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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?

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    $\begingroup$ Could you give a couple of examples of the companies please? the more well known the better. Would help if you could include time period used for beta estimation, and the rf and risk premium estimates. $\endgroup$ – Magic is in the chain Oct 10 '18 at 6:33
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    $\begingroup$ In theory, there's nothing inherently wrong with a negative beta. That said: (1) for typical companies, a negative market beta would set off alarm bells in my head. I'd be concerned it's a mistake or spurious result (2) the CAPM empirically doesn't work (even though perhaps my clients & bosses don't know this). So the whole exercise is of dubious utility. $\endgroup$ – Matthew Gunn Oct 10 '18 at 15:18
  • $\begingroup$ I completely agree. For example, if you take a MSFT stock and run 5 years trailing regression of Fama and French 3 factor model (1988m1 till 2017m12) to predict betas, and then using predicted betas you calculate cost of equity what you are going to have is that there are some negative values... The question is how to deal with them? $\endgroup$ – Alberto Alvarez Oct 10 '18 at 15:48
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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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