Certainty Equivalent Rate
Also written CER · Certainty equivalent
The 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.
In plain language
Offer a client two choices: a risky portfolio expected to earn 12%, or a completely safe deposit. At what safe rate would the client stop caring which one they get?
That rate is the Certainty Equivalent Rate (CER). The workbook defines it as the rate that a risk-free investment has to offer to be equally attractive with a risky investment. Investors are assumed to compare the utility value of a risky portfolio with a risk-free investment offering the same utility.
The CER is personal. It depends on how much the investor dislikes risk. Two investors looking at the same portfolio, with the same expected return and the same risk, can put very different CERs on it — which is why the same product can suit one client and be wrong for another.
How it works
The background (Chapter 14). Modern Portfolio Theory assumes investors maximise one-period expected utility, assign utility scores to portfolio choices, and base decisions solely on expected return and risk. Higher expected return raises the utility score; higher risk lowers it. Utility curves show diminishing marginal utility of wealth — each extra rupee adds less utility than the one before.
Three kinds of investor, three CERs:
| Investor | Attitude to risk | CER of a risky portfolio |
|---|---|---|
| Risk averse | Demands a risk premium; rejects a fair game; adjusts utility downward for risk | Below the portfolio's expected return. A highly risk-averse investor may put it below the risk-free rate and reject the portfolio; a less risk-averse investor assigns a higher CER and may accept it |
| Risk neutral | Judges solely on expected return; provides no penalty for risk | Equal to the expected rate of return on the risky portfolio |
| Risk seeking | Will engage in a fair game; adjusts utility upward for risk | (Implied) above the expected return |
A fair game is a prospect with a zero risk premium. Risk-averse investors reject it; risk-seeking investors engage in it.
The decision rule that follows. Compare the CER with the rate actually available on a risk-free investment. If the investor's CER for the risky portfolio is below the risk-free rate, the safe investment is preferred and the risky portfolio is rejected. If it is above, the risky portfolio is preferred.
A worked example
Illustrative figures — the workbook gives the concept, not numbers.
A balanced portfolio has an expected return of 12%. A risk-free investment currently pays 7%. Four clients assess the portfolio.
| Client | Profile | CER they assign | Compared with 7% risk-free | Decision |
|---|---|---|---|---|
| Mrs Joshi, 68, retired | Highly risk averse | 5% | Below | Rejects the portfolio |
| Mr Rao, 45 | Moderately risk averse | 8.5% | Above | Accepts |
| A risk-neutral investor | Ignores risk | 12% — the expected return | Above | Accepts |
| A risk seeker | Enjoys the gamble | Above 12% | Above | Accepts eagerly |
Take Rs 10,00,000 invested for a year. The portfolio is expected to end at Rs 11,20,000 but might well end lower. For Mrs Joshi, that uncertain prospect is worth no more to her than a certain Rs 10,50,000 — a 5% certainty. The safe option offers a certain Rs 10,70,000. She is right to take it, and an adviser who pushes the 12% portfolio on her is ignoring her own valuation of the risk.
For Mr Rao the same uncertain prospect is worth a certain Rs 10,85,000. The safe option gives him only Rs 10,70,000, so for him the risky portfolio is the better choice.
Same portfolio, same numbers, opposite correct answers. That is the whole job of the concept, and it is why risk profiling comes before product selection.
Why NISM asks about it
Chapter 14 (Introduction to Modern Portfolio Theory), section 14.3 on risk averse, risk seeking and risk neutral investors, with the MPT assumptions on utility in 14.2. Expect definition questions — what the CER is, what a risk-neutral investor's CER equals (the expected return), what a fair game is (zero risk premium) and who rejects it (the risk averse).
Common exam traps
- CER is a risk-free rate equivalent, not an expected return. It is what a certain return would have to be to match the risky one in the investor's eyes.
- For a risk-neutral investor, CER = expected return of the risky portfolio. Risk neutrals provide no penalty for risk.
- A highly risk-averse investor may put the CER below the risk-free rate and reject the risky portfolio altogether.
- A fair game has zero risk premium. Risk-averse investors reject it; risk seekers engage in it.
- Risk averse = downward utility adjustment; risk seeking = upward. Questions swap the directions.
- CER differs by investor for the same portfolio. It is a property of the investor's attitude, not of the portfolio alone.
Check yourself
1.For a risk neutral investor, the certainty equivalent rate of a risky portfolio is:
- a)The risk-free rate of return
- b)The expected rate of return on the risky portfolio
- c)Zero, since risk is irrelevant
- d)The risk-free rate plus half the risk premium
Show the answer
Answer: (b) The expected rate of return on the risky portfolio
The workbook states plainly: for a risk neutral investor, portfolio CER is the expected rate of return on the risky portfolio. He evaluates opportunities solely on the basis of expected return with no regard to risk and provides no penalty for risk, so he applies no discount to the expected return.
2.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.
Where this is taught
Free preparation for NISM Series X-ARelated terms
- Risk premiumThe extra return an investor demands over the nominal risk-free rate as compensation for uncertainty about future cash flows — the last and largest block in the required rate of return.
- Fair gameAn 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.
- Modern Portfolio TheoryMarkowitz's framework for building portfolios on expected return and risk together, in which the co-movement between holdings — not their individual riskiness — decides the risk of the whole.
- Risk averse investorAn investor who accepts risk only when paid a positive expected risk premium for it, and who demands a larger premium the greater the risk.
- 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.
- Utility scoreA single number that scores an investment for one particular investor: expected return minus a penalty for risk, scaled by that investor's own risk aversion.
- Decumulation or spending phaseThe stage of a person's financial life, usually after retirement, when living expenses are paid from accumulated investments and retirement savings rather than from a salary.
- 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.