Chapter 10. Properties & Pricing of Financial Assets 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

what are cash flows? 6 mos $300 1 yr. $300 1.5 yrs. $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 greater price sensitivity longer maturity why? “stuck” with the yield a longer time either very good or very bad

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

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

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 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