### CFA Practice Question

A portfolio that has a negative beta:
A. has an expected return more than the market's expected rate.
B. has an expected return less than the risk-free rate.
C. cannot exist.
Explanation: The CAPM equation is E(R) = Rf + b*(E(Rm) - Rf). Since the market risk premium, E(Rm) - Rf, is always positive, if a security has a negative beta, then its expected return is less than the risk-free rate.

User Comment
ahan Can anyone tell how beta becomes negative?
Sator What if E(Rm) is negative?
MikeBarlettano gold has a negative beta, and the return isn't necessary less than the risk-free rate
timspear Negative beta means when the market goes up the thing, on average, goes down. For example if you a security consisted of \$1000 cash plus being short some QQQs it would have a negative beta and probably return less than just cash.
mellyg The market return is always higher than risk-free rate, because of the systematic risk, which can't be diversified away.
swift how can it always be higher than rfr
- what happens when mkt goes down - theory schmeory!!
swift oh - and there are plenty of stocks with neagative betas!! doesn't mean they perform worse than the mkt - just in opposite direction
snider guys: E(M) means expected return, not actual return. Although the actual market return can be less than the risk free rate or even negative, the expected return of the market will be ALWAYS higher than the risk free return, otherwise nobody would choose the market portfolio anymore.
PedroEdmundo How can a Beta be negative will Beta=covariance(x,m)/var(m).
Variance cannot be negative
nike yes beta can be negative if the stock moves against the market.
volkovv variance cannot be negative but covariance can be:
covariance(a,b)=correlation coefficient*std(a)*std(b) and negative correlation coefficient will make covariance and hence beta negative

beta by definition is correlation coefficient between an asset and the market
hannovanwyk yes, volkovv's got the point right there. covariance can be negative...

i also made the mistake that covariance is always positive and therefore beta should always be positive.
moritz Stocks with negative beta provide an insurance against market losses. Since insurance is costly, the return needs to be negative or at least smaller than the risk free rate.