On 1 June, I purchased a 7%, $1000 bond that pays interest annually on 1 January – the price of the bond was quoted as
91.25 – my invoice from the broker would show an amount of: $912.50
–
Bond prices are not given in dollar terms but as a
percent of face value – a bond price of $950.94 would be quoted at “95.094”.
The following statements are true of Bond Price
Volatility: Bond yields and prices are inversely related.
Bonds of longer maturity tend to be more volatile.
Bonds of higher
coupon are less price volatile.
For a change in yields, the price % increase due to a decrease in ytm is
larger
than a decrease %
in price due to an increase in ytm.
Wrong answer: the % change in price due to an increase in yields is larger than the % change in
price for an equal decrease in yields.
I expect the following rates on 1 year bonds: now (4%), 1 yr (5%), 2 yrs (5.7%), 3 yrs
(6.2%), 4 yrs (6.5%) – According to the Unbiased (pure) Expectations theory of the yield curve, the rate on a 3 year bond
should be: 4.9%
.
The theory holds that future interest rates are the force of the yield curve; long term interest rates can be expressed
by the average of future short term rates – ie: 4% + 5% + 5.7% = 14.7% / 3 = 4.9%.
Add the rates up to the year before the future
rate and average.
Assume a 7%, 30 year, semiannual pay, $1000 bond is priced at 107. Current Yield = Annual CF / Price;
70 / 1070 = 0.0654
. The YTM (i/y) = N (30) PV (1070) PMT (70) FV (1000) = 6.4659% or 6.47%
.
The True/Correct Yield to
Maturity = 6.47%
.
The Current Yield is the annual cash flow divided by price of bond – it is a weak measure because it ignores both
capital gain/loss and time value.
The YTM is how bonds are quoted – using the calculator inputting years (semiannual inputs same
number as annual), price, annual payments, and the principal.
The True/Correct Yield to Maturity is the same
as the YTM, trick
question.
The Equivalent Taxable Yield for a municipal bond is: The yield on a muni bond that would result in the same after
tax yield as an equivalent taxable corporate bond.
Equivalent Taxable Yield = Tax Exempt Yield / 1Marginal Tax Rate; where Tax
Exempt Yield is the YTM of the bond.
Capital Gains are not exempt from taxes, so if the YTM includes capital gains, yield is in error.
Since marginal tax rate is that of the investor, the equiv taxable yield is different for investors in different tax bracket. State tax not
included in formula. It is not unusual to turn the equation around to find the tax rate that would make the yield on a muni = the yield
on a taxable instrument.
For a bond with a yield of 7%: MacDur is the change in price of the bond if the yield goes to 8%.
If
the change in HPR is 1%, the price change in % will be equal to the duration.
MacDur is the sensitivity of the bond price to the
interest rate – the greater the duration, the greater the change in bond price as yield changes.
A Bond has a DMod of 7.2 years at a
yield of 5%; if the yield goes to 4.7% the change in the bond price will be: %ΔP = MODD * ΔY; 7.2 * .003 = 0.0216%
.
DMod
is measured in basis points; .01% = .0001 = 1 basis point; .1% = .001 = 10 basis points – so you need to change the .3% to .003, or
30 basis points.
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 Spring '09
 Upton
 YTM

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