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Long-term Tests of Simple X% Rules

Posted in Technical Trading

A subscriber requested long-term tests of simple versions of the strategy described by Jason Kelly in The 3% Signal: The Investing Technique that Will Change Your Life. We start with a general strategy targeting an X% quarterly increase in a stock fund, as follows:

  1. Initiate X% rules with either 80%-20% or 60%-40% allocations to a stock fund and a bond fund.
  2. If over the next quarter the stock fund increases by more than X%, transfer the excess from the stock fund to the bond fund.
  3. If over the next quarter the stock fund increases by less than X%, make up the shortfall by transferring money from the bond fund to the stock fund.
  4. If at the end of any quarter the bond fund does not have enough money to make up a shortfall in the stock fund: either draw the bond fund down to 0 and add cash to make up the rest of the shortfall; or, draw the bond fund down to 0 and bear the rest of the shortfall in the stock fund.
  5. Consider two benchmarks: a 100% allocation to the stock fund (B&H); and, 60%-40% allocations to the stock and bond funds, rebalanced quarterly (60-40). Whenever adding cash to the bond fund per Step 4, add equal amounts to the benchmarks.

We consider for X% a range of 2% to 4% in increments of 0.5%. We employ stock and bond mutual funds with long histories: Fidelity Magellan (FMAGX) and Fidelity Investment Grade Bond (FBNDX). We assume there are no trading frictions when adding or withdrawing money from these funds. Using quarterly returns for these funds from the first quarter of 1972 (limited by FBNDX) through the first quarter of 2015 (43.25 years), we find that:

First we consider strategy variations that add cash as needed to cover all shortfalls in FBNDX when FMAGX fails to achieve the targeted quarterly return.

The following chart summarizes on the left axis terminal values of $10,000 initial investments at the end of December 1971 in:

  • X% rules with necessary cash additions and initial $8,000-$2,000 FMAGX-FBNDX allocations, with X% ranging from 2% to 4%.
  • Corresponding FMAGX B&H benchmarks with matching cash additions.
  • Corresponding 60-40 FMAGX-FBNDX benchmarks with matching cash additions.

The chart also shows on the right axis total cash additions for each X% rule. As reasonably expected, setting a higher quarterly return target increases total required cash additions, and higher cash additions translates to higher terminal values. Simple performance statistics may mislead because of occasional cash additions.

In general, the X% rules underperform both benchmarks.

For greater insight, we focus on the performance of a 3% rule and the corresponding benchmarks.

X-percent-rule-80-20-terminal-values-and-total-cash-adds

The next chart tracks on logarithmic scales the cumulative performance of the 3% rule with initial $8,000-$2,000 FMAGX-FBNDX allocations and corresponding benchmarks (left axis) and each required cash addition (right axis) over the available sample period. Results suggest that:

  • The 3% rule sometimes matches, sometimes outperforms and sometimes underperforms the benchmarks. Recently (the last 15 years or so), the 3% rule appears to outperform the benchmarks.
  • Requirements for cash additions tend to concentrate during bear markets, when it may be most difficult for investors to commit more money to stocks. The required total addition during March 2008 through March 2009 is exceptionally large ($427,887).

As noted above, simple performance statistics may mislead because of occasional cash additions.

How do results differ for initial 60%-40% allocations to FMAGX and FBNDX?

3-percent-rule-80-20-cumulatives-with-cash-additions

The next chart tracks on logarithmic scales the cumulative performance of the 3% rule with initial $6,000-$4,000 FMAGX-FBNDX allocations and corresponding benchmarks (left axis) and each required cash addition (right axis) over the available sample period. Terminal values and required cash additions are lower than in the preceding case, but qualitative results are similar.

What changes when there are no cash additions to make up for shortfalls in transfers from FBNDX?

3-percent-rule-60-40-cumulatives-and-cash-additions

The next chart tracks on a logarithmic scale the cumulative performance of the 3% rule with initial $8,000-$2,000 FMAGX-FBNDX allocations and the benchmarks with no cash additions. Whenever FBNDX does not have enough money to bring the allocation to FMAGX up to the targeted 3% quarterly increase, the stock allocation is left short of the target.

Results are qualitatively similar to those above, but terminal values are of course lower. Some key performance statistics are:

  • 3% rule – Compound annual growth rate (CAGR) is 10.2%. Average quarterly return is 2.7%, and standard deviation of quarterly returns 7.1%. Maximum drawdown is -30%.
  • FMAGX B&H benchmark – CAGR is 13.5%. Average quarterly return is 3.9%, and standard deviation of quarterly returns is 11.3%. Maximum drawdown is -63%.
  • 60-40 FMAGX-FBNDX benchmark – CAGR is 11.5%. Average quarterly return is 3.0%, and standard deviation of quarterly returns is 7.3%. Maximum drawdown is -44%.

With initial $6,000-$4,000 FMAGX-FBNDX allocations, CAGR for the 3% rule is 9.8% and maximum drawdown is -35%. The shape of the cumulative trajectory is similar.

Results suggest that the 3% rule suppresses maximum drawdown compared to the benchmarks, but with a substantial sacrifice in CAGR.

For another perspective we look at rolling five-year performance without cash additions.

3-percent-rule-80-20-cumulatives-without-cash-additions

The next chart  tracks rolling five-year annualized returns for the 3% rule with initial $8,000-$2,000 FMAGX-FBNDX allocations and the benchmarks with no cash additions. Results indicate that the 3% rule generally underperforms the two benchmarks from the late 1970s through 2000 and matches or beats the benchmarks thereafter.

Results are very similar for initial $6,000-$4,000 FMAGX-FBNDX allocations.

What happens if we substitute a more sedate equity mutual fund for FMAGX?

3-percent-rule-80-20-5-year-rolling-returns-without-cash-additions

The final two charts replicate the preceding two charts, substituting quarterly returns of Pioneer A (PIODX) for those of FMAGX. For comparison, over the entire sample period, PIODX has a CAGR of 10.7%, compared to 13.5% for FMAGX. Its average quarterly return (standard deviation of quarterly returns) is 2.9% (8.1%), compared to 3.9% (11.3%) for FMAGX.

CAGRs are 10.4%, 10.7% and 9.5%, respectively, for the 3% rule, the PIODX B&H benchmark and the 60-40 PIODX-FBNDX benchmark. Maximum drawdowns are -22%, -45% and -31%, respectively. The 3% rule is relatively more attractive for this choice of stock fund. Again, attractiveness derives mostly from the last 15 years or so of the sample period.

3-percent-rule-80-20-cumulatives-with-PIODX

3-percent-rule-80-20-rolling-5-year-returns-with-PIODX

In summary, evidence from simple tests offers little support for a belief that the 3% rule outperforms simple benchmarks over the long term, but it has beaten the benchmarks since about 2000.

Cautions regarding findings include:

  • The sample period is not long in terms of number of equity bear markets and number of interest rate regimes.
  • Results may be different for other stock funds (and bond funds), depending on average returns and volatilities of returns.
  • Costs of adding and removing money (such as loads) from the selected mutual funds may have varied over time and may be substantial for portions of the sample period. These costs would lower performance and may affect findings.
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