Bond pricing

The title may change as the content is developed. The intent is to show why a bond's price changes inversely with yield. Hopefully, this can be further developed to extend into a graphical definition of duration. Perhaps this can tie-in to reorganize the definitions of duration as shown in Duration - Definitions Refined. Another page can be built from this material- use of PV to determine if an investment is worthwhile. --LadyGeek 03:10, 9 March 2010 (UTC)

Bond price, or the price of any financial instrument for that matter, is the sum of the present value of the cash flows, which is determined by:
 * 1) The present value of the (semiannual) coupon payments
 * 2) The present value of the par or maturity value

The interest rate, or discount rate, that the investor wants from investing in a bond is called the required yield.

Present Value
In order to evaluate a financial investment, prices are referenced as if the amount of invested money is today. The amount of money that must be invested today is called present value. Using the same point in time allows comparison between different financial instruments, e.g. an "apples-to-apples" comparison.

The equation for Present Value can be expressed as :
 * PV = FV * 1 / (1 + i)N or PV = FV * (1 + i)-N
 * where
 * PV is the present value (amount of money today)
 * FV is the future value (amount of money at some point in the future)
 * i is the interest rate
 * N is the number of periods

The graph below is simplified view intended to show the general concept.

Fundamental Property #1
The first important property of present value is that the higher the interest rate (or discount rate ), the lower the present price.

The higher the interest rate today, the less that has to be invested to achieve the same value in the future.

Fundamental Property #2
The second important property of present value is that for a given interest rate (or discount rate), the farther into the future the investment will be received, the lower the present value.

Longer term investments have more time for the interest to accumulate, resulting in fewer dollars that need to be invested.

How to Compare Investments
Present value is used to compare one investment to another. If you are:
 * Purchasing a financial instrument: the higher price will cost more, choose the lower price (and vice-versa if the price is less)
 * Receiving payments from a financial instrument: the higher price means more funds are received, a good choice (and vice versa if the price is less)

p. 25, (3-7) p. 28 (3-10) example of what is the most one would pay

p. 24 (3-6) example of which received interest rate is better

p. 21 (3-4) different times

$140,000 over 3 years or $160,000 over 5 years, weighted costs can be considered like a center of mass in engineering.

Price/Yield Curve
Using the PV property #2, it can be seen that the price of a bond changes in the opposite direction of the yield. p. 53, Exhibit 5-1 in Excel, then add graph

Yield to Maturity
p. 74 p. 94 the yield curve

Distribution Yield vs Yield to Maturity

Duration
p. 187 (graph using center of mass concept for weighted average)