Utility Adjusted Return

Hello! Hope everyone is feeling good about this and is more ready than I am!

Here is a simple concept I wanted to get some clarification on. The Utility adjusted return formula is:

U = Rp - 0.005(A)(Variance of Portfolio), where A is the risk-aversion factor. From what I have seen, this factor is usually given, for simplicity, in a scale of 1-10 with 10 being the most risk-averse, and then it’s a simple plug from there on.

My confusion is, what if the scale is given as 1-8, with 8 being the most averse? If the investor’s risk averse factor is 6 on a scale of 1-8, what is “A” going to be? simply plug in 6? Or adjust the scale accordingly and enter 7.5 (because 6 is 75% of 8)

Thanks for the last minute help.


Thanks, so it’s not a ratio scale. I thought it was since all the examples given was in a scale of 1-10.

allt he examplesshould be on a scaleof 1-8

For what I know, as may or may not consistent with CFA curriculum, A is an estimated number derived from surveys that test what risk-averse level the investors are. For example, I give you a bunch of portfolios with returns and volatilities, you rank the ones you willing to invest. Beaded on your preference, I can estimate the value of A. The drivation of A involve a lot of math. The grater the A is, the more risk-averse you are. If you compliely ignores volatilities and only choose portfolios based on their returns, I will assign an A of 0, which indicates you are risk-neutral. It’s possible to have A less than 0. In that case, your utility increase as the volatility increase – you are a risk-lover/seeker. It’s also possible not able to estimate a value due to the inconsistent preference the investors may have, those are the results of behavioural biases that traditional finance considered irrational. And that’s the dawn of behavioural finance. Subjectively assigning a number to A as suggested by CFA curriculum seems problematic to me. Or maybe I read it wrong.