Investor with the Higher risk aversion Question

The Investor with the higher risk aversion is most likely to have a?

A) Steeper capital allocation line

B) Lower expected return

Thank you

Higher risk aversion means the investor gets less utility from risk, hence requires more return for the given level of risk. So B is out and A is the right answer, since steeper capital allocation line means higher return for given risk.

Thank you

Welcome! and good luck! :wink:

I may have misunderstood the question, but wouldn’t a person with a high risk aversion put most of its money in a risk free asset, thus having a lower expected return (at least in most cases)?

This was my thought too when I saw that question on one of the mocks.

Shauncore: Do you happen to know what the answer on the mock was? Or which mock it was? :slight_smile:

Guys, unfortunately could not find text in official curriculum, so let me back my answer with other resources.

A word file here (though not official one) contains a plot on the second page and some text after it. I’m quoting the text below, where A is denoted as a risk-aversion measure. “Note that the greater the value of A, the more return is required for a given increase in risk for the investor to be indifferent between a risky asset and the risk-free. In other words, the red line for A = 4 is above the blue line for A = 3. The more risk averse investor (A = 4) requires more return for a given level of risk.”

Since the more risk averse investor requires more return for a given level of risk, the curve will be steeper.

Other source (official one): Economic Synopses, 2007, number 19, by Hui Guo, PhD, University of Cincinnati “For a given level of stock market volatility, the more risk-averse investors are, the higher the expected equity premium must be for them to hold stocks in their portfolios.”

Another source: material from official website of Florida International University “risk aversion — all else equal, risk averse investors prefer higher returns to lower returns as well as less risk to more risk; thus, risk averse investors demand higher returns for investments with higher risk.”

Hope this will bring some clarity.

Found the mock exam that Shauncore may have referred to, whereby they are saying: Basically they are saying that if you compare two hypothetical investors (A and B). Investor A has a low risk aversion coefficient (see: A) and investor B has a large risk aversion coefficient, thus investor B has a lower risk tolerance when compared to A. So investor B (the one who is not keen of risk) will have a lower expected return on CAL.

More information: question 115 mock exam 2017, CFA on the candidate resource page or section 3.3 Portfolio Risk and Return Part 1.

So my question is, wouldn’t we all prefer to put or money in the asset that give us the most return per level of risk (read: highest Sharpe ratio and steepness)? However, the risk averse would assign a larger percentage of his portfolio to risk free assets, while the less risk averse would assign a larger percentage to the risk asset. I guess this is related to the indifference curve and that their corresponding tangency point. Would be great if someone could provide some input :slight_smile:

I would go for steeper CAL. The slope of the CAL is the Sharpe ratio,right? So a higher Sharpe ratio(excess return per unit of risk) is better for a risk averse investor.

S2000magician: Would be deeply appreciated if you could provide your input :slight_smile:

Does the steepness of Cal define risk aversion? Doesn’t hat depend on indifference curve? For same steep Cal a risk averse individual will have lower expected return because of steeper slope of indifference curve compared to a risk neutral or risk averse. Will be great if any experts can assist here.

Answer is Lower expected return… I have no idea why, but I am just going to memorize it.

The correct answer is B: They’d have a lower expected return. Here’s the logic:

If you were strictly talking about a world with no frisk-free asset, you would be discussing where on the efficient frontier an investor would choose to be. In that case, a risk-averse investor will choose a lower-risk, lower return portfolio (and there would be NO CAL, since there’s no RF asset).

However, since we’re talking CAL, we have a risk-free asset. In this case, EVERY investor would choose the CAL with the highest slope, which is the the Capital Market Line (the CAL that uses the market portfolio as the risky asset).

Regardless of risk preferences, the CML dominates all other CALs. It has the greatest slope, and sits above all other CALs. Therefore, for a given level of risk, being on the CML gives you an expected return that is greater than the return given you from being on any other CAL.

What the investor’s level of risk aversion determines is WHERE they would choose to be on the CML (i.e. what weight they’d put in the risk-free asset). And if they are more risk-averse, they’d choose a position with a higher weight in the Risk-Free asset, and therefore a LOWER expected return.

Fantastic explanation! Many thanks for you response. Made it very clear and logical!

busprof, thank you for your valuable input! Sorry guys for misleading all of you.

Not to worry - it’s a tricky question, and not apparent at first (and even second, or third) look.

Thank you. It can’t be explained in a better way.

We can also think of it this way - the whole efficient portfolio theory is based on the assumption that higher risk => higher return.

Which naturally implies lower risk (i.e. higher risk aversion) => lower return.

I agree. I saw the question at hand on two separate mocks. First one I said “lower expected return” and it was wrong (or at least “steeper CAL line” was correct). When I saw it a second time and even though it went against my opinion, I answered steeper line and it was right.

Steeper line just implies that the investor gets less utility out of risk, so every increment of risk they take on they need to be rewarded for, not that they are risk averse necessarily. They may be super risk un-averse but their risk utility is lower.