Negative Beta

[notjusttp]

Hi David,

Can beta of a portfolio be negative? As beta happens to be the slope of the line my guess is that it can be negative. However to my mind the following case does not intuit the actual practical position

Rf =4%
Rm= 9%
Beta = - 1.5

As per CAPM E(Rp) = Rf + beta(Rm-Rf)

= 4% + ( -1.5)(5%) = -3.5%.

I cannot understand as an investor how can I be invested in a portfolio which gives me a return even less than the risk free. Can you pls put some light on this situation?


Thanks & Best Rgds
Amit

 

[David Harper CFA FRM]

Hi Amit,

FYI, see similar query here @ http://forum.bionicturtle.com/viewthread/682/

I think ex post (i.e., after the fact performance analysis) is one thing. In this case, I think you are exactly correct to frame beta as merely the slope of a regression,
and because beta = Cov(i,M)/var(M) = correlation(i,M)*volatility(i)/volatility(M)...
since volatility is positive, ex post negative beta is easily explained by negative correlation

In regard to ex ante or expected beta, I agree with you that a *long* position in a negative beta assets does not generally seem desirable EXCEPT as a hedge (see thread) above, or similar, a SHORT position; e.g., short the S&P 500 futures has, under a "normal" CAPM a negative expected return, so why would you do that? to hedge your portfolio and make it market neutral. In fact, under the theory we study in Hull & Stulz, all hedges generally have a negative expected return (e.g., we expect F < E(St) and that is negative reutn to the hedger). And, you'll notice in the thread above, Andrew Lo appropriately found the dedicated short bias hedge fund strategy to exhibit negative beta.

David

 

[notjusttp]

Hi david,

thanks a ton for sharing this thread with me..I was not aware these questions were raised in investment section and i had browsed thru the entire foundations section of the forum...now i would review tomorrow the investment section also....

Believe me David of all the sections in BT i like forum the most ..for its twin benefits..it helps to get ur doubts clarified and it also helps u to get clarity on doubts which never occurs to u...but which occurs to other brilliant minds..thanks for this amazing share...Cheers.Amit