Beta

Updated  06/16/14

Beta is a classical measurement of the volatility of a security with respect to the divend-adjusted S&P 500 (SP-DA). FastTrack adds a feature: Beta can be calculated with respect to any issue or index, not just the S&P-500

Within FastTrack, Beta is used only within the spreadsheet. The calculation is a function of

• The Green Line.
• Correlation ( Cor= )to the green line (not the low risk basis)
• Standard Deviation.
• Length of the correlation set in parameters
• Position of the chart poles (determines period evaluated)
•  Click for math details.

Proper Use of Beta

Classically, a broad-market, US mutual fund with a Beta of 1.10 is expected to have  price fluctuations that are 10% greater than the fluctuations of the S&P 500.

Classical Beta is valid only when there is a reasonable correlation between the issue and the S&P 500. Issues that hold high proportions of gold stocks, international securities, or most sector investments are not be sufficiently well correlated to the S&P 500 to have a valid classical Beta. Generally, Cor= should  be greater than 50% to have any validity, and a Cor=> 70% for common usage.

Highly Correlated Beta

The charts shows a variety of lines that are highly correlated to the S&P-500.

Green Line: The S&P-500 index as published in The Wall Street Journal each day (not dividend-adjusted). By FastTrack-definition the Beta of the green line is always=1.0.

Red Line: The Vanguard S&P-500 Fund dividend-adjusted also has a Beta of 1.0, but note that the annualized return is a considerable 2% higher than S&-CP, but this doesn't matter. Beta is NOT a function of return.

Yellow Line: The Rydex Nova fund is an S&P-500 fund augmented with futures to have a Beta of 1.5 (by design of the fund manager). Indeed FastTrack shows RYNVX's  Beta  = 1.51 . . . but Nova return falls far short of a Beta predicted 1.5 * the return of VFINX.

Purple Line: The Rydex Ursa fund is an inverse S&P-500 fund designed to have an inverse Beta of -1.0. Combining these VFINX and RYURX funds in the same portfolio would essentially produce a straight line with little or no return . . . However, this may be an important strategy for those seeking to hedge holdings (protecting against losses) until the prior gains become long-term. (for taxes or to satisfy a fund company holding period).

Cyan Line: Fidelity Energy Services. The Beta is a low 1.11 . . . however, the SD= is a very high 11.89. This points out Beta's interpretation problems. For classic Beta, the target fund must have a high correlation with SP-CP, or Beta becomes difficult to interpret.  In this case, the low correlation(58.21), and high return of FSESX means that FSESX and VFINX could be held in the same portfolio for high return with moderate volatility. (i.e. diversification)

FastTrack FTAlpha - Related to Beta

The chart above includes a column for FTAlpha.

FTAlpha is a function of correlation, downside volatility, and return. FTAlpha is easier to interpret than Beta when looking for diversification. In this case the basis for FTAlpha is VFINX. Note the FTAlpha score of 0. This means that buying more VFINX will not change the risk or return of the current basis holdings of VFINX

Note that FSESX has the highest FTAlpha value indicating that it is the best bet for diversification when combined with SP-CP. The risk/reward ratio would improve both by increased return and reduced risk. The portfolio would have an SD= that is less than the average of the two issues' SD=, and a return that is greater than the average of the two returns.

Also note, that FTAlpha's second choice is VFINX . . .  while this paring would not affect risk, it would boost return. VFINX gains 2% more annually thus improving the risk/reward ratio.

RYURX has a negative FTAlpha. Do pair VFINX and RYURX. While volatility would be greatly reduced, return would be very low.

Using Flexible Beta

FSESX is  the most volatile of energy sector funds. By making FSESX the green line, Beta can rank all ENERGY family funds by Beta to  produce meaningful results.

Still Beta would be difficult to use in an exercise to pick the best Energy fund.

Picking the Best Energy Fund

By combining FSESX with the two highest ranked Energy funds (using FTAlpha) , it is possible to create a monthly equally rebalanced portfolio (yellow line). T

Note the yellow average line follows the green FSESX line, but has all of the return of FSESX with about half the volatility.

Click to see Morningstar's Principia Beta calculation in PDF form.

There is a significant difference in the FT and MS calculation. They subtract a Treasury constant from each of their monthly returns before calculating. This is introduces a linear adjustment in the a calculation that produces a nonlinear result. Also, the concept of return without risk embodied in this calculation fell apart in the 2008 financial crisis making the MS beta values indeterminate based on estimated T-Bill returns.

There are many different equations for computing Beta. here are some of the significant differences between MS and FT.

• MS lists Beta with respect to "SP 500 TR". I guess this is equivalent to FT's SP-DA (S&P 500 adjusted for dividends), but that is strictly a guess. They may be correlating to what FT's calls SP-CP (S&P w/o dividends published in the WSJ).
• FT offers a variable correlation and Standard deviation sampling period. FT's Daily sampling is most accurate. MS does monthly sampling.
• The calculation can be done using market days or it can be done using calendar days. We use market days. MS uses calendar months. I am sure this introduces variation in the calculation as there are as few as 19 market days in a month and as many as 22.

Finally, the correlation of these funds is pretty low to the S&P 500. As correlation drops 95%, Beta becomes a useless figure with low correlation offsetting volatility. The interpretation of a Beta of 1.5 (meaning 1.5 x performance of the S&P) is always suspicious. Compare the performance of VFINX (beta 1.0) to RYNVX o( 1.5) over any multi-year period. 

Consider using the Ulcer Performance Index for the fund relative risk/return instead of Beta. It has the distinct advantage of measuring only downside volatility.