7/30/2019 342 Chapter 10

1/45

7/30/2019 342 Chapter 10

2/45

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

7/30/2019 342 Chapter 10

3/45

divisibility/denomination

minimum amount to buy/sell asset

money, bank deposits -- $.01

bonds--$1000 to $10,000 commercial paper--$25,000

7/30/2019 342 Chapter 10

4/45

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

7/30/2019 342 Chapter 10

5/45

cash flows

size and timing of promised cashflows

dividends, interest, face value,options, resale price

7/30/2019 342 Chapter 10

6/45

maturity

time until last cash flow

may be uncertain

convertibility asset converts to different assets

convertible bonds

7/30/2019 342 Chapter 10

7/45

currency

is cash flow in domestic or foreigncurrency?

exchange rates impact value ofcash flows

7/30/2019 342 Chapter 10

8/45

liquidity

how easy is it to sell?

how cheap is it to sell?

Tbills are liquid

real estate is not

related to

-- moneyness-- reversibility

7/30/2019 342 Chapter 10

9/45

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

7/30/2019 342 Chapter 10

10/45

currency risk

-- exchange rates affect value ofcash flows

regulatory risk-- tax treatment changes

risk rises with time horizon

7/30/2019 342 Chapter 10

11/45

complexity

rules governing cash flow size,timing

complex assets are more difficultto value

7/30/2019 342 Chapter 10

12/45

tax treatment

depends on issuer for bonds

-- municipal, Treasury, corporate

depends on holding period-- for capital gains

7/30/2019 342 Chapter 10

13/45

II. Pricing of Financial Assets

basic rule:

price of asset

= present value offuture cash flows

7/30/2019 342 Chapter 10

14/45

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

7/30/2019 342 Chapter 10

15/45

discount rate

may include

real interest rate

inflation premium default premium

maturity premium

liquidity premium exchange rate risk premium

7/30/2019 342 Chapter 10

16/45

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

7/30/2019 342 Chapter 10

17/45

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?

7/30/2019 342 Chapter 10

18/45

price =

365daysr1

F

365

9005.1000,10

= $9878.20

7/30/2019 342 Chapter 10

19/45

example 2

Tbill, 180 days to maturity

F = $10,000, P = $9700

what is r?

7/30/2019 342 Chapter 10

20/45

365

days

r1

FP

F365

days

r1P

days

365

1P

F

r

7/30/2019 342 Chapter 10

21/45

days

3651

P

Fr

180

3651

9700

000,10r

= 6.27%

7/30/2019 342 Chapter 10

22/45

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

7/30/2019 342 Chapter 10

23/45

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.

7/30/2019 342 Chapter 10

24/45

what is r? discount rate where

PV cash flows = $9850

7/30/2019 342 Chapter 10

25/45

what are cash flows?

6 mos $3001 yr. $3001.5 yrs. $300

.

.

.

3 yrs $10,300

7/30/2019 342 Chapter 10

26/45

r solves

63

2

2r1

300,10...

2r1

300 2

r1

300

2r1

3009850

7/30/2019 342 Chapter 10

27/45

how to solve?

trial-and-error

financial calculator

spreadsheet bond table

7/30/2019 342 Chapter 10

28/45

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

7/30/2019 342 Chapter 10

29/45

bond table

approx r = 6.5%

r = 6.56%

7/30/2019 342 Chapter 10

30/45

note

P and r are inversely related

P falls as r rises

P rises as r falls true for ALL debt securities

7/30/2019 342 Chapter 10

31/45

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

7/30/2019 342 Chapter 10

32/45

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)

7/30/2019 342 Chapter 10

33/45

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

7/30/2019 342 Chapter 10

34/45

Maturity

why?

stuck with the yield a longer time

either very good or very bad

longermaturity

greaterpricesensitivity

7/30/2019 342 Chapter 10

35/45

Coupon rate

why?

higher coupon rate, receive more

cash flows sooner

lowercouponrate

greaterpricesensitivity

7/30/2019 342 Chapter 10

36/45

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

7/30/2019 342 Chapter 10

37/45

why?

from 5 to 6 is an increase of 20%

from 10 to 11 is an increase of 10%

7/30/2019 342 Chapter 10

38/45

Bond Duration

measure price sensitivity

taking N, coupon, r into account

approx. % change in P when rchanges by 1 percentage pt.

7/30/2019 342 Chapter 10

39/45

example

7 year bond, 7% yield, 6% coupon

10 year bond, 7.5% yield, 8% coupon

which bond has greater interest raterisk?

7/30/2019 342 Chapter 10

40/45

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

7/30/2019 342 Chapter 10

41/45

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)

7/30/2019 342 Chapter 10

42/45

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

7/30/2019 342 Chapter 10

43/45

in general,

higherduration

greaterpricesensitivity

7/30/2019 342 Chapter 10

44/45

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

7/30/2019 342 Chapter 10

45/45

why hold a bond with low

duration?

plan to sell bond prior to maturity

believe interest rates are going torise

highly risk averse