rebalancing (part 3)

As contemplated, I've rounded out our examination of rebalancing with some random number generation...

The Test

Have Excel generate artificial returns over 500 weeks for each of 10 artificial stocks. This was accomplished by using the random number generator utility that allows one to select the statistical distribution (I selected a Normal distribution in keeping with Modern Portfolio Theory) and the associated parameters (mean, variance). I specified the random numbers be drawn from a Normal distribution with a mean annual return of 20% and an annualized standard deviation of 20%.

Observations

Under these conditions, I found that Rebalancing provided for a higher return than Buy&Hold only 4 out of 10 times (not very conclusive). However, the Rebalanced portfolio was always much less volatile than the Buy&Hold portfolio, which provided for a higher Sharpe Ratio every time. The Sharpe Ratio is basically just Return divided by Standard Deviation, which helps provide a feel for the 'significance' of the total Return over the investment period relative to how much that Return bounced around during the investment period (technical note: for simplicity I assumed the risk free rate = 0% when calculating the Sharpe Ratio).

[Caution: these are 'long-term' results (i.e. 500 weeks = approx. 10 years). In fact when I ran the test 10 times using an extreme annualized variance of 100%, rather than the more realistic 20%, I found the Rebalanced portfolio was actually MORE volatile than the Buy&Hold portfolio in 7 of the 10 trials. I think the reason is because under conditions of such extreme volatility, it takes longer than 10 years to begin to observe the 'long-term' result where a Rebalancing strategy can benefit from Reversion to the Mean.]

In terms of Alpha, the Rebalanced portfolio only outperformed 6 out of 10 times (again, not very conclusive) - I'm not sure why (a mystery for another day). However, in keeping with the theme of lower volatility, the Rebalanced portfolio had a Beta less than 1.0x every time (as calculated against the Buy&Hold portfolio).