What it means
Most of us would rather have a guaranteed $50,000 than a coin-flip for $100,000, even though the two are worth the same on average. A risk neutral person would not mind either way, because they judge options purely by expected value, which is the probability-weighted average of the possible outcomes.
No real person is perfectly risk neutral, but large diversified organisations can come close for small decisions. A big company making a modest bet, where a loss would not hurt it, may sensibly choose by expected value alone.
This is why many corporate finance rules say to accept any project with a positive expected net value. The concept also plays a quieter role in pricing.
Models for options often assume investors are risk neutral, which makes the maths much simpler, and the answer still comes out right because of how the price can be replicated. We return to this idea in the entry on risk-neutral measures.
It helps to compare the three standard attitudes. A risk averse person demands a reward for taking risk, a risk lover will pay to take it, and a risk neutral person asks for no reward at all.
Real markets reward risk, which suggests most investors are risk averse. A common nuance is that risk neutral pricing does not mean that investors in the real world are risk neutral.
It is a mathematical device that produces correct prices without needing to know anyone's attitude to risk. Managers can use the idea as a sanity check on their own decisions.
Ask whether the decision-maker should be risk neutral given the size of the bet relative to the company's resources. If the answer is no, the expected value is only the first step and a margin for the downside is also needed.
In practice
Real-world examples.
Example
A large retailer chooses between two ad campaigns. One gives a certain $400,000 gain and the other has a 50% chance of $900,000 and a 50% chance of a $100,000 loss, which averages $400,000, and management treats them as equal.
Example
An insurance company writes thousands of similar policies. Because it pools so many small risks, it behaves almost risk neutral and prices policies from the expected claims plus costs.
Example
A quantitative analyst at a bank prices an option by assuming a risk neutral world. This lets her discount the expected payoff at the risk-free rate and avoid estimating investors' preferences.
Formula
Calculation
A risk neutral investor values an asset at the discounted expected payoff:
Value = Expected Payoff / (1 + Discount Rate)
Expected Payoff = (probability 1 x payoff 1) + (probability 2 x payoff 2)
Worked example: An asset pays $140 with a 50% chance or $80 with a 50% chance. The discount rate is 10%.
Expected payoff = (0.5 x $140) + (0.5 x $80) = $70 + $40 = $110
Value = $110 / 1.10 = $100
A risk neutral investor would pay up to $100. A risk averse investor would pay less than $100, because they want compensation for the uncertainty.
Compare this with a risk averse buyer. If that investor needs a certain $92 to feel as happy as the gamble, the gap of $100 - $92 = $8 is the compensation they demand for the uncertainty. A risk neutral investor demands none of it.Case study
Seen in the real world.
Greenfield Foods is a fictional food producer deciding whether to test a new product in 50 stores. In this illustrative case, the finance team estimated a 40% chance of a $2,500,000 profit and a 60% chance of a $500,000 loss.
The expected value was (0.4 x $2,500,000) + (0.6 x -$500,000) = $1,000,000 - $300,000 = $700,000. Because the company was large enough that a $500,000 loss would not threaten it, management acted risk neutral and approved the trial.
The team still ran a downside check. They confirmed that even if three such trials failed in a row, the total loss of $1,500,000 would be well within the firm's annual marketing budget, so the risk neutral approach was a fair way to decide.
Watch out
Common mistakes.
- Thinking risk neutral means risk free. A risk neutral person still faces risk but does not ask for compensation for it.
- Assuming risk neutral behaviour is sensible for every decision. A bet that could bankrupt you needs more than an expected value test.
- Confusing risk neutral with risk averse. The first is indifferent to uncertainty, while the second dislikes it.
Questions
People also ask.
Why do finance models assume risk neutrality?
It makes pricing derivatives much simpler, and the resulting prices still work because they can be replicated with traded assets.
Are real investors risk neutral?
Almost never. Markets generally pay a premium for bearing risk, which suggests most investors prefer certainty.
Can a company be risk neutral?
Large, diversified companies can be close to risk neutral on small decisions, but not on bets big enough to threaten the business.
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