bond? what happens to these if a bond's price rises?

The coupon rate is the annual dollar coupon expressed as a percentage of face value. The current yield is the annual dollar coupon divided by the current price.If a bond's price rises, the coupon rate won't change, but the current yield will fall.

Why is current yield not a good indicator of bond returns? (Relate your answer to maturity considerations.)

The current yield does not consider the length of time to maturity. A dollar received this year is worth more than dollars received in future years.

What happens to duration as the coupon rate on a bond issue declines from 12% to 0% with the maturity date remaining constant?

The duration increases. Duration and coupon rates are inversely related.

in the united states, what is the normal face value for corporate and US government bonds? how are coupons calculated? how often are coupons paid?

The face value is normally $1,000 per bond. The coupon is expressed as a percentage of face value (the coupon rate), so the annual dollar coupon is calculated by multiplying the coupon rate by $1,000. Coupons are normally paid semi-annually; the semi-annual coupon is equal to the annual coupon divided by two.

Explain the general meaning of the pure expectations theory as it relates to the term structure of interest rates.

The hypothesis is that any long-term rate is an average of the expectation of future short-term rates over the applicable time horizon. Thus, if lenders expect short-term rates to be continually increasing in the future, they will demand higher long-term rates. Conversely, if they anticipate short-term rates to be declining, they will accept lower long-term rates.

the yield to maturity on a bond is

The interest rate that makes the present value of the payments equal to the bond price.

Why is the reinvestment rate assumption critical to bond portfolio management?

The reinvestment rate determines the ultimate value of the portfolio. It may be different from the computed yield on the investment.

Explain the liquidity preference theory as it relates to the term structure of interest rates.

The shape of the term structure of interest rates tends to be upward sloping more than any other pattern. This reflects recognition of the fact that long-term maturity obligations are subject to greater price change movements when interest rates change. Because of the increased risk of holding longer-term maturities, investors demand a higher return to hold longer-term securities relative to short-term securities. This is called the liquidity preference theory of interest rates. Since short-term securities are more easily turned into cash without the risk of large price changes, investors will pay a higher price and receive a lower yield.

What is a bond swap investment strategy? Explain how it might relate to tax planning.

The term "Swap" refers to the procedure of selling out of a given bond position and immediately buying into another one with similar attributes in an attempt to improve overall portfolio return or performance. For tax planning purposes, you might sell a bond on which you have a large loss to offset other income. You then take the proceeds from the sale and reinvest in a bond of equal risk, and you will have increased your total cash returns because of tax benefits.

What is the meaning of term structure of interest rates?

The term structure of interest rates depicts the relationship between maturity and interest rates. It is sometimes called a yield curve because yields on existing securities, having maturities anywhere from three months to 30 years, are plotted on a graph to develop the curve.

Under what circumstances would the yield spread on different classes of debt obligations tend to be largest?

The yield spread represents the difference in returns for different classes of bonds based on ratings. The yield spread tends to be largest when there is a low degree of confidence in the economy as in the early phases of a recession as investors attempt to shift out of low grade securities into strong instruments.

is the yield to maturity (YTM) on a bond the same thing as the required return? is the YTM the same thing as the coupon rate? suppose that today a 10% coupon bond sells at par. two years from now, the required return on the same bond is 8%. what is the coupon rate on the bond now? the YTM?

The yield to maturity is the required rate of return on a bond expressed as an a nominal annual interest rate. For noncallable bonds, the yield to maturity and required rate of return are interchangeable terms. Unlike YTM and required return, the coupon rate is not used as the interest rate in bond cash flow valuation but is a fixed percentage of par over the life of the bond used to set the coupon payment amount. For the example given, the coupon rate on the bond is still 10%, and the YTM is 8%.

How might the market segmentation theory help to explain why short-term rates on government securities increase when bank loan demand becomes high?

When bank loan demand becomes high, banks are likely to partially withdraw from investments in government securities. Since banks are an important part of the short-term side of the market, their reduced demand will likely drive up short-term rates on government securities.

What does an ascending term structure pattern tend to indicate?

When the term structure is in an ascending posture (short-term rates are lower than long-term rates), it is a general signal that interest rates will rise in the future.

Why is it said that zero-coupon bonds lock in the reinvestment rate?

Zero-coupon bonds lock in the reinvestment rate because there is no interest during the life of the bonds to be reinvested. The original yield is effectively the reinvestment rate as long as the bonds are held to maturity.

which of the following is not a property of duration?

a bigger coupon generally yields a longer duration

the interest rate risk of a noncallable bond is most likely to be positively related to the:

bond's time to maturity

How can zero coupon bonds solve target date immunization problems?

buying a zero coupon bond that matures on the horizon date will produce sufficient cash flow regardless of interest rates

immunization

constructing a portfolio to minimize the uncertainty surrounding its target date value

which of the following states the correct relationship among yield measures for discount bonds?

coupon rate < current yield < yield to maturity

which of the following states the correct relationship among yield measures for premium bonds?

coupon rate > current yield > yield to maturity

in which of the following cases is the bond selling at a discount?

coupon rate is less than current yield, which is less than yield to maturity

dedicated portfolio

designed to generate sufficient cash flow in each period to match the series of obligations faced by the investor

duration in a zero coupon bond

duration = maturity

which of the following strategies is most likely to yield the best interest rate risk immunization results for a bond portfolio?

duration matching

another term for bond duration is

effective maturity

what if zero coupon bonds are not available?

find a bond with a duration equal to the horizon date (target date/due date)

yield curve

graphs relationship between yield to maturity for a group of bonds that are similar in every respect except maturity

when are yield to maturity and current yield on a bond equal?

if the coupon and market interest rate are equal

yield to call

is a yield measure that assumes a bond will be called at its earliest possible call date.

yield to maturity

is the discount rate that equates the bond's price with the computed present value of its future cash flows

term structure of interest rates

is the relationship between time to maturity and interest rates for default-free, pure discount instruments, "zero coupon yield curve"

when interest rates decline, what happens to the duration of a 30-year bond selling at a premium?

it increases

which statement is true for the macaulay duration of a zero coupon bond?

it is equal to the bond's maturity in years

duration is always _____ than maturity except for zero coupon bond

less

what is a target date immunization?

matching the duration of a bond portfolio to the due date of the liability. you are hedging interest rate risk

duration

measure's a bond sensitivity to interest rate changes

which of the following states the correct relationship between Macaulay duration and modifies duration?

modified duration = macaulay duration / ( 1 + YTM/2 )

negative butterfly

short end and long end of the curve are going down

positive butterfly

short end and long end of the curve going up

explain why modified duration is a better measure than maturity when calculating the bond's sensitivity to changes in interest rates

takes into consideration coupon rate, YTM and maturity date

the duration of a bond normally increases with an increase in:

term to maturity

Consider a 5 year bond with a 10% coupon selling at a yield to maturity of 8%. If interest rates remain constant, one year from now the price of this bond will be:

will be lower