Interpreting Negative CAPM Cost of Equity Estimates

Summary

The document discusses how to interpret negative cost of equity estimates produced from CAPM beta calculations. It argues that a negative expected return can be consistent with portfolio theory: an asset that offsets another asset’s risk may have a negative expected excess return while the combined position offers a riskless return above the risk-free rate. A negative estimate therefore should not automatically be treated as an error.

The answer also flags unusually large positive and negative estimates as possible signs of an overfit factor model or corrupted data. Setting negative estimates to zero can distort portfolio expected returns by retaining the apparent risk-offsetting benefit while removing its associated return cost. The example is illustrative rather than an empirical test, and the document gives no procedure for diagnosing a specific model or validating its input data.

Key ideas

• A negative CAPM cost of equity estimate may be theoretically consistent with an asset’s role in offsetting portfolio risk.
• The example uses perfectly negatively correlated assets with matching volatility to illustrate the point.
• Extreme positive and negative estimates can indicate model overfit or corrupted data.
• Replacing negative estimates with zero can make expected portfolio returns look too high by ignoring the return cost of risk offsets.

Tags

# What if CAPM cost of equity is negative?


# What if CAPM cost of equity is negative?












Dear Community members,

I calculate 5 years trailing beta using capm. After that I calculate estimated cost of equity. However, what I have is that most of the observations have negative cost of equity values. Does anyone knows how shall I deal with negative value?

## Answer by Charles Fox (score 1)

https://quant.stackexchange.com/a/42167

The negative value may be correct.

Stock A a positive expected return, B has a 0% expected return, and the risk free rate is 0%. A and B are perfectly negatively correlated and have the same standard deviation. In this case, you could buy equal amounts of the two stocks and earn a risk-less return in excess of the risk free rate. By contradiction, the sum of the expected excess returns of two perfectly negatively correlated stocks with the same standard deviation must be zero.

If you have a factor model which produces large positive and negative cost of equity values, your model may be over-fit or you data could be corrupted.

Overriding the negatives with zero is unlikely to be a correct solution because it would make the portfolio expected return look unrealistically attractive. It would appear as if a long only portfolio could offset the factor risks without offsetting the expected returns.

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