When a Risky Asset Can Have a Required Return Below the Risk-Free Rate

Summary

The document asks whether a security with positive variance can rationally offer a return below the risk-free rate. The main response says it can be attractive as part of a portfolio if its returns are negatively correlated with other assets that have attractive risk-free returns. Its value comes from the diversification or hedging benefit it contributes to the combined portfolio, rather than from its standalone return and risk.

The same response says such an asset would not be attractive in a single-security portfolio. A second answer disagrees in broad terms, arguing that investors would prefer a higher risk-free return, and points to imperfect risk measurement as a possible source of confusion in practice. The document presents competing, brief views rather than a formal asset-pricing derivation, and does not specify a portfolio model or quantify how much negative correlation would be needed.

Key ideas

• An asset can be useful at a below-risk-free expected return if its negative correlation improves a broader portfolio.
• The portfolio benefit does not imply the asset is attractive on its own.
• The responses disagree about the possibility and give no formal model to resolve the difference.
• Imperfect measurement of risk or conditional risk may complicate real-world assessments.

Tags

# Is it possible that a security with a positive variance can have a required return that is less than the risk free rate?


# Is it possible that a security with a positive variance can have a required return that is less than the risk free rate?












I'm not sure of the answer but I think it's possible. What I don't get is what characteristics this asset would need to have and why it would mean that an investor would accept a return less than the risk free rate when there is uncertainty about the asset's future payoffs.

## Answer by Brian B (score 2)

https://quant.stackexchange.com/a/14921

If the security has negative correlation with other assets that enjoy attractive risk-free rates, then it can be attractive at a return rate under the risk-free level.

It would, of course, never be attractive in a single-security portfolio.

## Answer by vikram (score 0)

https://quant.stackexchange.com/a/14896

Theoretically, such an asset would not exists with standard deviation less than the risk free rate. You have rightly pointed out that if risk free rate is higher than any rational investor would not invest in the instrument, given lower return along with some amount of risk, when the investor can earn more amount without any risk.

In the real world we do not appropriate measure of risk/conditional risk estimation, which may add to the confusion.

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