Market beta

Discussion on Quantitative Methods in Finance
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nextstep
Posts: 38
Joined: Fri Sep 09, 2011 2:20 pm

Market beta

Postby nextstep » Thu May 03, 2012 1:32 pm

Hello, Carol.
I have one question about market beta. Suppose we define beta as : beta = SUM (weights_i * beta_i ) (vol. II.1.2 equation 1.2). So, if I have long-short portfolio my portfolio value can be very small and weights can be vary high. It leads that market beta cab very large, due to the high weights. My question is: can I define beta without weights? Beta = mean (beta_i)? Will be it correct? Thank you.
Best regard, Aleksei

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Market beta

Postby coalexander » Fri May 04, 2012 1:04 pm

Hi Aleksai,

No, it would not be corrected to omit the weights. Equations (II.1.3) and (II.1.4) are deduced from (II.1.2) and the expression of the portfolio return as the weighted sum of the asset returns.

The problem you are experiencing is a general problem with returns on long short portfolios. They are not properly defined because portfolio value could theoretically be zero. I discussed this right at the beginning of volume 1 and I always recommend that when you work with long short portfolios, you work with profit and loss (P\&L) which is always well-defined. You can compute betas based on the P\&L of the stocks and the market, and express the portfolio P\&L and a weighted sum of the stock P\&Ls, that's the way to go about your problem,

Carol

nextstep
Posts: 38
Joined: Fri Sep 09, 2011 2:20 pm

Re: Market beta

Postby nextstep » Mon May 07, 2012 9:14 am

So, for long-short portfolio market beta = Covariance (Portfolio P&L, Factor P&L)/Variance ( Factor P&L ) . Am I right ? In case study III 2.6.3 you define number of contracts as : Correlation ( Portfolio P&L, Underlying P&L ) * Std.Dev (Portfolio P&L) / Std.Dev ( Underlying P&L). Is this formula correct ? Thank you
Best regard, Aleksei.

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Market beta

Postby coalexander » Mon May 07, 2012 6:47 pm

Both formulas are correct -- check the definition of corr= cov/product of stdevs to see why, cheers, Carol

nextstep
Posts: 38
Joined: Fri Sep 09, 2011 2:20 pm

Re: Market beta

Postby nextstep » Tue May 08, 2012 7:44 am

Thank you Carol for your answers. I have one more question. Suppose I have long-short portfolio and I try to hedge this portfolio using gold futures. Contract size of gold futures is 100 troy ounces. Does it mean that I should multiply Futures P&L by 100, when calculate number of contracts ( Correlation ( Portfolio P&L, Futures P&L ) * Std.Dev (Portfolio P&L) / Std.Dev ( Futures P&L) ). Thank you.
Best regard, Aleksei.

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Market beta

Postby coalexander » Tue May 08, 2012 9:53 am

If your portfolio price is $ per ounce, and futures price is $ per 100 ounces, then divide the futures price by 100 to get $ per ounce

lestertarry
Posts: 2
Joined: Sat Aug 25, 2012 11:08 am

Re: Market beta

Postby lestertarry » Sat Aug 25, 2012 12:08 pm

The problem I have is a general problem with the performance of long short portfolios. They are not well defined, because the portfolio's value could theoretically be zero

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Market beta

Postby coalexander » Sat Aug 25, 2012 12:57 pm

Yes, that is why we use P&L not returns. See the discussion on returns in Volume I, chapter 1 -- especially for returns on long-short portfolios. See also the material on hedging spot with futures in Volume III, where the same problem is discussed. Carol


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