Risk-Free Returns Above the Minimum-Variance Portfolio and CAPM Equilibrium

Summary

The note considers a Markowitz portfolio setup in which the risk-free rate exceeds the expected return of the minimum-variance risky portfolio. Under the stated assumptions, the tangency portfolio lies on the inefficient part of the risky frontier, implying investors would take short positions in risky assets when combining them with the risk-free asset.

The answer argues this allocation is inconsistent with market equilibrium: if all investors want to short risky assets, the market needs buyers. It therefore concludes that CAPM equilibrium does not hold in this situation, although the CAPM equation can still be derived. The discussion is brief and offers no formal derivation or treatment of constraints such as short-sale limits, investor heterogeneity, or firms issuing shares, so its conclusion should be read within the simplified setup posed by the question.

Key ideas

• When the risk-free rate exceeds the minimum-variance portfolio's expected return, the tangency point may lie on the inefficient frontier.
• In the described setup, investors would seek short positions in risky assets.
• Universal demand to short risky assets creates a market-clearing problem because those positions require counterparties.
• The answer treats this setup as inconsistent with equilibrium and therefore with CAPM equilibrium.

Tags

# Markowitz w/ riskless asset & CAPM


# Markowitz w/ riskless asset & CAPM












If risk free rate ($R_0$) is bigger than expected return on minimum variance portfolio ($\bar{\mu}$), so $R_0>\bar{\mu}$. I.e. the tanget portfolio is on the risky inefficient portfolio frontier and we want to short sell risky portfolio. Question 1: Why is this not consistent with CAPM? Question 2: Is it consistent with general notion of securities market equilibrium??

## Answer by markowitz (score 1)

https://quant.stackexchange.com/a/45102

This situation is not consistent with equilibrium at all because any investors should be hold always and only short position in risky assets. Who buy them? Note that in long only case, the usual, the firms sell their stock.

As a consequence also CAPM equilibrium not hold, even if CAPM equation can be derived yet. Read this related topic: Under the CAPM, how do I deal with market returns being below the risk-free rate?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.