Risk averse investor
An investor who accepts risk only when paid a positive expected risk premium for it, and who demands a larger premium the greater the risk.
In plain language
Offered two investments with the same expected return, a risk averse investor picks the one with lower risk. Offered a riskier one, she wants to be paid extra for the risk.
The workbook's definition: risk averse investors invest in risk-free opportunities or in opportunities with a positive expected risk premium. The greater the risk, the greater the demand for risk premium.
Risk aversion is not a behavioural flaw. It is one of the core assumptions of standard finance and of Modern Portfolio Theory, and it is what the utility score formula is built on.
How it works
In Modern Portfolio Theory (Chapter 15, sections 15.2–15.3). Investors want to maximise return for a given level of risk: between two assets with equal return, they choose the lower-risk one. They assign utility scores to competing portfolios — higher scores for higher expected return and lower risk.
How the degree of risk aversion is measured. The utility function includes A, an index of the investor's risk aversion:
U = E(r) − ½ × A × σ²
The larger A, the bigger the penalty for risk. The investment is worthwhile if U exceeds the risk-free rate. This is what makes a good portfolio not equally attractive to all investors — unlike the Sharpe ratio, which treats everyone alike.
Elsewhere in the workbook:
- Chapter 1 (section 1.3.1): highly risk averse investors pursue capital preservation, which requires no or minimal risk taking.
- Chapter 14 (section 14.1): "investors are risk averse" is one of the five assumptions of standard finance.
- Prospect theory: people are risk-averse about gains (realising them early) but risk seeking about losses (holding on longer).
The formula
U = E(r) − ½ × A × σ² (decimals)
U = E(r) − 0.005 × A × σ² (whole-number percentages)
Invest if U > risk-free rate
A worked example
Illustrative figures. An equity portfolio offers an expected return of 13% with a standard deviation of 15%. The risk-free rate is 7%. Two clients each have ₹30 lakh.
Nikhil, A = 2: U = 13 − 0.005 × 2 × 15² = 13 − 0.005 × 2 × 225 = 13 − 2.25 = 10.75% → above 7%, invest.
Lata, A = 6: U = 13 − 0.005 × 6 × 225 = 13 − 6.75 = 6.25% → below 7%, do not invest.
Both are risk averse — each penalises risk. The difference is how much. For Nikhil, the portfolio's 6% risk premium (13% − 7%) is ample payment for the risk. For Lata, the same premium is not enough; she would rather hold the risk-free asset, which on ₹30 lakh gives a certain ₹2.1 lakh a year.
The workbook's own example: A = 3, expected return 15%, risk 10%, risk-free 8% → U = 13.5%, which exceeds 8%, so invest.
Why NISM asks about it
Chapter 15 (Introduction to Modern Portfolio Theory), section 15.3, defines the risk averse investor and introduces the utility score; the Chapter 15 caselets test the decision rule. Chapter 15's sample question 5 asks which investors expect higher return for higher risk — answer: risk averse. Chapter 1 links high risk aversion to capital preservation, and Chapter 14 lists risk aversion among the assumptions of standard finance.
Common exam traps
- Investors expecting higher return for higher risk are risk averse — not risk seekers. The sample question turns on this.
- The workbook's section 15.3 heading promises definitions of risk seeking and risk neutral investors, but the text defines only the risk averse investor. Do not expect the workbook to supply the other two.
- Risk aversion ≠ loss aversion. Risk aversion is a standard-finance assumption; loss aversion is a behavioural bias.
- A higher A means more risk averse, and a lower utility for any risky portfolio.
- Prospect theory's risk aversion is about gains only. For losses, people are risk seeking.
Where this is taught
Free preparation for NISM Series XXI-BRelated terms
- Sharpe ratioReturn earned above the risk-free rate divided by standard deviation — how much reward an investment produced for each unit of total risk its holder had to live with.
- Behavioural financeThe study of how psychology shapes the decisions of market participants, individually and in groups, and how those decisions show up as gaps and anomalies in financial markets.
- Prospect theoryKahneman and Tversky's 1979 theory of choice under risk: outcomes are judged as gains or losses from a reference point, and losses hurt more than equal gains please.
- 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.
- 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.
- Capital PreservationAn investment objective of minimising or avoiding any erosion of the principal. Pursued by highly risk-averse investors and by anyone who needs the money in the immediate short term.
- Illiquidity risk premiumThe extra return investors demand for holding an unlisted or thinly traded investment, to compensate for not being able to buy or sell it quickly at a fair, continuously-updated price.
- Risk Aversion IndexThe 'A' in the Markowitz utility formula U = E(r) − 0.5 × A × σ² — a number capturing how heavily an individual investor's utility is penalised for taking on variance.
- Semi varianceA downside-risk measure that looks only at the dispersion of returns below the mean (or a target return), ignoring the upside swings that standard deviation counts equally alongside the downside ones.
- Absolute return objectiveA return goal stated on its own, such as 15% a year, with no comparison to a benchmark — the opposite of a relative return objective.
- BB&K modelA psychographic framework that sorts investors into five personality types — Adventurer, Celebrity, Individualist, Guardian and Straight Arrow — using confidence and carefulness as its two axes.
- 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.
- 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.