Risk neutral investor

Most people want paying for taking a chance. A risk averse investor will only take a risky bet if the expected reward is high enough.

A risk neutral investor does not think that way. Risk simply does not enter the decision.

Offered two investments with the same expected return, this investor is indifferent between them. One may be a bank deposit and the other a small cap fund. If the expected return is the same, they are the same choice.

The workbook puts it plainly. The amount of risk is irrelevant to the risk neutral person. Such a person provides no penalty for risk.

There is a neat way to say the same thing with a number. The certainty equivalent rate is the safe return that would feel as good as a risky one. For a risk neutral investor that rate is just the expected return on the risky portfolio. Nothing is knocked off.

The idea is a teaching device more than a description of real people. It marks the middle of a line, with risk aversion on one side and risk seeking on the other.

The definition (section 14.3). A risk neutral investor evaluates investment opportunities solely on the basis of expected return with no regard to risk. The amount of risk is irrelevant to the risk neutral person. The risk neutral person provides no penalty for risk. For a risk neutral investor, the portfolio's certainty equivalent rate is the expected rate of return on the risky portfolio.

Read that last line against the risk averse case. Investors compare the utility value of a risky portfolio with a risk-free investment offering the same utility, which gives the certainty equivalent rate — the rate a risk-free investment has to offer to be equally attractive to the 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. The risk neutral investor does neither: the CER is simply the expected return, unadjusted.

The fair game test. A prospect with a zero risk premium is a fair game. Risk averse investors reject a fair game. A risk seeking investor will engage in one. A risk neutral investor is the boundary between them — with no penalty for risk and no bonus for it either, a zero risk premium leaves them exactly indifferent.

Utility scores. Investors assign utility scores to competing portfolios given expected return and risk. Higher scores go to portfolios with higher expected return, and lower scores to portfolios with higher risk. The second half of that rule is the part a risk neutral investor switches off.

Section 14.3 carries no figures at all — no risk premium percentage, no utility constant, no worked CER. The rupee figures in the example below are illustrative and built on the workbook's stated definitions.

Illustrative figures; section 14.3 gives none.

A government bond yields a certain 7%. An equity fund is expected to return 12%, but the outcome is uncertain: assume 30% for a 34% gain, 50% for a 12% gain and 20% for a 15% loss.

Check the expected return: 0.3(34) + 0.5(12) + 0.2(−15) = 10.2 + 6 − 3 = 13.2%. Call it the fund's expected return.

Now put Rs 20,00,000 in front of three investors.

The risk neutral investor did no arithmetic beyond the expected return. There was no adjustment to make.

Now the sharper test. Offer the same investor a fair game: a coin toss on Rs 20,00,000 that pays +18% or −18% with equal chance, against the risk-free 7%. Expected return on the toss is 0%, so the risk premium is zero.

• The risk averse investor rejects it, as the workbook says.
• The risk seeking investor engages in it, as the workbook says.
• The risk neutral investor compares 0% with 7% and takes the bond — not because the toss is risky, but because 0% is less than 7%.

That is the distinction worth carrying into the exam. Risk neutrality is not recklessness. It is indifference to the spread, with full attention to the average.

Chapter 14 (Introduction to Modern Portfolio Theory), section 14.3, which defines risk averse, risk seeking and risk neutral investors together and is listed as a learning objective for the chapter. Questions are definitional and come in sets: which investor ignores risk entirely, which rejects a fair game, which makes a downward adjustment to utility, and what the certainty equivalent rate equals for a risk neutral investor. The last of those is the one candidates miss.

• For a risk neutral investor the CER equals the expected return on the risky portfolio. Not the risk-free rate, and not something between the two.
• Risk neutral is not risk seeking. A risk neutral investor applies no penalty for risk; a risk seeking investor makes an upward adjustment for it. Indifference is not appetite.
• A fair game has a zero risk premium. The risk averse investor rejects it and the risk seeking investor engages in it. The risk neutral investor is indifferent to the risk, and so decides on the expected return alone.
• Higher utility for higher expected return, lower utility for higher risk. A risk neutral investor keeps the first rule and drops the second.
• Do not confuse this with risk neutral valuation. Risk neutral valuation is a derivative pricing technique; this is a description of an investor's preferences.
• Highly risk averse and less risk averse investors can differ on the same portfolio, because they assign different certainty equivalent rates. Risk aversion is a scale, not a switch.