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April 22, 2009

Building a Better Beta: Not all Beta is created equal

Most investors understand the concept of Beta, but do not appreciate that all Betas are not created equal.  We'll start with a little Beta primer.  Let's say you have two stocks, Huntington Banc (HBAN) and Invesco (IVZ), which both have a Beta of approximately 2. If the market moves 1% you would expect HBAN and IVZ to move 2%.  Investors that are trying to dampen market sensitivity may Beta adjust by multiplying the actual position size (for example we'll say 3% current positions for both HBAN and IVZ) by the Beta to get a Beta adjusted position size of 6%.  Here is the issue, investors assume 6% position size for both assets to make portfolio management decisions, but only about 50% of the movement of HBAN is explained by its Beta (measured by correlation), while over 80% of IVZs change is explained by market movement.  They are simply not the same and should not be treated as such.

The Beta problem lies in its universality.  You can calculate a Beta for anything.  I can calculate a Beta for how many leaves fall in my backyard to the number of emails I get per hour or calculate a beta for how many books my wife reads per month to the price of rice in China.  Because Beta can compare any two items, it has to be graded so that you know if it is worth using.  That grade is called an R-squared and is simply correlation squared.  Unfortunately not all Betas matter or I'd be long rice and my wife would never stop reading.

***Brief explanation of subtle statistical differences between Beta and Correlation.  Beta = expected change in Y given a change in X (Beta can be any cardinal number).  Correlation = how much of the movement of Y is caused by X (correlation can be between -1 and 1, so a correlation of .8 means that 80% of the movement of Y is caused by the movement in X).***

So Beta is only as good as its correlation.  A correlation of  0 means the variables have nothing to do with each other and 1 or -1 means that predictive power of Beta is perfect.  Let's make a better Beta by adjusting Beta by its predictive power.  The equation is simple:

abs(correlation)*Beta+(1-abs(correlation))*1

So using our examples above:

HBAN:  51.6% * 2 + (1-51.6%) * 1 = 1.52 Beta = 1.52 * 3% position size = 4.55% Beta adjusted position

IVZ:  80.4% * 2 + (1-80.4%) * 1 = 1.80 Beta = 1.80 * 3% position size = 5.41% Beta adjusted position

These are huge differences from a portfolio management standpoint and they more accurately reflect the impact of the position from a market movement standpoint.  In the HBAN equation, we are essentially assuming that 51.6% of the time Beta predicts the movement and 48.4% it does not.  This is a more accurate reflection of the movement of the asset in the portfolio.  Alpha Theory has now Built a Better Beta which allows investors to utilize Beta only when it matters, which leads to much better portfolio management decisions. 

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