• Table of Contents • Introduction • 1-Time Value • 2-Risk/Return • 3-Accounting • 4-Securities • 5-Business • 6-Regulatory • Case Studies • Student Papers

## 2.4.2 Valuing Certainty Equivalents

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>>)

 2.4.1 Valuing Probability Distributions 2.4.3 Adjusting Discount Rates