This is the third part of a series "Momentum Vs. Rebalancing". In the first article of this series "Momentum Vs. Rebalancing: Which Is Better?", the groundwork was laid down regarding the thesis and objective of the studies, which was to basically compare and contrast two common portfolio management strategies executed on a typical stock/bond mix. The next two articles "Momentum Vs. Rebalancing (Part 2): Effect Of Lookback Horizon" and "Momentum Vs. Rebalancing (Part 2B): Effect Of Lookback Horizon" looked more closely at the momentum portfolio, specifically how the results would be impacted by the duration of the lookback horizon. Interested readers are encouraged to read the previous articles as well as the comment stream from the articles, which contains many insightful comments from experienced proponents and practitioners of the momentum/rotation strategy.

As the previous two articles have looked more at the momentum side of things, I thought that I could focus more in detail at the rebalancing portfolio in this article. Previously, the rebalanced portfolios were all equally weighted between stocks, i.e. the SPDR S&P 500 ETF (NYSEARCA:SPY) or the Vanguard 500 Index Fund (MUTF:VFINX), and bonds, i.e. the iShares 20 Year Treasury Bond ETF (NYSEARCA:TLT) Vanguard Long-Term Treasury Fund(MUTF:VUSTX).

In the first article, astute reader wboz asked:

Would the same trend hold for a different allocation, say 70/30 in favor of equities? Thinking about how much of the outperformance is due to the split chosen vs the rebalancing. Not sure how I would examine systematically but looking at another split would give a clue. Interesting workup...

This article seeks to find out!

**The two portfolios**

- Momentum strategy: Each month, buy
**either**VFINX or VUSTX depending on which ETF has had the superior N-month trailing returns (i.e., at any time, you are 100% invested in only one of the two ETFs). N is varied from 1 to 12, in increments of 1. - Rebalanced strategy: Each month, rebalance the portfolio so that it is invested in
**X%**of VFINX and**(100-X%)**VUSTX (i.e., at the start of the month, you rebalance to a certain percentage of stocks and the remainder in bonds). In this study, X was varied from 0 to 100, in increments of 10.

Portfolio Visualizer was used for this backtest study.*

(*As mentioned by astute reader Varan, Portfolio Visualizer has look-forward bias because trades are assumed to take place at the same instant (end of month) that trailing returns are calculated, which is not possible in reality. However it is my opinion that switching in the last 5 minutes of market close, when next month's choice of asset is nearly assured, should not lead to a big difference in results).

**Results**

The CAGR and standard deviation of the rebalanced strategy for the VFINX/VUSTX pair from 1987-2016 as a function of stock percentage is shown below.

What beautiful and smooth curves, something that every scientist wants to see in his results! We can see that there is a gradual increase in CAGR as the stock allocation is increased from 0% (CAGR: 8.16%) to 100% (CAGR: 9.91%). This is expected because stocks have overall outperformed bonds during the past 30 years. However, the curve for the standard deviation of results instead looks like a parabola, with minimum variability at 30% stocks. It is therefore interesting and perhaps slightly counterintuitive to note that introducing stocks into a 100% bond portfolio can actually * decrease* overall volatility.

What that also means is that 100% stocks, even though it had the highest CAGR, did not have the highest risk-adjusted return. This can be assessed using metrics such as the Sharpe ratio, Sortino ratio and MAR ratio, as shown in the following chart:

The chart above shows that the optimum for Sharpe ratio was 40% stocks, the optimum for Sortino ratio was 30% stocks, while the optimum for MAR ratio was 20% stocks. (And look at those wonderful, smooth curves!)

The U.S. market correlation and maximum drawdown for the rebalanced portfolio is shown below.

As expected, the U.S. market correlation of the rebalanced strategy increases as the % of stocks is increased. For maximum drawdown, it's worth noting that increasing the asset mix from 0% to 20% stocks actually led to a decrease in maximum drawdown. This of course is followed by a continual increase in maximum drawdown as the % of stocks is increased to 100%.

**Comparison between rebalanced and momentum portfolios**

How does these results compare to those of the momentum strategy? To visualize this, I plotted the CAGR and standard deviation of both the rebalanced and momentum portfolios on the same chart. Note that the momentum portfolio's x-axis is at the top of the graph, and show the lookback horizon in months (I couldn't figure out how to add a second x-axis in Excel). The momentum curves are in dotted lines.

We can see from the chart above that the rebalanced strategy had, across all stock/bond compositions, a **lower CAGR** than the momentum strategy except for lookback periods of 7 and 8 months. This suggests that in general, the momentum/rotation strategy is able to generate higher returns than the rebalanced strategy.

On the other hand, the rebalanced strategy had, at all stock/bond compositions, **lower standard deviation** than the momentum strategy for all lookback periods. This indicates that the rebalanced portfolio is less volatile than the momentum portfolio.

Let's now take a look at the risk-adjusted performance metrics of both strategies plotted in the same graph:

The above chart shows that the highest Sharpe (0.76) and Sortino (1.21) ratios for the rebalanced strategy were slightly superior to the highest Sharpe (0.74) and Sortino (1.14) ratios for the momentum strategy. The biggest difference can be found with the MAR ratio, with the rebalanced portfolio having a maximum MAR ratio (0.79) that is significantly greater than the MAR ratio (0.59) for the momentum strategy.

**Discussion and conclusion**

Previous studies looked at the effect of varying the lookback period on the performance of the momentum strategy on a classic stock and bond mix. Inspired by comments in those articles, I then turned to study the effect of changing the stock and bond ratio on the rebalanced portfolio.

The results showed that as expected, increasing the stock component led to a higher CAGR over the nearly 30-year period. However, the optimum risk-adjusted metrics were actually achieved at relatively low stock percentages, of 20 to 40%. Additionally, the best Sharpe, Sortino and MAR ratios of the rebalancing portfolio were actually comparable or superior to those of the momentum portfolio.

So if the rebalanced portfolios generally have superior risk-adjusted metrics, why consider the momentum portfolio at all? Simply put, the answer is raw returns -- the best CAGR (12.00%) of the momentum strategy is over two percentage points higher than the best CAGR (9.91%) of the "rebalanced" portfolio (in quotation marks because that is achieved at 100% stocks) -- and that can make a big difference in the long run.

But for more conservative investors who favor lower drawdowns and less volatility, the rebalanced portfolio could possibly be more appropriate.

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**Author's note**

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I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.