Fair game
An investment opportunity that offers no risk premium at all — an equal chance of gaining or losing, with nothing extra to compensate for the risk taken — which a risk-averse investor is assumed to reject.
In plain language
Taking on risk is normally expected to come with a reward for doing so — a risk premium, extra expected return above what a safe investment would pay. A fair game is the special case where that reward is exactly zero.
A risk-averse investor, the type Modern Portfolio Theory assumes is typical, turns this kind of opportunity down. There is genuine risk here, but no extra return on offer to justify taking it — such an investor would rather hold a genuinely risk-free asset, or a risky one that does carry a positive premium.
A risk-seeking investor behaves the opposite way. This type of investor is willing to engage in a fair game, accepting risk for its own sake even without being paid extra for it.
How it works
The workbook defines the fair game directly: a prospect that has a zero risk premium is called a fair game. Risk-averse investors reject it, preferring either a genuinely risk-free investment or a risky one that offers a positive expected risk premium instead.
The three investor types the workbook builds around this idea: the risk-averse investor rejects a fair game and makes a downward adjustment for utility when facing risk; the risk-neutral investor evaluates opportunities purely on expected return, with no penalty for risk at all, so a fair game and a risk-free asset offering the same expected return look identical; and the risk-seeking investor actively engages in a fair game, making an upward adjustment for the utility of taking on risk.
A worked example
Illustrative. A coin-toss bet offers a 50% chance of winning Rs 10,000 and a 50% chance of losing Rs 10,000 — an expected value of exactly zero, with no extra reward for the risk of playing. This is a textbook fair game.
A risk-averse investor declines the bet outright, preferring to keep the Rs 10,000 with certainty. A risk-neutral investor is indifferent between playing and not playing, since both have the same expected value. A risk-seeking investor takes the bet purely for the thrill of the uncertain outcome, even though the expected payoff promises nothing extra for doing so.
Why NISM asks about it
Chapter 14 (Introduction to Modern Portfolio Theory), section 14.3 (Definition of risk averse, risk seeking and risk neutral investor), defines the fair game and ties it directly to the three investor types. Expect a question defining a fair game, or one describing an investor's behaviour toward a zero-risk-premium bet and asking which investor type it represents.
Common exam traps
- A fair game has zero risk premium, not zero risk. The risk is real; only the extra compensation for bearing it is absent.
- Only a risk-seeking investor accepts a fair game willingly — a risk-averse investor rejects it, and a risk-neutral investor is indifferent, evaluating it purely by its expected return.
- Do not confuse fair game with the Certainty Equivalent Rate — CER is the rate a risk-free investment would need to offer to match a risky portfolio's utility; the fair game is a specific example of a risky prospect with a zero premium.
Check yourself
1.A prospect that has a zero risk premium is called:
- a)A risk-free investment
- b)A fair game
- c)A certainty equivalent
- d)An efficient portfolio
Show the answer
Answer: (b) A fair game
A prospect with a zero risk premium is called a fair game. A risk-free investment carries no risk at all, which is different from carrying risk with no premium. The certainty equivalent rate is the risk-free rate that would make an investor equally happy with a risky portfolio.
2.Which of the following describes a risk seeking investor?
- a)One who rejects a fair game and makes a downward adjustment for utility
- b)One who will engage in a fair game and makes an upward adjustment for utility
- c)One who ignores risk entirely and looks only at expected return
- d)One whose certainty equivalent rate always equals the risk-free rate
Show the answer
Answer: (b) One who will engage in a fair game and makes an upward adjustment for utility
A risk seeking investor is the one who will engage in a fair game, and makes an upward adjustment for utility, unlike a risk averse investor who makes a downward adjustment. Option 1 describes the risk averse investor and option 3 the risk neutral investor.
Where this is taught
Free preparation for NISM Series X-ARelated terms
- Certainty Equivalent RateThe rate a risk-free investment would have to offer to be exactly as attractive to an investor as a given risky portfolio — lower than the expected return for a risk-averse investor.
- Diminishing marginal utility of wealthThe idea, underlying Modern Portfolio Theory, that each additional rupee of wealth adds a little less satisfaction than the rupee before it — the reason most investors are risk averse.
- Expected utilityThe satisfaction score an investor is assumed to assign to each possible outcome of an investment, weighted by the probability of that outcome — the quantity Modern Portfolio Theory assumes investors actually maximise.
- Risk neutral investorAn investor who judges an investment only by its expected return and applies no penalty at all for risk, so the certainty equivalent rate equals the expected return on the risky portfolio.
- Risk seeking investorAn investor who will engage in a fair game — one with zero risk premium — because he makes an upward adjustment to utility for risk, where a risk averse investor makes a downward one.