chapter 5 (8 in my version) - interest rates and bond valuation

Question 1

coupon rate

Answer 1

= annual coupon / face value

note:
most bonds have face value of $1000
accordingly, it’s very easy to get the coupon
a bond with 10% coupon rate will have annual coupon payments of $100
bond with 15% coupon rate will have annual coupon payments of $150 and so on

another note:
most bonds pay coupon semi-annually
these means the $100 annual coupon payment in the above example of a bond with 10% coupon rate will be paid as two separate $50 payments throughout the year

Question 2

YTM

Answer 2

To determine the value of a bond at a particular point in time, we need to know the number of
periods remaining until maturity, the face value, the coupon, and the market interest rate for bonds with
similar features. This interest rate required in the market on a bond is called the bond’s yield to
maturity (YTM). This rate is sometimes called the bond’s yield for short.

Question 3

interest rate risk for bonds with longer maturity

Answer 3

Intuitively, shorter-term bonds have less interest rate sensitivity because the $1,000 face amount is
received so quickly. For example, the present value of this amount isn’t greatly affected by a small
change in interest rates if the amount is received in, say, one year. However, even a small change in the
interest rate, once compounded for, say, 30 years, can have a significant effect on present value. As a
result, the present value of the face amount will be much more volatile with a longer-term bond.

The other thing to know about interest rate risk is that, like many things in finance and economics, it
increases at a decreasing rate. For example, a 10-year bond has much greater interest rate risk than a 1-
year bond has. However, a 30-year bond has only slightly greater interest rate risk than a 10-year bond.

Question 4

interest rate risk for bonds with lower coupon rates

Answer 4

reason that bonds with lower coupons have greater interest rate risk is essentially the same. As
we discussed earlier, the value of a bond depends on the present value of both its coupons and its face
amount. If two bonds with different coupon rates have the same maturity, the value of the lower-coupon
bond is proportionately more dependent on the face amount to be received at maturity. As a result, its
value will fluctuate more as interest rates change. Put another way, the bond with the higher coupon has
a larger cash flow early in its life, so its value is less sensitive to changes in the discount rate.

Question 5

YTM vs. current yield

Answer 5

bond’s yield to maturity should not be confused with its current yield, which is simply a bond’s annual coupon divided by its price

In the present example, the bond’s annual coupon is $80, and its price is $955.14. Given these numbers, we see that the current yield is $80/955.14 = 8.38 percent,
which is less than the yield to maturity of 9 percent. The reason the current yield is too low is that it only
considers the coupon portion of your return; it doesn’t consider the built-in gain from the price discount.
For a premium bond, the reverse is true, meaning the current yield would be higher because it ignores
the built-in loss.

Question 6

another name for zero coupon bonds

Answer 6

zeroes

Question 7

treasuries vs. munis

Answer 7

Treasury issues, unlike essentially all other bonds, have no default risk because (we hope) the Treasury can always come up with the money to make the payments.

Second, Treasury issues are exempt from state income taxes (though not federal income taxes). In other words, the coupons you receive on a Treasury note or bond are only taxed at the federal level.

State and local governments also borrow money by selling notes and bonds. Such issues are called
municipal notes and bonds, or just “munis.” Unlike Treasury issues, munis have varying degrees of
default risk. The most intriguing thing about munis is that their coupons are exempt from federal income
taxes (though not necessarily state income taxes), which makes them very attractive to high-income,
high–tax bracket investors. Because of this enormous tax break, the yields on municipal bonds are much
lower than the yields on taxable bonds.

Question 8

what do bond ratings measure?

Answer 8

debt ratings are an assessment of the creditworthiness of the corporate issuer. The definitions of creditworthiness used by Moody’s and S&P are based on how likely the firm is to default and the protection creditors have in the event of a default.

It is important to recognize that bond ratings are concerned only with the possibility of default.
Earlier, we discussed interest rate risk, which we defined as the risk of a change in the value of a bond
resulting from a change in interest rates. Bond ratings do not address this issue. As a result, the price of a highly rated bond can still be quite volatile.

Question 9

what are investment-grade ratings?

Answer 9

BBB by S&P or Baa by Moody’s

Question 10

what are crossover or 5b bonds?

Answer 10

Rating agencies don’t always agree. For example, some bonds are known as “crossover” or “5B”
bonds. The reason is that they are rated triple-B (or Baa) by one rating agency and double-B (or Ba) by
another, implying a “split rating.”

