Here is a favorite question among corporate finance interviewers: " Can betas be negative? And if so, what exactly do they tell us?" The reason negative betas pose a conundrum to many finance students is that they seem to go against intuition. After all, if a beta of one is average risk and a beta of zero is riskless, how can an investment have negative risk?

Here is the answer. Yes, betas can be negative. To see how and why, consider what betas measure: the risk added by an investment to a well diversified portfoli0. By that definition, any investment that when added to a portfolio, makes the overall risk of the portfolio go down, has a negative beta. A more intuitive way of thinking about this is that a negative beta investment represents insurance against some macro economic risk that affects the rest of your portfolio adversely. A standard example that is offered for a negative beta investment is gold, which acts as a hedge against higher inflation (which devastates financial investments such as stocks and bonds). It is also true that puts on stocks and selling forward contracts against indices will have negative betas.

What are the consequences of a negative beta? The expected return on that investment will be less than the riskfree rate; the nominal returns on gold over the last 40 years have been 2% less,on average annually, than the riskfree rate. However, that makes complete sense if you think of it as buying insurance. You are paying for the insurance by settling for a very low or even negative return.

Are there actual investments out there that have negative betas? I know that there are stocks with negative regression betas, but those are the mostly the result of something strange happening during the period of the regression - an extended lawsuit or acquisition battle throwing off the correlation with the market- rather the true betas. In fact, in my fifteen years of updating betas by sector, I have still not found a sector with a negative beta. Furthermore, even assets that, in theory, could have negative betas (gold, for instance) seem to have positive betas when securitized (gold shares, gold ETF). There seems to be something about the securitization process that makes real assets behave more like financial assets.

## 43 comments:

We often talk about Gold as negative beta or a hedge against inflation, recession. Also it is often mentioned as a back up currency. It would be great if you could demystify Gold as an asset class in itselt without the securitization affect.

Thanks for making it clear. I often used to think a lot about beta and try to search answers in various text books or try to seek help from my faculties but my query has never been solved. On my question of negative beta they told me to vary the length of time period till you get positive beta or otherwise use "Risk free rate+Risk Premium" formula for that stock. And all these seemed so unrealistic and awkward which made me think that all these concept are made to fool individuals.

However I want to know only one thing that in bottom up beta what should be the criteria to select a time period for the stocks before calculating their individual betas and removing the leverage effect from the stocks.

Dear Prof Damodaran

I would like to ask you a question.

(not linked to the topic)

For example, we calculate the NPV of a project at time 0. Three years pass, and we want to calculate the NPV of this project again (at the end of the 3rd year). How do we have to treat the outlays made within these 3 years? Do we have to include them in the NPV calculation? If yes, how we should discount them (or compound?)?

Thank you for your answer in advance

Vadim

NPV is always forward looking. Thus, cash flows that have already occurred will not be part of the computation - they are not incremental.

AS for demystifying gold, I am afraid I cannot do it, because the allure of gold is based on mystery going back as far as time stretches. My guess is that at the time of its choice, there were other competitors but gold won out.

Hello Prof. Damodaran,

I am a bit confused about the following statement you made in your blog.

"By that definition, any investment that when added to a portfolio, makes the overall risk of the portfolio go down, has a negative beta."

Wouldn't the portfolio beta also go down if I add an investment of lower beta than the overall portfolio beta. e.g. a stock of beta 0.75 if added to a portfolio of beta 1.5 would still reduce the overall portfolio risk.

What if I know the exact amount of gold yet to be mined from this planet?

Hi professor Damodaran,

Also I graduated in a non finance major I am greatly inspired by your book and website.

Here is my thought about negative beta,

by definition,

beta=Cov(Ra,Rm)/Var(Rm),

Correlation coefficient=Cov(Ra,Rm)/(Asset Volatility* Market Volatility)

so we have, beta = Correlation Coefficient * (Asset Volatility / Market Volatility)

Since correlation coefficient can be negative, so we can also have negative beta for assets, which implies the asset has an inverse relationship with the market.

Please correct me if I am mistaken, thank you!

OK betas can be negative.

But then what is the cost of capital for a firm with a negative beta?

Can a firm's cost of equity indeed be less than its cost of debt?

I'm not sure of the answer. On the one hand, I'd say, no: equity is always riskier than debt and commands a higher expected return. But if I measure the cost of equity with the CAPM, the answer has to be, yes.

Is the CAPM applicable in this case?

Obviously if ur using the CAPM to arrive at cost of capital in a situation of the firm having negative beta, ur cost of capital will be lower than ur risk free rate.

When a stock has a beta greater than one, it is perceived to be riskier than the index (with an obvious upside of being able to generate a return in excess of the index). However, would the analogy hold if the beta were in fact negative?

To paraphrase, are stocks that have a Beta of greater than one and less than zero riskier than the index, or is it the stocks that have a Beta of greater than one, and less than negative one that are riskier?

Greetings Prof.

Good point to discuss guyz. Theortically, we arive at beta by dividing the covariance between the Asset (security) and market portfolio by variance of the market portfolio.

So, anytime you see an asset having negative covariance with the market portfoliio, you would eventually see a negative beta.

This scenario is rare just because an asset rarely displays a negative covariance with the group it is a part of.

Beta is nothing but the slope of a linear equation where Y axis (Independent Variable) could be an Index like S&P 500 and X axis (dependent variable)could be MS ( Microsoft.

