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A borrowing arrangement where the borrower
issues an IOU to the investor. |
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Treasury Bonds and Notes |
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Corporate Bonds |
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Other Issuers |
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State and Local Governments (Munis) |
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Government Agencies |
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Callable Bonds |
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Convertible Bonds |
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Puttable Bonds |
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Floating Rate Bonds |
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Preferred Stock |
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Allows the issuer to repurchase the bond at a
specified price (call price) before
the maturity date. |
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Frequently, there is a period of call
protection, during which the bonds cannot be called. Such bonds are called deferred callable
bonds. |
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Bondholders get the option to exchange each bond
for a specified number of shares of stock for each bond (conversion ratio). |
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Example: |
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Bond selling at 990; convertible into 40 shares. |
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Current share price = $20; value of converted
shares = $800 (conversion value) -- conversion suboptimal |
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Conversion premium = $990 - 800 = $190. |
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The put bond gives the investor the option to
extend or retire the bond at the call date. |
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If the bonds coupon rate exceeds market yields,
the bondholder will choose to extend |
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If the bonds coupon rate is too low, it will be
optimal to retire the bond and reinvest the proceeds at current yields. |
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Interest payments are tied to some measure of
current market rates. E.g., the
rate might be adjusted annually to Prime plus 2%. |
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However, payments are not adjusted for changes
in the firms financial condition. |
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The risk to the firm is that the yield spread is
fixed over the life of the bond. |
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Preferred stock is equity, because: |
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dividends are paid at the firms discretion |
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payment priority at liquidation is below all
bonds. |
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It resembles debt because: |
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Dividend amounts are fixed, and potentially |
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adjustable like coupon payments. |
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Corporate bonds are subject to potential
default. Therefore, the promised yield is the maximum possible yield to
maturity of the bond, not necessarily the actual yield to maturity. |
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To compensate investors for the possibility of
bankruptcy, a corporate bond must offer a default premium, a differential
between the promised yield and the expected yield to maturity. |
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The default premium depends on : |
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the probability of default |
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the likely loss in the event of default. |
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Assume |
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the probability of default, p, is constant from
year to year, |
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the loss on a bond that defaults equals a
proportion l of the bond's market price in the previous year |
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y = the promised yield-to-maturity |
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y* = the expected yield-to-maturity |
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d = y - y* = default premium |
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Risky bonds may also have to provide a risk
premium. |
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The risk premium is the difference between the
expected yield and the yield on a comparable default-free T-bond. |
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A risk premium is needed only if the bond risk
is not diversifiable. |
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Sinking Funds |
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Limitations on Further Debt issuance |
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Subordination of Further Debt |
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Negative Pledge |
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Dividend Restrictions |
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Collateral |
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Restrictions on Sale and Leaseback |
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A T-period bond with coupon payments of $C per
period and a face value of F. |
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The value of this bond can be computed as the
sum of the present value of the annuity component of the bond plus the
present value of the FV. |
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Normally, bonds pay semi-annual coupons: |
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The bond value is given by: |
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where the first component is, once again, the
present value of an annuity, and y is the bonds yield-to-maturity. |
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If F = $100,000; T = 8 years; the coupon rate is
10%, and the bonds yield-to-maturity is 8.8%, the bond's price is computed
as: |
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= $106,789.52 |
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Consider a 2 year, 10% coupon bond with a $1000
face value. If the bond yield is
8.8%, the price is 50 +
1000/(1.044)4 = 1021.58. |
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Now suppose the market bond yield drops to
7.8%. The market price is now given
by 50 + 1000/(1.039)4
= 1040.02. |
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As the bond yield drops, the bond price rises,
and vice-versa. |
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Yield to Maturity
A measure of the average rate of return on a bond if held to
maturity. To compute it, we define
the length of a period as 6 months, and then calculate the internal rate of
return per period. Finally, we
double the six-monthly IRR to get the bond equivalent yield, or yield to
maturity. |
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Effective Annual Yield
Take the six-monthly IRR and annualize it by compounding. |
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An 8% coupon, 30-year bond is selling at
$1276.76. First solve the following
equation: |
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This equation is solved by r = 0.03. |
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The yield-to-maturity is given by 2 x 0.03 = 6% |
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The effective annual yield is given by (1.03)2
- 1 = 6.09% |
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A 3 year, 8% coupon, $1000 bond, selling for
$949.22 |
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Period Cash flow Present Value |
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9%
11% 10% |
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40 $38.28 $37.91 $38.10 |
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2
40 $36.63 $35.94 $36.28 |
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3
40 $35.05 $34.06 $34.55 |
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4
40 $33.54 $32.29 $32.91 |
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5
40 $32.10 $30.61 $31.34 |
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6 1040 $798.61 $754.26
$776.06 |
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Total $974.21 $925.07 $949.24 |
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The bond is selling at a discount; hence the
yield exceeds the coupon rate. At a
discount rate equal to the coupon rate of 8%, the price would be 1000. Hence try a discount rate of 9%. At 9%, the PV is 974.21, which is too
high. Try a higher discount rate of 11%, with a PV of $925.07, which is too
low. Trying 10%, which is between
9% and 11%, the PV is exactly equal to the price. Hence the bond yield = 10%. |
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If a bond is selling at par, yield = coupon
rate. If the bond sells at a
discount, yield > coupon rate.
Hence the following approximation: |
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The Yield-to-Maturity measure implicitly assumes
that all coupons can be invested at the internal rate of return. |
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An alternative ex-post yield measure can be
computed that takes the actual reinvestment rates. |
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The holding period return differs from the
previous two measures in that it is computed for the actual period of time
that the bond is held. |
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Example:
If a bond is purchased for $1100, pays a coupon of $120 at the end of the
year, and is then sold for $1210, the holding period return = (120 +
1210-1100)/1100 = 20.91% |
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Bonds, like any other asset, represent an
investment by the bondholder. |
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As such, the bondholder expects a certain total
return by way of capital appreciation and coupon yield. |
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This implies a particular pattern of bond price
movement over time. |
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Coupons are paid semi-annually. Hence the bond price would increase at
the required rate of return between coupon dates. |
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On the coupon payment date, the bond price would
drop by an amount equal to the coupon payment. |
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To prevent changes in the quoted price in the
absence of yield changes, the price quoted excludes the amount of the
accrued coupon. |
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Example: An 8% coupon bond quoted at 96 5/32 on
March 31, 1996 would actually require payment of 961.5625 + 0.5(80/2) =
$981.5625 |
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The price appreciation on original issue
discount (OID) bonds is an implicit interest payment. Hence the IRS calculates a price
appreciation and imputes taxable interest income. Additional gains or losses due to market yield changes are
treated as capital gains. |
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Example: An 8% 30 yr. bond issued at 81.071% of
par is sold for 820.95 at the end of the year. If interest income is taxed at 36% and capital gains at 28%,
the tax paid equals 0.36(80 + 811.80 - 810.71) + 0.28(820.95-811.80) =
$31.75.
(YTM at issue = 10%; yearend price using this YTM = 811.80) |
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