Portfolio Management Series: A Conundrum of Negative Beta!

A few days back, while teaching ‘Portfolio Management’ and while discussing the concept of ‘Beta’, a student asked me “Sir, can beta be negative?”

This is one question which baffles a lot of finance students.  Let me deliberate on what causes the confusion and what could be the plausible explanation of the so called ‘conundrum’.

To the un-initiated- Beta is the measure of risk (specifically, systematic risk). From a portfolio perspective, systematic risk is what prevails and specific/idiosyncratic risks get washed away due to the diversified composition of the portfolio. Hence we look at beta as the measure of ‘relevant’ risk. Beta of one indicates ‘average risk’portfolio at par with the overall market.  Riskless investment would have nearly zero beta (though the converse is not always true!). Therefore, should it follow that negative beta means negative risk? Can an asset or investment have negative risk? It seems counter intuitive, as any asset at best should have zero risk.Gold is one such asset which has negative beta.

Asset returns tend to be volatile. That is why we term these assets as risky assets.  To that extent, even gold is a risky investment. However, gold is negatively correlated with the market, delivers positive return in a declining market and zero or negative or low positive returns in a rising market.  Adding gold to the portfolio is likely to diffuse the overall volatility of the portfolio (due to its counter movement). Hence the incremental portfolio risk due to the addition of gold is negative. Simply put,

Risk (Portfolio with Gold) < Risk (Portfolio without Gold)

Applying Capital Asset Pricing Model (CAPM) - we realise that asset with negative beta is expected to deliver return lower than the risk free return.  For instance, let say beta of an asset is -0.5, the risk free return is 7% and market risk premium is 10%. Applying CAPM,

Asset Return = Risk Free Return + Beta* Market Risk Premium
Asset Return = 7% + (-0.5*10%) = 2%

Can an investor do with a measly 2% return for such an asset?  The answer is ‘Yes’.

The explanation lies in the ‘hedge’ or the ‘insurance’ utility that such an asset brings to the portfolio. As discussed, such negative beta asset when added to the portfolio brings down the portfolio risk; provides some kind of a hedge to the downward movement of the remaining portfolio. Therefore the investors are willing to accept lower returns from such asset (almost like sacrificing return in return for lower risk).

Adding gold or a put option on portolio or a short position in positive beta asset (or its futures) to an existing portfolio, effectively creates the impact of negative beta.

Keep learning!

Amit Parakh
A Finance Enthusiast. SFM/ CFA/ FRM Trainer
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