Expected utility
The 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.
In plain language
Modern Portfolio Theory does not assume investors simply chase the highest return. It assumes something a little more careful: investors weigh a mix of outcomes and their odds, and score how satisfied each combination would leave them.
That score is utility. Expected utility is the utility score, averaged across every possible outcome, each weighted by how likely it is. The theory's core assumption is that an investor picks whichever investment gives the highest expected utility — not necessarily the highest expected return on its own.
Higher utility scores go to portfolios with a better mix of return and risk: more expected return raises the score, more risk lowers it. This is what ties expected utility back to why risk matters to an investor at all.
How it works
The workbook lists maximising one-period expected utility as a core assumption of Modern Portfolio Theory: investors choose the action with the maximum expected utility, and assign utility scores to the various portfolio choices in front of them. Utility curves feed into this from another assumption, diminishing marginal utility of wealth — the shape of an investor's utility curve is what decides how much a given amount of risk actually costs them in utility terms.
The workbook does not attach a formula to expected utility itself, but it does work numerically with the closely related idea of expected return: for two stocks A and B, across boom, normal and recession states with probabilities 0.3, 0.5 and 0.2, RA = 0.3(15%) + 0.5(10%) + 0.2(2%) = 9.9% and RB = 0.3(25%) + 0.5(20%) + 0.2(1%) = 17.7%. Expected utility applies this same probability-weighted logic, but scores the satisfaction an investor gets from each outcome rather than the return figure alone — which is exactly why a highly risk-averse investor can rationally prefer Stock A's lower 9.9% return over Stock B's higher 17.7%, if B's risk is high enough.
A worked example
Illustrative utility scores, using the workbook's own stock A and B returns as the outcomes. Suppose an investor scores utility from 0 to 100. For Stock A, expected return 9.9%, she assigns a utility score of 70 — a modest, low-risk outcome she is comfortable with. For Stock B, expected return 17.7% but with much wider swings between the boom and recession states, she assigns a utility score of only 55, because the higher average return does not compensate her enough for the wider range of outcomes.
Even though Stock B has the higher expected return, this investor picks Stock A, because it has the higher expected utility — the whole point of the assumption.
Why NISM asks about it
Chapter 14 (Introduction to Modern Portfolio Theory), section 14.2 (Assumptions of the theory), lists expected utility maximisation as a founding assumption, and section 14.4 works the RA/RB expected-return example that the same utility logic is built on. Expect a conceptual question on what MPT assumes investors maximise, or one testing why two investors can rank the same two investments differently.
Common exam traps
- Expected utility is not the same as expected return. An investment with a lower expected return can still have higher expected utility for a risk-averse investor, once risk is priced into the utility score.
- The workbook gives a worked expected return calculation (RA, RB), not a worked expected utility formula — do not present a fabricated utility formula as the workbook's own.
- This assumption sits on top of diminishing marginal utility of wealth — the two are linked, not interchangeable labels for the same idea.
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.
- 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.
- Probability distribution of expected returnsThe list of returns an investment might deliver, each with the chance of it happening — the form in which Modern Portfolio Theory assumes an investor sees every investment choice.
- 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.
- Expected Portfolio ReturnThe weighted average of the expected returns of the holdings in a portfolio, each weight being that asset's share of portfolio value — the return half of Modern Portfolio Theory.