1. Chapter 10. Properties & Pricing of Financial Assets
price sensitivity

2. 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

3. divisibility/denomination
minimum amount to buy/sell asset
money, bank deposits -- $.01
bonds--$1000 to $10,000
commercial paper--$25,000

4. 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

5. cash flows
size and timing of promised cash flows
dividends, interest, face value, options, resale price

6. maturity
time until last cash flow
may be uncertain
convertibility
asset converts to different assets
convertible bonds

7. currency
is cash flow in domestic or foreign currency?
exchange rates impact value of cash flows

8. liquidity
how easy is it to sell?
how cheap is it to sell?
Tbills are liquid
real estate is not
related to
-- moneyness
-- reversibility

9. 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 of debt securities

10. currency risk
-- exchange rates affect value of cash flows
regulatory risk
-- tax treatment changes
risk rises with time horizon

11. complexity
rules governing cash flow size, timing
complex assets are more difficult to value

12. tax treatment
depends on issuer for bonds
-- municipal, Treasury, corporate
depends on holding period
-- for capital gains

13. II. Pricing of Financial Assets
basic rule:
price of asset
= present value of
future cash flows

14. problems default risk weight cash flows by likelihood of getting them
maturity may be uncertain
cash flow unknown
timing of cash flows unknown
proper discount rate

15. discount rate may include real interest rate inflation premium
default premium
maturity premium
liquidity premium
exchange rate risk premium

16. 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

17. 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?

18. price =
= $

19. example 2 Tbill, 180 days to maturity F = $10,000, P = $9700
what is r?

21. = 6.27%

22. 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

23. 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.

24. what is r?
discount rate where
PV cash flows = $9850

25. what are cash flows? 6 mos $300 1 yr. $300 1.5 yrs. $300 .

26. r solves

27. how to solve? trial-and-error financial calculator spreadsheet
bond table

28. 6% coupon bond, F=$10,000

29. bond table
approx r = 6.5%
r = 6.56%

30. note P and r are inversely related P falls as r rises
P rises as r falls
true for ALL debt securities

31. 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

32. relationship between r and coupon
if r > coupon
then P < F (discount)
if r < coupon
then P > F (premium)
if r = coupon
then P = F (par)

33. 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 price sensitivity

34. Maturity why? “stuck” with the yield a longer time
greater
price
sensitivity
longer
maturity
why?
“stuck” with the yield a longer time
either very good or very bad

35. Coupon rate why? higher coupon rate, receive more cash flows sooner
lower
coupon
rate
greater
price
sensitivity
why?
higher coupon rate, receive more cash flows sooner

36. Level of yield increase of 5% to 6% NOT same as increase of 10% to 11%
lower
initial
yield
greater
price
sensitivity
increase of 5% to 6% NOT same as
increase of 10% to 11%
5% to 6% means larger decrease in bond prices

37. why?
from 5 to 6 is an increase of 20%
from 10 to 11 is an increase of 10%

38. Bond Duration measure price sensitivity
taking N, coupon, r into account
approx. % change in P when r changes by 1 percentage pt.

39. example 7 year bond, 7% yield, 6% coupon
which bond has greater interest rate risk?

40. generate price changes as yield rises above and below initial level:
7 year bond
10 year bond
yield
6.5% 7%
7.5%
price
$972
$945
$919
yield 7%
7.5% 8%
price
$1071
$1035
$1000

41. Duration high price - low price = initial price (high r - low r)
D7 =
= 5.6
945 ( )
D10 =
= 6.9
1035 ( )

42. 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 price sensitive

43. in general,
greater
price
sensitivity
higher
duration

44. why hold a bond with high duration?
plan to hold bond until maturity
do not care about price fluctuations
believe interest rates are going to fall
big increase in bond price

45. why hold a bond with low duration?
plan to sell bond prior to maturity
believe interest rates are going to rise
highly risk averse