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