One possible method would be to estimate the
relative probability of different future possibilities
and then discount them to present value. For example,
if we believed it was equally likely that an investment
after one year would produce either $5 or $12
or $20, and the current rate for a risk-free one-year
investment were 6.3%, we could compute the investment's
present value:
Return |
Probability |
Expected return |
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 |
$11.60 |
But this method depends on estimating the probabilities
of many different results. If you assume a different
probability distribution (let's say, 50-25-25)
the expected returns change, and the present value
is $9.88 -- a significantly lower valuation.
In addition, and more problematic, this method
does not take into account the variability of
returns (the dispersion of the return distribution).
If we assume an investment with returns more concentrated
around the mean, but with the same overall expected
return, we get the same present value.
Return |
Probability |
Expected return |
Present value |
$10 |
33.33% |
$3.33 |
$3.33 / (1 + .063) =
$3.14 |
$12 |
33.33% |
$4.00 |
$4.00 / (1 + .063) =
$3.76 |
$15 |
33.33% |
$5.00 |
$5.00 / (1 + .063) =
$4.70 |
|
Total |
$12.33 |
$11.60 |
But this cannot be right. We know that risk averse
investors will value less variable returns more
highly. There has to be some way to take into
account risk volatility. |
2.4 Relationship of Risk and Return