Chapter 10.Properties & Pricing of Financial Assets • properties • pricing • price sensitivity
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
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
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
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
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
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
II. Pricing of Financial Assets • basic rule: price of asset = present value of future cash flows
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
discount rate • may include • real interest rate • inflation premium • default premium • maturity premium • liquidity premium • exchange rate risk premium
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
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?
price = = $9878.20
example 2 • Tbill, 180 days to maturity • F = $10,000, P = $9700 • what is r?
= 6.27%
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
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.
what is r? • discount rate where PV cash flows = $9850
6 mos $300 1 yr. $300 1.5 yrs. $300 . . . • what are cash flows? 3 yrs $10,300
r solves
how to solve? • trial-and-error • financial calculator • spreadsheet • bond table
6% coupon bond, F=$10,000
bond table • approx r = 6.5% • r = 6.56%
note • 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
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 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
Maturity • why? • “stuck” with the yield a longer time • either very good or very bad greater price sensitivity longer maturity
Coupon rate lower coupon rate greater price sensitivity • why? • higher coupon rate, receive more cash flows sooner
Level of yield 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
why? • from 5 to 6 is an increase of 20% • from 10 to 11 is an increase of 10%
Bond Duration • measure price sensitivity • taking N, coupon, r into account • approx. % change in P when r changes by 1 percentage pt.
example • 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: 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
Duration high price - low price = initial price (high r - low r) 972 - 919 D7 = = 5.6 945 (.075 - .065) 1071 - 1000 D10 = = 6.9 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
in general, greater price sensitivity higher duration
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
why hold a bond with low duration? • plan to sell bond prior to maturity • believe interest rates are going to rise • highly risk averse
