re-Balancing your Portfolio: an appendix to Part II.
  • We select twenty years of RANDOM gains for two assets, say Stocks and Bonds.
  • These gains have a Normal distribution, with Mean & Standard Deviation:
    Stocks: Mean = 10%, SD = 25%     higher Gain and larger volatility
    Bonds:  Mean =  6%, SD =  8%     lower Gain and smaller volatility
  • Below, plots of some typical 20-year scenarios, the right plot of each pair gives the 20-year gain with and without rebalancing ... and its dependence upon the Stock:Bond allocation.
  • The left plot shows the growth of $1.00, invested in either Stocks or Bonds.

Figure 1


Figure 2


Figure 3


Figure 4


Figure 5

Again we select twenty years of RANDOM gains for two assets, as above ... but with annual investments:
  • Initial portfolio is $1000 and we invest an additional $100 at the end of each year.
  • Below, plots of some typical 20-year scenarios, the right plot of each pair gives the portfolio after 20 years, with and without rebalancing ... and its dependence upon the Stock:Bond allocation.
  • The left plot shows the growth of just the $1000, invested in either Stocks or Bonds.

Figure 6


Figure 7


Figure 8

    Notes:

  1. The right plots begin and end with the same value (percent stock ="0%" or "100%")
  2. Usually (but not always - see Figure 4, above) the portfolio with rebalancing lies completely above or below the portfolio without rebalancing meaning that, if with/without is better at 20% Stock, it's also better with 30% Stock or 40% or 50% ...
  3. Whether with (or without) is "better" is ... unpredictable!
  4. The word "better" is in need of a definition