Another method to value
a range of future results is to find the present
value of their "certainty equivalent."
Return to our example of an investment that will
return either $5 or $12 or $20 after one year,
with an assumed current rate of 6.3% for a risk-free
one-year investment. Perhaps we could determine
the expected value of this investment, and then
determine the equivalent certain amount
this investment is worth, given the variability
of its returns. Once we determine this "certainty
equivalent" we could then compute its present
value -- in effect, the investment's value.
Return |
Probability |
Expected return |
Certainty equivalent |
Present value |
$5 |
33.33% |
$1.67 |
|
$1.67 / (1 + .063) =
$1.57 |
$12 |
33.33% |
$4.00 |
|
$4.00 / (1 + .063) =
$3.76 |
$20 |
33.33% |
$6.67 |
|
$1.67 / (1 + .063) =
$6.27 |
|
Total |
$12.33 |
$11.75 |
$11.75/(1+.063)
= $11.05 |
Notice the expected value is $12.33 -- but given
the variance of returns, we have concluded the
"certainty equivalent" is only $11.75.
And if we are promised a certain $11.75 in one
year, we can compute its present value -- in this
case, by discounting using a risk-free rate of
6.3%. The investment has a risk-adjusted
value of $11.05.
But this method depends on calculating -- really
guessing -- a "certainty equivalent."
For whatever reason, people in the financial world
do not think in terms of certainty equivalence.
Perhaps they should!
|
Example
Pfeifer sues his employer for
workplace negligence. He wins an award of $325,000
as compensation for 12.5 years of lost wages
($26,000 per year). The court refuses to take
into account inflation and award cost-of-living
adjustments, on the theory that "future
inflation shall be presumed equal to future
interest rates with these factors offsetting."
Is this right? How should a court
determine a lump-sum award meant to compensate
an employee for a stream of future lost wages?
( More>>)
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2.4.1 Valuing Probability Distributions