Question 11

what are fallen angels

Answer 11

Bonds that drop from investment grade into junk territory

Question 12

what is NCAA

Answer 12

stands for “no coupon at all”

high yield bonds that default even before it comes time to make their first interest payment (i.e. they default before six months after issuance)

Question 13

what is largest securities market in the world?

Answer 13

Most people would guess the New York
Stock Exchange. In fact, the largest securities market in the world in terms of trading volume is the U.S.
Treasury market.

One reason the bond markets are so big is that the number of bond issues far exceeds the number
of stock issues. There are two reasons for this. First, a corporation would typically have only one
common stock issue outstanding, though there are exceptions. However, a single large corporation could
easily have a dozen or more note and bond issues outstanding. Beyond this, federal, state, and local
borrowing is simply enormous. think about how many cities there are in the US and you’ll get the idea.

Question 14

is bond market transparent?

Answer 14

Because the bond market is almost entirely OTC, it has historically had little or no transparency. A
financial market is transparent if its prices and trading volume are easily observed. On the New York
Stock Exchange, for example, one can see the price and quantity for every single transaction. In
contrast, it is often not possible to observe either in the bond market. Transactions are privately
negotiated between parties, and there is little or no centralized reporting of transactions.

Although the total volume of trading in bonds far exceeds that in stocks, only a very small fraction
of the total outstanding bond issues actually trades on a given day. This fact, combined with the lack of
transparency in the bond market, means that getting up-to-date prices on individual bonds can be
difficult or impossible, particularly for smaller corporate or municipal issues.

However, unlike the
situation with bond markets in general, trading in Treasury issues, particularly recently issued ones, is
very heavy. Each day, representative prices for outstanding Treasury issues are reported

Question 15

what is tick size

Answer 15

For historical reasons, Treasury prices are quoted in 32nds. Thus, the bid price on the 8.000 Nov
2021 bond, 135:22, actually translates into , or 135.688 percent of face value. With a $1,000
face value, this represents $1,356.88. Because prices are quoted in 32nds, the smallest possible price
change is . This is called the “tick” size.

Question 16

what is the bellwether bond

Answer 16

last bond listed is often called the “bellwether” bond. This bond’s yield is
the one that is usually reported in the evening news. So, for example, when you hear that long-term
interest rates rose, what is really being said is that the yield on this bond went up (and its price went
down).

Beginning in 2001, the Treasury announced that it would no longer sell 30-year bonds, leaving
the 10-year note as the longest maturity issue sold. However, in 2006, the 30-year bond was resurrected
and once again assumed bellwether status.

Question 17

how do you calculate real interest rates

Answer 17

1 + R = (1 + r) * (1 + h)

R = nominal rate
r = real rate
h = inflation

Question 18

how do you calculate real interest rates

Answer 18

1 + R = (1 + r) * (1 + h)

R = nominal rate
r = real rate
h = inflation

can rearrange the equation (carry out the multiplication via FOIL):

R = r + h + (r * h)

this tells us is that the nominal rate has three components. First, there is the real rate on the
investment, r. Next, there is the compensation for the decrease in the value of the money originally
invested because of inflation, h. The third component represents compensation for the fact that the
dollars earned on the investment are also worth less because of inflation. the r * h component is small so we often drop it; therefore, an approximation is:

R = r + h

Question 19

inferring market’s inflation expectations

Answer 19

look at yield on TIPS relative to yield on normal treasuries

As of July 2008, the real
yield on a 20-year TIPS was about 2 percent and the (nominal) yield on a 20-year Treasury bond was
about 4.6 percent. As a first approximation, one could argue that the differential of 2.6 percent implies
that the market expects an annual rate of inflation of 2.6 percent over the next 20 years

Question 20

fisher effect

Answer 20

A rise in the rate of inflation causes the nominal rate to rise just enough so that the real
rate of interest is unaffected. In other words, the real rate is invariant to the rate of
inflation.

this is just a hypothesis; it may or may not be true

Question 21

term structure of interest rates

Answer 21

the relationship between short-term and long-term interest rates.

To be a little more precise, the term structure of interest rates tells us the nominal
interest rates on default-free, pure discount bonds of all maturities. These rates are, in essence, “pure”
interest rates because they contain no risk of default and involve just a single, lump-sum future
payment. In other words, the term structure tells us the pure time value of money for different lengths
of time.

