BOND PRICING. Review of Basic Principles & Another Way of Looking at Bond Prices. Basic Present Value/Future Value. Rearranging gives:. More General Relationship. i = annual nominal rate p = # of periods per year i/p = periodic discount rate n = # of years
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Review of Basic Principles
Another Way of Looking at Bond Prices
i = annual nominal rate
p = # of periods per year
i/p = periodic discount rate
n = # of years
n*p= Total # of periods
Mortgage to Mortgages
In these cases, the annual nominal rate, i, is good enough to rank investments
Only when you are comparing across classes, do you have to worry about controlling for compounding
Matters more at higher yields
paid by the issuer
Is it reasonable to believe that the right discount rate for cash flows received thirty years from now is the same as that for discounting cash flows received in 6 months?
The right answer is “NO” – but traditional bond pricing uses a single discount rate so we will too – for a while.
Note that almost all calculators
Return the periodic discount rate,
r, expressed in % not decimal.
However, EXCEL works in decimal
rates of return, not %.
vary with the Discount Rate in a predictable way
Solve for PV=106.624254
Solve for PV=102.5313
Notice that the investor required yield for cash flows received four years
From now is 8%. However, the required yields for earlier cash flows are
Less than that.
The price calculated this way (106.95) is greater than the price
calculated using a constant 8% (106.62) because the early cash flows
are discounted at lower required yields
These three securities represent very different bundles
of cash flows
It seems unlikely that the market required yield for all three would be the same
With no-arbitrage pricing, the “yield” on these securities will vary reflecting the
Timing of the cash flows and the current yield curve.
Notes: 1) Zero coupon bond is undervalued using the six percent while the
12% coupon is overvalued. This is because all the cash flows from the zero come at t=20 where YTM was 6.27%.
2) Price difference is smaller when cash flows are similar to those of the 6% bond
3) A 6% bond would be perfectly priced (at par).
Note that every 10-year bond has a different YTM because each bond
represents a different combination of elements from the same yield curve.