I.  Properties of Financial Assets that affect value

• moneyness
• can asset be used as a medium of exchange, or easily converted to money?
• money--yes
• checking account--yes
• Tbill--easily converted
• real estate--no
• divisibility and denomination
• minimum amount to sell or purchase an asset
• money, deposits -- $.01
• bonds -- $1000 to $10,000
• commercial paper -- $25,000
• reversibility
• cost of investing in asset, then selling it for cash
• deposits -- cost close to zero
• bonds, stocks -- commissions and bid/ask spread of dealers
• costs are small for thick markets (with a lot of buying/selling) but larger for thin markets
• Tbills are a thick market, small company stocks are a thin market
• cash flows
• what cash flows are you promised as owner of this asset?
• dividends, coupon payments, face value payment, resale price, options
• when are the cash flows promised?
• both size and timing of cash flows are important
• maturity
• length of time until final payment
• maturity may be uncertain
• convertibility
• is assets convertible to another type of asset?
• some bonds convertible to stock
• currency
• if cash flow is not in domestic currency, exchange rate fluctuations after value of cash flows in domestic currency
• liquidity
• how easily is the assets converted to cash?
• how easy is the asset to buy/sell?  how cheap is it the asset to buy/sell?
• Treasury securities--very liquid; real estate--not very liquid
• risk/ return predictibility
• risk = variability in return
• most assets have some risk
• investors are risk averse, so must be compensating for taking on risk
• risk of default--not receiving promised cash flows in full and/or on time
• interest rate risk--fluctuations in the interest rate cause the value of assets to fluctuate
• all debt securities carry some interest rate risk
• currency risk--exchange rate fluctuations affect value of nondomestic asset
• regulatory risk--changes in laws affect the tax treatment of asset or prospects of an issuer of assets
• uncertainty increases with time horizon
• complexity
• assets are combinations of simpler assets
• derivative assets with uncertain future cash flows can be difficult to value
• tax treatment
• tax treatment of bond interest income depends on issuer:  municipal, Treasury/U.S. Gov't, corporate
• taxes on capital gains depend on holding period

• Basic rule:  the price of an asset is equal to the present value of expected future cash flows


simple, right?  but this equation is not so simple for assets where

there is some default risk (so promised cash flows must be weighted by the likelihood of receiving them)

the maturity of the asset is uncertain (like with stock, callable bonds, or putable bonds)

the cash flow is unknown (future stock dividends, future resale price, derivatives)

the timing of the cash flows is unknown

where the appropriate discound rate (i.e. interest rate) is not known, which is basically all the time

• The appropriate discount rate may include
• real interest rate
• an inflation premium
• default risk premium
• maturity premium
• liquidity premium
• exchange-rate risk premium
• Pricing zero coupon bonds (also known as discount bonds)
• zero coupon bonds pay out their face value, F (also known as par value) at maturity, N
• and are purchased for some price, P , less than F (hence the bond is sold at a discount)
• this is the simplest pricing case because there is only 1 future cash flow to worry about
• example:
• Treasury bill, 90 days to maturity (N=90/365), F= $10,000, r = 5%
• price = F/[1+r(d/365)] = 10000/[1+(.05)(90/365)] = 9878.20
• so the discount on this bond is about $222.
• example:
• Treasury bill, 180 days to maturity, F = $10,000, P = $9700
• r = (F/P - 1)(365/180) = 6.27%
• note that although this bond has a longer time to maturity than the first example (thus the face value is discounted over a longer period), it is sold at a greater discount, which results in a higher yield to maturity
• Pricing coupon bonds
• coupon bonds pay out their face value at maturity, but also pay interest in between, based on the bond's coupon rate
• in the U.S. most bonds pay interest semiannually (evey 6 months)
• the price of a coupon bond may be greater than, less than, or equal to the face value
• the relationship between P and F depends on how current market interest rates compare to the coupon rate on the bond
• example:
• N=3, coupon = 6%, F = $10,000, P = $9850, semiannual pmts.
• interest payments = .06 x 10,000 x .5 = $300
• use a financial calculator or a bond table to find, r, the yield to  maturity

r	3 years	5 years	10 years	15 years
5.0%	10,275	10,438	10,779	11,047
5.5%	10,137	10,216	10,381	10,506
6.0%	10,000	10,000	10,000	10,000
6.5%	9,866	9,789	9,637	9,525
7.0%	9,734	9,584	9,289	9,080
7.5%	9,604	9,384	8,958	8,663

• since $9866 is closest to 9850, the approximate yield to maturity is 6.5%
• using a calculator or spreadsheet, 6.56%
• there are 3 things to note in the table above
• r and P are inversely related:  the bond price rises and the yield falls, and the bond price falls as the yield rises
• this is true of ALL debt securities:  their value is inversely related to the interest rates
• the size of the price response depends on the maturity of the bond
• the longer the maturity, the larger the price response to a given change in interest rates
• the relationship between yield and coupon rate determine the relationship between price and face value
• if r = coupon rate, then P = F
• if r > coupon rate, then P < F
• if r < coupon rate, then P > F

• if r changes by 1%, how much will the price of a bond change?
• the depends on the characteristics of the bonds
• Factors affecting price sensitivity
• maturity, N
• longer maturity implies greater price sensitivity, or greater interest rate risk
• why?  because you are "stuck" with the yield a longer period of time, which is very good is market interest rates fall, but very bad if market interest rates rise
• coupon rate
• bonds with higher coupon rates are less price sensitive than bonds with lower coupon rates
• why?  because with a higher coupon rate, you are receiving more cash flows sooner, thus the value of the bond is less dependent on the discount rate used (i.e. the interest rate)
• level of yield
• bonds are less price sensitive when yields are higher
• if yields rise from 5% to 6%, then price decrease will be larger than if yields rise from 10% to 11%
• thus the level of the yield is important, as well as the change in the yield
• Measuring price sensitivity
• If we are comparing two bonds with different N, coupon, and r, how do we decide which is more price sensitive?
• use a measure called duration, which is the approximately % change in the price of a bond, when yields change by 1%
• durations combines all three factors into one number, so that any two bonds can be compared
• example
• 7 year bond, 7% yield, 6% coupon   vs.    10 year ond, 7.5% yield, 8% coupon
• F=$1000, which bond has greater interest rate risk?
• to calculate duration of each bond, generate price changes as yield rises above and below their initial levels:

7 year bond yield                   price 6.5%                  $972 7.0%                  $945 7.5%                  $919

10 year bond yield                   price 7.0%                 $1071 7.5%                 $1035 8.0%                 $1000

duration = (high price - low price)/[initial price x (high r - low r)]
D7 = (972 - 919)/[945(.075-.065)] = 5.6
D10 = (1071 - 1000)/[1035(.08-.07)] = 6.9
• the 7-year bond price will change by 5.6% when yields change by 1% (starting at 7%)
• the 10-year bond price will change by 6.9% when yields change by 1% (starting at 7.5%)
• the 10-year bond is more price sensitive since its duration is larger
• When would an investor hold a bond with a high duration?
• If she plans to hold the bond unitl maturity, so price fluctuations do not matter
• If she believes that interest rates are going to fall (thus bond prices will rise)
• When would an investor hold a bond with a low duration?
• If she plans to sell the bond prior to maturity
• If she believes that interest rates may rises in the future
• If she is highly risk averse