Question 22

shape of term structure

Answer 22

When long-term rates are higher than short-term rates, we say that the term structure is upward
sloping, and, when short-term rates are higher, we say it is downward sloping. The term structure can
also be “humped.” When this occurs, it is usually because rates increase at first, but then decline at
longer-term maturities. The most common shape of the term structure, particularly in modern times, is
upward sloping, but the degree of steepness has varied quite a bit.

What determines the shape of the term structure? There are three basic components. The first two
are the ones we discussed in our previous section, the real rate of interest and the rate of inflation.

However, the real rate
of interest appears to have only a minor impact on the shape of the term structure.

the prospect of future inflation very strongly influences the shape of the term structure.
Investors thinking about loaning money for various lengths of time recognize that future inflation erodes
the value of the dollars that will be returned. As a result, investors demand compensation for this loss in
the form of higher nominal rates. This extra compensation is called the inflation premium.

If investors believe that the rate of inflation will be higher in the future, long-term nominal interest
rates will tend to be higher than short-term rates. Thus, an upward-sloping term structure may reflect
anticipated increases in the rate of inflation. Similarly, a downward-sloping term structure probably
reflects the belief that the rate of inflation will be falling in the future.

third, and last, component of the term structure has to do with interest rate risk. As we
discussed earlier in the chapter, longer-term bonds have much greater risk of loss resulting from
increases in interest rates than do shorter-term bonds. Investors recognize this risk, and they demand
extra compensation in the form of higher rates for bearing it. This extra compensation is called the
interest rate risk premium. The longer the term to maturity, the greater is the interest rate risk, so
the interest rate risk premium increases with maturity. However, as we discussed earlier, interest rate
risk increases at a decreasing rate, so the interest rate risk premium does as well

Question 23

what changes the real rate of interest

Answer 23

The real rate of interest is the compensation investors demand for forgoing the use of their money. real rate of interest is a function of many factors. For example, consider expected economic
growth. High expected growth is likely to raise the real rate, and low expected growth is likely to lower
it. Also, the real rate of interest may differ across maturities, due to varying growth expectations among other
factors. For example, the real rate may be low for short-term bonds and high for long-term ones because
the market expects lower economic growth in the short term than the long term.

Question 24

yield curve

Answer 24

plots yield vs. maturity

As you probably now suspect, the shape of the yield curve is a reflection of the term structure of
interest rates. In fact, the Treasury yield curve and the term structure of interest rates are almost the
same thing. The only difference is that the term structure is based on pure discount bonds, whereas the
yield curve is based on coupon bond yields. As a result, Treasury yields depend on the same three components
that underlie the term structure—the real rate, expected future inflation, and the interest rate risk
premium

Question 25

what additional factors affect corporate bonds and not treasuries?

Answer 25

consider the possibility of default, commonly called credit risk. Investors recognize that issuers
other than the Treasury may or may not make all the promised payments on a bond, so they demand a
higher yield as compensation for this risk. This extra compensation is called the default risk premium.

lower-rated bonds have higher yields.

remember that a bond’s yield is calculated assuming that all the promised
payments will be made. As a result, it is really a promised yield, and it may or may not be what you will
earn. In particular, if the issuer defaults, your actual yield will be lower. This fact is
particularly important when it comes to junk bonds. Thanks to a clever bit of marketing, such bonds are
now commonly called high-yield bonds, which has a much nicer ring to it; but now you recognize that
these are really high promised yield bonds

recall that munis are mostly tax-free. so, investors demand the extra yield on a taxable bond
as compensation for the unfavorable tax treatment. This extra compensation is the taxability
premium

bonds have varying degrees of liquidity. As we discussed earlier, there are an enormous
number of bond issues, most of which do not trade on a regular basis. As a result, if you wanted to sell
quickly, you would probably not get as good a price as you could otherwise. Investors prefer liquid
assets to illiquid ones, so they demand a liquidity premium on top of all the other premiums we have
discussed. As a result, all else being the same, less liquid bonds will have higher yields than more liquid
bonds

Question 26

summary of factors that affect bond yields

Answer 26

real int. rate

inflation expectations&raquo_space; investors demand inflation premium

interest rate risk&raquo_space; investors demand interest rate risk premium

default risk/credit risk&raquo_space; investors demand default risk premium

taxability&raquo_space; investors demand taxability premium

lack of liquidity&raquo_space; investors demand liquidity premium