2
$\begingroup$

In the mean-variance framework, the only way to get a higher expected return is to be exposed to a higher beta, and the more risk-averse an agent, the lower the beta of their portfolio (lending portfolios). However, could it be that a more risk-averse individual has a higher discount rate than a less risk-averse individual (i.e., the more risk-averse individual is less keen to provide financing for a particular venture). Or does the risk-return trade-off need to hold in all models that assume rationality and market efficiency (ie., higher expected returns are only achieved by higher risk exposure, given a certain level of aggregate risk aversion as in the mean-variance framework)?

$\endgroup$

1 Answer 1

1
$\begingroup$

The mean-variance framework is about optimal portfolio choice given the distribution(s) of asset prices/returns. On the other hand, the risk-return trade-off comes from an asset pricing model that produces the distribution(s). Therefore, the following is not quite right:

In the mean-variance framework, the only way to get a higher expected return is to be exposed to a higher beta.

This follows from the asset pricing model, not the optimization framework. Hypothetically, if the asset pricing model implied higher risk assets had lower expected returns, exposure to a higher beta would not lead to a higher expected return – whether we use mean-variance optimization or not.

However, could it be that a more risk-averse individual has a higher discount rate than a less risk-averse individual?

Risk aversion for a particular individual is characterized by their utility function, not the discount rate. The discount rate may characterize impatience, though. This is in the context of portfolio optimization, e.g. the mean-variance framework. Meanwhile, in an asset pricing model the discount rate characterizes the risk aversion of a representative individual in a market equilibrium.

Or does the risk-return trade-off need to hold in all models that assume rationality and market efficiency?

The trade-off is due to the asset pricing model. Hypothetically, we could introduce an asset pricing model where the trade-off goes the other way (higher risk brings about lower expected return) or there is not trade-off at all.

$\endgroup$
3
  • 2
    $\begingroup$ Not sure how much this helps you, but at least I found answering the question at least a little bit illuminating. $\endgroup$ Apr 17, 2023 at 8:25
  • $\begingroup$ About your point on impatience affecting the discount rate, would you say that an investor that gains utility from selling an asset right now (albeit at a "below fair" price for the overall market) (e.g., because they need the money), would you say that the "correct" price for the investor and the market differ for the same asset or is this a behavioural bias, or could be both? $\endgroup$
    – lkonoplev
    Apr 25, 2023 at 23:54
  • $\begingroup$ Just noticed your comment now. At a quick glance, I think I would say that "correct" price for the investor and the market differ for the same asset. I am not sure under what models this is the case, though. Perhaps some models does not allow that. $\endgroup$ Sep 14, 2023 at 12:35

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.