chapter 10. properties & pricing of financial assets properties pricing price sensitivity...
TRANSCRIPT
Chapter 10.Chapter 10.Properties & Pricing of Financial Properties & Pricing of Financial AssetsAssets
Chapter 10.Chapter 10.Properties & Pricing of Financial Properties & Pricing of Financial AssetsAssets
• properties
• pricing
• price sensitivity
• properties
• pricing
• price sensitivity
I. Properties that affect valueI. Properties that affect valueI. Properties that affect valueI. 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
• moneyness• is asset a medium of exchange?• or easily converted to one?• checking account--YES• Tbills--easily converted• real estate--NO
• divisibility/denomination• minimum amount to buy/sell asset• money, bank deposits -- $.01• bonds--$1000 to $10,000• commercial paper--$25,000
• divisibility/denomination• minimum amount to buy/sell asset• money, bank deposits -- $.01• bonds--$1000 to $10,000• commercial paper--$25,000
• 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
• 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
• cash flows• size and timing of promised cash
flows• dividends, interest, face value,
options, resale price
• cash flows• size and timing of promised cash
flows• dividends, interest, face value,
options, resale price
• maturity• time until last cash flow• may be uncertain
• convertibility• asset converts to different assets• convertible bonds
• maturity• time until last cash flow• may be uncertain
• convertibility• asset converts to different assets• convertible bonds
• currency• is cash flow in domestic or foreign
currency?• exchange rates impact value of
cash flows
• currency• is cash flow in domestic or foreign
currency?• exchange rates impact value of
cash flows
• liquidity• how easy is it to sell?• how cheap is it to sell?• Tbills are liquid• real estate is not• related to
-- moneyness
-- reversibility
• liquidity• how easy is it to sell?• how cheap is it to sell?• Tbills are liquid• real estate is not• related to
-- moneyness
-- reversibility
• 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
• 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
• currency risk
-- exchange rates affect value of cash flows• regulatory risk
-- tax treatment changes• risk rises with time horizon
• currency risk
-- exchange rates affect value of cash flows• regulatory risk
-- tax treatment changes• risk rises with time horizon
• complexity• rules governing cash flow size,
timing• complex assets are more difficult
to value
• complexity• rules governing cash flow size,
timing• complex assets are more difficult
to value
• tax treatment• depends on issuer for bonds
-- municipal, Treasury, corporate• depends on holding period
-- for capital gains
• tax treatment• depends on issuer for bonds
-- municipal, Treasury, corporate• depends on holding period
-- for capital gains
II. Pricing of Financial AssetsII. Pricing of Financial AssetsII. Pricing of Financial AssetsII. Pricing of Financial Assets
• basic rule:
price of asset
= present value of
future cash flows
• basic rule:
price of asset
= present value of
future cash flows
problemsproblemsproblemsproblems
• 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
• 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
discount ratediscount ratediscount ratediscount rate
• may include• real interest rate• inflation premium• default premium• maturity premium• liquidity premium• exchange rate risk premium
• may include• real interest rate• inflation premium• default premium• maturity premium• liquidity premium• exchange rate risk premium
Pricing Zero Coupon bondsPricing Zero Coupon bondsPricing Zero Coupon bondsPricing 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
• discount bonds
• pay face value, F, at maturity, N• par value
• purchase price, P• P < F• purchased at a discount
• only one cash flow
example 1example 1example 1example 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?
• Tbill, 90 days to maturity• N = 90/365
• F = $10,000, r = 5%(annual)
• r = yield to maturity
• bond equivalent basis
• what is P?
price =
365daysr1
F
3659005.1
000,10
= $9878.20
example 2example 2example 2example 2
• Tbill, 180 days to maturity
• F = $10,000, P = $9700
• what is r?
• Tbill, 180 days to maturity
• F = $10,000, P = $9700
• what is r?
365daysr1
FP
F365daysr1P
days
3651
P
Fr
days
3651
P
Fr
180
3651
9700
000,10r
= 6.27%
Pricing Coupon BondsPricing Coupon BondsPricing Coupon BondsPricing 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
• 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
exampleexampleexampleexample
• N = 3, coupon rate = 6%
• F = $10,000, P = $9850
• semiannual pmts.
