Kirk,
***Critical Beta Calculation of Model Portfolio I***
The beta of Model Portfolio I was 1.0 per MARKETIMER as of December 31, 1999. Initially, I was surprised at the market equivalent beta of the portfolio given the two high octane funds in the portfolio. These funds have betas of 1.2 est. and 1.13 and made up over 60% of the portfolio as of 12/31/99. (The 1.20 beta fund represented 37.5% and the 1.13 beta fund represented 23.5%). Also, there is another fund with a beta of 1.15 that made up another 10% of the portfolio. So, these three funds that have high betas made up over 70% of Model Portfolio I. Furthermore, there is yet another fund that has a beta of 1.0 that made up 17% of the portfolio. So, these four funds made up 88% of Model Portfolio I as of 12/31/99.
Now there are 3 international funds with relatively low betas: .55, .72, and .72, but they made up only 12% of the portfolio as of 12/31/99. So how can it be that MARKETIMER calculates the beta of this portfolio as 1.0?
Well, after further analysis, it seems that the calculation of beta for the portfolio might be calculated in a way that might give a false impression as to the true beta of the portfolio in its current state. It seems that the respective betas are given the weight of the original allocation (or the allocation that one would use if they were initiating a new portfolio) and not the current weighting in the portfolio.
For example, the 1.20 est. beta fund that had a 37.5% weighting in the portfolio as of 12/31/99 was only 20% originally. MARKETIMER chooses to calculate the beta of Model Portfolio I as if the fund was still only 20% of the portfolio.
Also, the 3 low beta funds which represented only 12% of the portfolio as of 12/31/99 carry a 25% weighting in the calculation. This calculation is flawed in that it gives more weight to the low beta funds than should be given and give less weight to the high beta funds than should be given.
If calculated correctly to show the true beta of the actual portfolio in question the beta of Model Portfolio I is north of 1.7! Thus, the argument that Model Portfolio I takes on less risk than the broad market is bogus. Not only did Model Portfolio I underperform the the S&P 500 and Wilshire 5000 over the period you showed, it is very likely that it did so with MORE risk.
Best Regards.
Rillinois |
