Risk seeking investor

Ask most investors to toss a coin for a large sum, with nothing extra offered for the trouble, and they will decline. The odds are even, so there is no reward for the worry.

A bet with no reward for its risk has a special name. The workbook calls it a fair game, meaning the risk premium is zero.

A risk averse investor rejects a fair game. A risk seeking investor takes it.

The reason is how the two treat risk when scoring a choice. The risk averse investor knocks something off for risk. The risk seeking investor adds something on.

So for this investor the spread of outcomes is not a cost. It is part of the attraction.

In between the two sits the risk neutral investor, who neither adds nor subtracts. Those three positions are the whole of the workbook's classification, and every later idea about risk premiums rests on it.

The definition (section 14.3). A risk seeking investor is the one who will engage in a fair game. Such investors make an upward adjustment for utility, unlike a risk averse investor who makes a downward adjustment for utility.

Unpack the two halves, because each is separately examinable.

Fair game. The presence of risk means more than one outcome is possible. Investors demand a risk premium for bearing risk, and whether a given risk premium is adequate is described as a central theme in investment management. A prospect that has a zero risk premium is a fair game. Risk averse investors reject a fair game and will invest only in risk-free opportunities or in opportunities with a positive expected risk premium; the greater the risk, the greater their demand for premium.

Utility adjustment. Investors assign a utility score to competing portfolios given expected return and risk. Higher utility scores go to portfolios with a better risk-return profile — higher scores for higher expected return, lower scores for higher risk. A risk seeking investor reverses the sign of that second rule for himself, which is what an upward adjustment for utility means.

The certainty equivalent consequence. The certainty equivalent rate is the rate a risk-free investment must offer to be equally attractive to a risky one. A highly risk averse investor may assign a risky portfolio a CER below the risk-free rate and reject it. A less risk averse investor may assign a higher CER and accept the same portfolio. For a risk neutral investor the CER is the expected return itself. The workbook does not state the risk seeking case, so do not assume a number for it — the safe reading is only that a risk seeker will accept prospects that a risk averse investor will not, including a fair game.

Section 14.3 carries no figures — no risk premium threshold, no utility constant, no worked example. The rupee figures below are illustrative.

Illustrative figures; section 14.3 gives none.

Three investors are each offered the same two choices on Rs 15,00,000.

Choice 1 — the risk-free option. A deposit paying a certain 7%, so Rs 16,05,000 at the end of the year.

Choice 2 — a fair game. An equal chance of +24% or −24%. Expected return is 0.5(24) + 0.5(−24) = 0%, so the risk premium over a 0% baseline is zero. The two outcomes are Rs 18,60,000 or Rs 11,40,000 — a swing of Rs 7,20,000.

Now make the bet slightly worse than fair. Same swing, but the odds tilt: 45% chance of +24% and 55% chance of −24%. Expected return = 0.45(24) + 0.55(−24) = 10.8 − 13.2 = −2.4%, an expected loss of Rs 36,000.

A risk averse investor rejects this even more firmly. A risk neutral investor rejects it too, because −2.4% is worse than 0%. The risk seeking investor may still take it, because the upward adjustment he makes for the risk itself can outweigh a negative expected return.

That is the practical warning for an adviser. A client who takes fair games is not simply optimistic about returns. He is being paid, in his own utility, by the volatility — which is precisely why risk profiling has to measure both the willingness and the ability to bear loss. Rs 11,40,000 is the real outcome half the time, whatever the client feels about it.

Chapter 14 (Introduction to Modern Portfolio Theory), section 14.3, which the chapter's learning objectives name directly: definition of risk averse, risk seeking and risk neutral investor. The classic question gives the fair game and asks who accepts it. The second most common asks which investor makes an upward adjustment to utility and which a downward one. Section 14.3 also supplies the fair game, risk premium, utility score and certainty equivalent rate definitions that the same question set draws on.

• A fair game has a zero risk premium. It does not mean an even chance of gain and loss in general, and it does not mean the bet is honest.
• Risk averse investors reject a fair game; risk seeking investors engage in it. These are the workbook's own words and the exam uses them.
• Upward adjustment for the risk seeker, downward for the risk averse investor. The direction is the whole distinction.
• Risk seeking is not risk neutral. A risk neutral investor applies no penalty for risk; a risk seeker applies a bonus. Three positions, not two.
• The workbook does not give the risk seeker's certainty equivalent rate. It gives the highly risk averse case (CER below the risk-free rate), the less risk averse case and the risk neutral case. Do not invent the fourth.
• Higher risk always lowers a portfolio's utility score in the general rule. The risk seeker is the exception the workbook names, not a restatement of the rule.