Fixed Income Securities
Fixed Income Securities, FIRE 314, Fall 2009
THE GOLDEN RULE OF VALUATION
The Golden Rule of valuation for all assets is:
Equivalent assets should have equivalent prices
.
A simpler version of this is the “Law of one Price” from economics: the same asset should not sell for
two different prices.
But often we must value assets that are dissimilar in many ways, but still
equivalent, so that the dollar values will be different.
The easy example is a difference in size.
Consider
two annuities:
one of $10, one of $100.
Assume the timing and risk of both annuities is the same.
How
can we apply the Golden Rule in such cases?
The approach is to find the rate of return required of annuities of the given level of risk.
Then, equivalent
price means the price that will result in both assets having the same rate of return.
So, we could restate
the Golden Rule as:
Equivalent assets should have the same rate of return.
The “equivalent price” found by equating the rates of return of equivalent assets is sometime called the
intrinsic value
or the economically justified price.
For the moment we will assume that the “required rate of return” is known.
Once we get a feel for how
assets are valued
given
the required rate, we will turn to a discussion of risk and the required rate.
BOND VALUATION AND YIELD
VALUATION IMMEDIATELY AFTER PAYMENT DATE
From the above discussion of time value, the
intrinsic value
of a bond is the present value of the cash
flows at the required rate of return:
EXAMPLE:
What is the value of a 20 year, 10%, annual pay bond, if the
true annual yield
to similar bonds is
10.6%?
Using the calculator, we can find the present value of the cash flows at a rate of 10.6%.
On an HP-12C, you would enter: 20 = N, 10.6 = %I, 100 = PMT, 1000 = FV
On a Texas Instruments BA-35 calculator, you would enter: 20 = N, 10.6 = %I, 100 = PMT,
1000 = FV, CPT = PV.
This gives the value of the bond as $950.94.
Bonds prices are generally not given in dollar terms but rather as a per cent of face value.
This bond
would typically be quoted as “95.094.”
ACCRUED INTEREST
The seller of the bond is probably not a total dummy, however, and will want his/her share of the next
interest payment.
Thus, bond prices are understood to include payment of accrued interest (unless
specifically said to be trading "flat").
You get this back, since you get all of the next interest payment.
The method of computing accrued interest differs between corporate (360 day year of twelve 30 day
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