• interest payments• .06(10,000) = $600 per year• $300 every 6 mos.
• N = 3, coupon rate = 6%
• F = $10,000, P = $9850
• semiannual pmts.
• interest payments• .06(10,000) = $600 per year• $300 every 6 mos.
• what is r?
• discount rate where
PV cash flows = $9850
• what is r?
• discount rate where
PV cash flows = $9850
• what are cash flows?• what are cash flows?
6 mos $3001 yr. $3001.5 yrs. $300...
3 yrs $10,300
r solvesr solvesr solvesr solves
63
2
2r1
300,10...
2r1
3002r1
300
2r1
3009850
how to solve?how to solve?how to solve?how to solve?
• trial-and-error
• financial calculator
• spreadsheet
• bond table
• trial-and-error
• financial calculator
• spreadsheet
• bond table
yield/N 3 5 105.50% -$10,136.56 -$10,216.00 -$10,380.68
6% -$10,000.00 -$10,000.00 -$10,000.006.50% -$9,865.69 -$9,789.44 -$9,636.52
7% -$9,733.57 -$9,584.17 -$9,289.38
6% coupon bond, F=$10,0006% coupon bond, F=$10,0006% coupon bond, F=$10,0006% coupon bond, F=$10,000
bond tablebond tablebond tablebond table
• approx r = 6.5%
• r = 6.56%• approx r = 6.5%
• r = 6.56%
notenotenotenote
• P and r are inversely related• P falls as r rises• P rises as r falls• true for ALL debt securities
• P and r are inversely related• P falls as r rises• P rises as r falls• true for ALL debt securities
• 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
• 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
• 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)
• 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)
III. Price SensitivityIII. Price SensitivityIII. Price SensitivityIII. 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
• 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
MaturityMaturityMaturityMaturity
• why?• “stuck” with the yield a longer time• either very good or very bad
• why?• “stuck” with the yield a longer time• either very good or very bad
longer maturity
greater pricesensitivity
Coupon rateCoupon rateCoupon rateCoupon rate
• why?• higher coupon rate, receive more
cash flows sooner
• why?• higher coupon rate, receive more
cash flows sooner
lowercoupon rate
greater pricesensitivity
Level of yieldLevel of yieldLevel of yieldLevel of yield
• increase of 5% to 6% NOT same as
increase of 10% to 11%• 5% to 6% means larger decrease in
bond prices
• increase of 5% to 6% NOT same as
increase of 10% to 11%• 5% to 6% means larger decrease in
bond prices
lowerinitial yield
greater pricesensitivity
• why?• from 5 to 6 is an increase of 20%• from 10 to 11 is an increase of 10%
• why?• from 5 to 6 is an increase of 20%• from 10 to 11 is an increase of 10%
Bond DurationBond DurationBond DurationBond Duration
• measure price sensitivity• taking N, coupon, r into account
• approx. % change in P when r changes by 1 percentage pt.
• measure price sensitivity• taking N, coupon, r into account
• approx. % change in P when r changes by 1 percentage pt.
exampleexampleexampleexample
• 7 year bond, 7% yield, 6% coupon
• 10 year bond, 7.5% yield, 8% coupon
• which bond has greater interest rate risk?
• 7 year bond, 7% yield, 6% coupon
• 10 year bond, 7.5% yield, 8% coupon
• which bond has greater interest rate risk?
generate price changes as yield rises above and below initial level:
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
DurationDurationDurationDuration
= high price - low price
initial price (high r - low r)
D7 = 972 - 919
945 (.075 - .065)= 5.6
= 6.9D10 = 1071 - 1000
1035 (.08 - .07)
• 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
• 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
in general,in general,in general,in general,
higherduration
greater pricesensitivity
why hold a bond with high why hold a bond with high duration?duration?why hold a bond with high why hold a bond with high duration?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
• plan to hold bond until maturity• do not care about price
fluctuations
• believe interest rates are going to fall• big increase in bond price
why hold a bond with low why hold a bond with low duration?duration?why hold a bond with low why hold a bond with low duration?duration?
• plan to sell bond prior to maturity
• believe interest rates are going to rise
• highly risk averse
• plan to sell bond prior to maturity
• believe interest rates are going to rise
• highly risk averse