Rodc wrote:Kevin M wrote:
The data is below in format: ending balance, SD, Sharpe. Here are some observations. <snip>
I expect rebalancing providing a higher return is likely due to the wild swings of the last 15 years, and unusual and while clearly possible is not generally to be expected.
I recall that Bill Bernstein's research on this indicated that for a rebalancing bonus you want to combine volatile asset classes. I think the results here are consistent with that, since long-term bonds are more volatile than intermediate-term bonds, and they did indeed provide a larger rebalancing bonus.
Based on the volatility argument, one might expect an even larger rebalancing bonus from long-term zero-coupon bonds, since these are even riskier than long-term coupon Treasuries due to higher duration and hence larger term risk.
Other than volatility, another benefit to bonds with more term risk has been declining yields since 1982, boosting the total return of longer-term bonds. To check this, I'll look at the asset class numbers for 1972-1981, during which time yields increased significantly.
60/40 US stocks/intermediate-term or long-term bonds
Not rebalanced:
18,526, 12.86%, -0.06: intermediate-term Treasuries
16,618, 13.69%, -0.12: long-term Treasuries
Rebalanced annually:
19,391, 13.63%, -0.01: intermediate-term Treasuries
17,303, 14.16%, -0.09: long-term Treasuries
Somewhat surprising is that there still was a small rebalancing bonus. However, note that in this case the rebalancing bonus was larger for the portfolio with the less-risky intermediate-term Treasuries.
Also note the negative Sharpe ratios. Explanation? During this period cash/money-market, used as the risk-free asset in the Sharpe ratio calculation, generated higher returns than did stocks or bonds. Since the risk-free rate is subtracted from the mean return of the risky asset being measured with Sharpe ratio (and then this result is divided by standard deviation), the result is a negative number.
Here are the numbers for 100% US stocks, 100% cash/money-market, and 60/40 US stocks / cash/money-market:
Not rebalanced:
19,456, 22.06%, 0.05: 100% US stocks
21,157, 3.36%, N/A: 100% cash/money-market
20,136, 12.26%, 0.01: 60/40 US stocks/cash/money-market
Rebalanced annually:
21,194, 13.19%, 0.05: 60/40 US stocks/cash/money-market
Rodc wrote:Higher return using long bonds should be expected because they have a higher return than shorter maturity bonds, usually, due to higher risk, but the same sharpe over the longer term suggests you are simply being rewarded for the higher risk. The shorter term results suggest that while one might expect risk vs reward to work out long term in the shorter term risk may or may not show up so you may or may not do better than expected.
Makes sense! We saw the term risk show up in 1972-1981, while it generally was rewarded 1982-2015.
Thanks for the observations, Rod.
Kevin
If I make a calculation error, #Cruncher probably will let me know.