Hi David,

Given the formula of beta (slide 16), I was thinking hard that can beta be negative and if yes then what will be the impact on the expected return?

Considering the formula = Beta = Cov (m,i)/var m, if we use the formula for correlation then this will become Beta = correlation(m,i) * var i , now if this is correct, then in case if the security is having negative correlation then beta should be negative.

But how do we interpret negative beta, and are there any securities with negative beta…

In addition to this, is there any relation between CML and SML ? 

Look fwd to your guidance on this..

thnx
OM

Hi OM,

Yes, exactly, beta can be negative. Note, I get a slightly different ratio: Cov(i,M)/var(M) = correlation(i,M)*volatility(i)/volatility(M); i.e., it’s just like the minimum variance hedge ratio. Since volatilities and variances are always (+), negative correlation implies negative beta.

Re interpretation: a regression of stock’s excess returns against market excess return has negative slope. Higher market returns imply lower instrument returns. I don’t have a security example *but* Andrew Lo’s assigned hedge fund replication reading gives (as we’d expected) a negative beta for the dedicated short bias strategy; as market goes up, fund has some negative factor exposures. (that’s in a multifactor model, but it’s the same idea). So, the use could be for a hedge.

David

Thanx David for the explanation and correction in the derivation of the beta, in a way now I can link the concept with the min variance hedge ratio as well…

sure thing, i forgot to share link to screencast on beta last week . David

Hi everyone,

I have a question about negative beta and Capital asset pricing model (CAPM)

I understand it is possible to get a negative beta, mathematically, and it is logical. But in CAPM we have the following formula,

Ri = Rf + Beta_i * (Rm - Rf)

where
Ri: return on asset i,
Beta_i : beta of asset i
Rf : return of risk free asset,
Rm :  return of market.

When beta negative, asset is less risky and we expected less maybe negative return ??
How we will interpret this equation with a negative beta..
I appreciate any explanation
Thanks a lot