Imagine Beta as Duration in the Bonds, which practically can never be negative.

Imgaine Beta here as "Duratiion" in the Fixed Income.

I am MBA finance student from India. Sir I have listened to the first 11 of your lectures on corporate finance and will finish the rest in a few days. Sir there was a viva in our college, I was asked that can Beta be negative? My answer was yes and I also told them that in such a case the cost of equity will be less than risk free rate and people might hold such shares as a measure of insurance on the market. The next question was a company due to its bad management has negative beta for the last 1 yr., what should be the cost of equity? I said for that period the cost of equity will be less than risk free rate according to the capm, but they are not agreeing to it at all, there point is cost of equity can never be negative. Sir can you please share your views on this?

Eagerly waiting for your reply

I am MBA finance student from India. Sir I have listened to the first 11 of your lectures on corporate finance and will finish the rest in a few days. Sir there was a viva in our college, I was asked that can Beta be negative? My answer was yes and I also told them that in such a case the cost of equity will be less than risk free rate and people might hold such shares as a measure of insurance on the market. The next question was a company due to its bad management has negative beta for the last 1 yr., what should be the cost of equity? I said for that period the cost of equity will be less than risk free rate according to the capm, but they are not agreeing to it at all, there point is cost of equity can never be less than risk free rate. Sir can you please share your views on this?

Eagerly waiting for your reply

Regarding negative betas, couldnt you say that a CDS would always have a negative Beta, given that it always move inverse to the market?

Could you also say that shorting a stock in your portfolio would create a negative beta?

Hi Prof:

Was doing some research and came across a stock with a negative downside beta of -.03, with a regulat beta of .42. What is your take on this? How would this affect a portfolio? Thanks!

Hello,

I agree that stocks can have negative betas on certain occasions. However, a negative beta upsets the CAPM model and ideology. How?

The CAPM says there is a risk free rate (rf) to which a risk premium (rm * beta) is added. The total of rf and rm*beta gives the exp. rate of return. Now if the beta is negative then the exp. rate of return will be less than risk free rate like rightly said by Prof. Damodaran. So exp. return < risk free rate is actually meaningless because you expect atleast that much return for a risk free asset. This is one big flaw which makes CAPM irrelevant and not applicable for negative betas.

Similarly when you say risk premium you are denoting an addition or positive value. A negative beta means subtraction or reduction - which is contradicting the fundamental ideology and logic of CAPM.

Its not possible for a model (particularly CAPM) to predict the expected rate of return from a stock or a portfolio.

If there is a negative beta and we calculate the CAPM USING THIS NEGATIVE NUMBER, does it Still make sense to do so and is the calculation still perceived as correct?

The possibility of a decrease in the worth of a protection plan device resulting from a decrease in the worth of the assets incorporated in the investment profile underlying the insurance device.

This reduction can also be affected by a modify in the interest rate.

Investing in Insurance Risk

I think it's hard to find a true negative beta stock because for any good (even insurance type goods like gold, guns, ammunition, doomsday prep stuff), there is a chunk of the population more willing to buy the good when times are good. I.E. some guy who goes out and spends a christmas bonus on gold/guns. This is what makes finding a non-financial/derivative negative beta stock so hard.

Would it be possible that a stock has a true negative beta if the majority of the company's equity value is in cash and equivalents, in which the most is held in short term investments returning a higher rate (say 3.5% in China vs. 1% in US)?

Just a question regarding impact of beta on security... Assume that the market gains 100%, in the same period, what will happen to a stocks having beta 2, 1, 0.5, 0, -0.5 and -1. Also, can beta go below -1, and if yes what will be the significance???

give anothee example of can astock have negative beta?

I am trying to construct a 'Taleb' style portfolio using Calls on ETFs. In my research, I have found about 20 that show a negative beta (according to ETFDB.com) I didn't believe it could exist, which led me to this blog. Most of these are metals, commodities or VIX futures. It seems like it fits with the thread of this discussion that these would be negative bets vs. the market. Any thoughts? Or is my data source just wrong?

Ticker Beta

NUGT -13.19

UVXY -10.72

AGQ -7.64

VXX -5.35

VIXY -5.31

GDXJ -4.97

ERX -4.61

GDX -4.24

EDC -4.14

SLV -3.7

IAU -2.6

XME -2.56

XOP -2.28

OIH -2.15

FXI -1.64

EWZ -1.62

IYT -1.57

EWA -1.54

XLE -1.49

DBC -1.18

XLI -1.16

XLK -1.04

Thanks for your information, it was one of the best source for inverse to the market.

regards

Workers Compensation Insurance Fort worth

respected sir,

I would like to ask you a question.

If S.D of two securities have been given, also beta of these two securities have been given and also S.D of market has been given, is it possible to find out correlation between these two securities. is it possible to find out S.D of the portfolio which consists these two securities?

If yes please suggest the method.

Dear Sir, As Taleb mentioned in Antifragility book - there are investments which are effectively a hedge against your portfolio and those can very well have a negative beta. For eg. creating a short against CMBS/CDOs in 2006/early 2007 would very well have served the purpose of hedging almost any portfolio and must be considered to have a negative beta then!

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High beta stocks are only good for traders.

This question was in my midterm and it caught me off-guard... however, my guess was correct if this article is anything to go by.

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We often talk about Gold as negative beta or a hedge against inflation, recession. Also it is often mentioned as a back up currency. It would be great if you could demystify Gold as an asset class in itselt without the securitization affect.

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