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7/30/2019 342 Chapter 10
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I. Properties that affect value
moneyness
is asset a medium of exchange?
or easily converted to one? checking account--YES
Tbills--easily converted
real estate--NO
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divisibility/denomination
minimum amount to buy/sell asset
money, bank deposits -- $.01
bonds--$1000 to $10,000 commercial paper--$25,000
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reversibility
cost of buying asset, then selling it
deposits--near zero
stocks--commissions costs low for thick markets
-- Tbill market
costs higher for thin markets-- small company stocks
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cash flows
size and timing of promised cashflows
dividends, interest, face value,options, resale price
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maturity
time until last cash flow
may be uncertain
convertibility asset converts to different assets
convertible bonds
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currency
is cash flow in domestic or foreigncurrency?
exchange rates impact value ofcash flows
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liquidity
how easy is it to sell?
how cheap is it to sell?
Tbills are liquid
real estate is not
related to
-- moneyness-- reversibility
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risk/return predictibility
risk = variability in return
investors are risk averse
default risk--not receiving cash flows
interest rate risk
--changes in rates affect value ofdebt securities
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currency risk
-- exchange rates affect value ofcash flows
regulatory risk-- tax treatment changes
risk rises with time horizon
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complexity
rules governing cash flow size,timing
complex assets are more difficultto value
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tax treatment
depends on issuer for bonds
-- municipal, Treasury, corporate
depends on holding period-- for capital gains
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II. Pricing of Financial Assets
basic rule:
price of asset
= present value offuture cash flows
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problems
default risk
weight cash flows by likelihood ofgetting them
maturity may be uncertain
cash flow unknown
timing of cash flows unknown
proper discount rate
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discount rate
may include
real interest rate
inflation premium default premium
maturity premium
liquidity premium exchange rate risk premium
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Pricing Zero Coupon bonds
discount bonds pay face value, F, at maturity, N
par value
purchase price, P
P < F
purchased at a discount only one cash flow
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example 1
Tbill, 90 days to maturity
N = 90/365
F = $10,000, r = 5%(annual) r = yield to maturity
bond equivalent basis
what is P?
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price =
365daysr1
F
365
9005.1000,10
= $9878.20
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example 2
Tbill, 180 days to maturity
F = $10,000, P = $9700
what is r?
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365
days
r1
FP
F365
days
r1P
days
365
1P
F
r
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days
3651
P
Fr
180
3651
9700
000,10r
= 6.27%
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Pricing Coupon Bonds
Pay face value at maturity
pay interest based on coupon rate
every 6 months Price may be face value
depends on coupon rate vs.
market interest rates
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example
N = 3, coupon rate = 6%
F = $10,000, P = $9850
semiannual pmts. interest payments
.06(10,000) = $600 per year
$300 every 6 mos.
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what is r? discount rate where
PV cash flows = $9850
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what are cash flows?
6 mos $3001 yr. $3001.5 yrs. $300
.
.
.
3 yrs $10,300
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r solves
63
2
2r1
300,10...
2r1
300 2
r1
300
2r1
3009850
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how to solve?
trial-and-error
financial calculator
spreadsheet bond table
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yield/N 3 5 10
5.50% -$10,136.56 -$10,216.00 -$10,380.68
6% -$10,000.00 -$10,000.00 -$10,000.00
6.50% -$9,865.69 -$9,789.44 -$9,636.527% -$9,733.57 -$9,584.17 -$9,289.38
6% coupon bond, F=$10,000
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bond table
approx r = 6.5%
r = 6.56%
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note
P and r are inversely related
P falls as r rises
P rises as r falls true for ALL debt securities
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size of change in P depends on N
as r rises, P falls
how much?
-- for greater N, P falls a lot-- for smaller N, P falls a litte
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relationship between r and coupon
if r > couponthen P < F (discount)
if r < coupon
then P > F (premium)
if r = coupon
then P = F (par)
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III. Price Sensitivity
price volatility, interest rate risk
if r changes by 1 percentage pt.,
how much does P change? a lot (bond is sensitive)
a little (bond is not sensitive)
several factors affect pricesensitivity
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Maturity
why?
stuck with the yield a longer time
either very good or very bad
longermaturity
greaterpricesensitivity
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Coupon rate
why?
higher coupon rate, receive more
cash flows sooner
lowercouponrate
greaterpricesensitivity
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Level of yield
increase of 5% to 6% NOT same as
increase of 10% to 11%
5% to 6% means larger decreasein bond prices
lowerinitialyield
greaterpricesensitivity
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why?
from 5 to 6 is an increase of 20%
from 10 to 11 is an increase of 10%
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Bond Duration
measure price sensitivity
taking N, coupon, r into account
approx. % change in P when rchanges by 1 percentage pt.
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example
7 year bond, 7% yield, 6% coupon
10 year bond, 7.5% yield, 8% coupon
which bond has greater interest raterisk?
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generate price changes as yield rises
above and below initial level:
7 year bond 10 year bond
yield6.5%7%7.5%
yield7%7.5%8%
price$972$945$919
price$1071$1035$1000
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Duration
= high price - low priceinitial price (high r - low r)
D7 =972 - 919
945 (.075 - .065)= 5.6
= 6.9D10 =1071 - 1000
1035 (.08 - .07)
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7 year bond price fall by approx. 5.6%,
when yield rises from 7% to 8% 10 year bond price fall by approx.
6.9%,
when yield rises from 7.5% to 8.5%
so 10-year bond is more pricesensitive
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in general,
higherduration
greaterpricesensitivity
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why hold a bond with high
duration?
plan to hold bond until maturity
do not care about pricefluctuations
believe interest rates are going to fall
big increase in bond price
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why hold a bond with low
duration?
plan to sell bond prior to maturity
believe interest rates are going torise
highly risk averse
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