6- Valuing Bonds

increases in consumer prices

increase in monetary supply (money + demanded deposits)
- causes a currency devaluation

computed without inflation

computed after inflation

has a downward sloping curve

has a horizontal curve

debt instruments with a coupon and face value and return is determined by interest rate

regular payments before maturity (certain)

amount of money borrowed and paid back at maturity

determined as a percentage of the face value

bonds with only face value (single payment)

bonds with only coupons

bond sold at a price less than face value
- coupon is less than yield to maturity
- increasing value of bond

bond sold at a price greater than face value
- coupon is greatedr than yield to maturity
- declining value of bond

bond sold at a price equal to face value
- coupon equals yield to maturity

yield that an investor recieves if it holds the bond till maturity
- measures the interest rate of a bond
- is the discount rate that explains the bond price

because of default risk, the yield on corporate bonds are higher than those of government bonds

determined by the rates of return prevailing in the financial market
- if the future cash flow is absolutely safe, discount rate is the interest rate of safe securities (US gov debt)
- if the future cash flow is uncertain, discount rate must be the expected rate of return offered by equivalent risk securities

Present Value Bond = PV(annuity of coupon payments)+PV(final payment of principle)

in opposute directions, the higher the interest rate the lower the price
when bond prices fall interest rates rise and when interest rates fall bond prices increase
longer bonds are subjected to increased interest rate fluctuations so theyre more sensative

= coupon income + price change / investment

date of its final payment
- used to know average time to each payment

the weighted average of times to each of the cash payments
- depends on maturity and coupon
it indicates the time necessary for the bonds to repay with the coupons, the capital initially invested
- therefore the higher the coupon the shorter duration (less time needed for coupons to pay back initially invested capital)

direct relationship between bond duration and exposure of price to changes in interest rate, as the longer the duration the greater effect on price of a change in interest rate

presevent value of the cash flow recieved at the time divided by the total present value of the bond

modified duration, measuring the percentage change in bond price for a 1 percentage point change in yield

volatility % = duration/1+yield

the higher the duration the higher the volatility, the higher the interest rate the lower the duration

the relationship between short and long term interest rates
- refers to the spot rates (market interest rates) on bonds with same risk but different lengths of time to maturity

the term structure of spot rates is upward sloping
- interest rates should grow over time (hence upward slope)

P0 = C/(1+y)

y = (Vn/P)^(1/n) - 1

the same commodity must sell at the same price within a well functioning market
- therefore, all safe cash payments delivered on same date must be discounted at the same spot rate

equal to the interest rate on zero coupon bonds
- used to measure the term structure of interest rates

forecasts short term interest rate based on current long term interest rates, it implies that two investment opportunities spread over the same time horizon should have the same yield
- bonds are priced so that sucession of short term bonds = same return as 1 long term bond

- the only reason for an upward sloping term structure is that investors expect short term rates to rise
- the inverse is also true, investors expect short term rates to fall

Risk
- the volatility of long term bonds creates extra risk for investors, who would hold long term bonds only if they offer conpensation of higher return

if inflation is a source of risk for long term investors, borrowers must offer extra incentives if they want investors to lend long
- this we see a steeply upward sloping term structure when inflation is uncertain

= nominal cash flow at t/(1+inflation rate)^t

approx. real interest rate = nominal interest rate - inflation rate

1. peoples willingness to save (supply of capital)
2. opportunities for productive investment opportunities by governments and businesses (the demand for capital)

+ investment opportunities = + real interest rate
- investment opportunities = - real interest rate

a change in the expected inflation rate causes the same proportionate change in the norminal interest rate
- no effect on the required real interest rate

1 + nominal rate = (1 + real rate)(1+i)