What Is the Certainty Equivalent?
Let me explain the certainty equivalent directly: it's the guaranteed return you'd accept right now instead of gambling on a higher but uncertain return later. In other words, it's the sure amount of cash you'd see as equally desirable as a risky asset.
This concept boils down to the guaranteed money an investor like you would take immediately rather than risking for more in the future. It differs from person to person based on risk tolerance—say, a retiree would demand a higher certainty equivalent because they're not keen on jeopardizing their nest egg. It's tied closely to risk premium, which is the extra return you need to pick a risky investment over a safe one.
What Does the Certainty Equivalent Tell You?
Investments have to offer a risk premium to make up for the chance you won't get your money back—the riskier it is, the bigger that premium needs to be above the average return.
Suppose you have a choice between a U.S. government bond at 3% interest and a corporate bond at 8%. If you go for the government bond, that difference in payoff is your certainty equivalent. The company would need to bump its offer above 8% to get you to bite.
If you're a company hunting for investors, use the certainty equivalent to figure out how much extra you need to pay to make the riskier choice appealing. It varies because everyone's risk tolerance is different. In gambling, it's the payoff amount that makes you indifferent between a sure thing and the bet—that's the gamble's certainty equivalent.
Example of How to Use the Certainty Equivalent
You can apply the certainty equivalent to an investment's cash flow. It's the risk-free cash flow you'd equate to a higher but riskier expected cash flow. The formula is: Certainty Equivalent Cash Flow = Expected Cash Flow / (1 + Risk Premium).
The risk premium comes from subtracting the risk-free rate from the risk-adjusted rate of return. Calculate expected cash flow by weighting each possible cash flow by its probability and summing them up.
Here's an example: Imagine you can take a guaranteed $10 million or an option with a 30% chance of $7.5 million, 50% chance of $15.5 million, and 20% chance of $4 million. The expected cash flow is 0.3 × $7.5M + 0.5 × $15.5M + 0.2 × $4M = $10.8 million.
If the risk-adjusted return is 12% and risk-free is 3%, the risk premium is 9%. So, certainty equivalent is $10.8M / (1 + 0.09) = $9.908 million. If you're risk-averse, you'd take any guaranteed offer over $9.908 million.
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