Tactical Asset Allocation During Cheap Markets

Tactical Asset Allocation During Cheap Markets

August 22, 2014 Key Research, Tactical Asset Allocation Research
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(Last Updated On: January 1, 2017)

In our last post, we looked at tactical allocation using valuation metrics and trend-following measures.

Our conclusion from the analysis is that discerning robust trading signals based on  market valuations is difficult at best.

This research piece attempts to dig a little deeper and addresses the following questions:

  • Opportunity Costs
    • How do other asset classes perform during different CAPE regimes? Why go all-in on equity if bonds are the asset class that outperforms?
  • Diversification
    • Do we abandon diversification and shift heavily into equities following cheap markets?
  • Real Equity Premium
    • CAPE ratios are absolute pricing measures, but what we care about is the equity premium. If equity is expected to earn 15% real and bonds are expected to earn 15% real, equity isn’t cheap.

Strategy Background

The following 3 data series are used in our tests:

  1. LTR: Merrill Lynch 7-10 year government bond index—ML1US10 INDEX
  2. SPX: SP500 Total Return Index—SPXT INDEX
  3. Shiller P/E: Shiller’s Cyclically Adjusted PE ratio—10-year average real earnings /real price

Simulation results are from January 1, 1929 through April 30, 2014.

No transaction costs are included in any of our analysis. All results are gross of any transaction fees, management fees, or any other fees that might be associated with executing the models in real-time. The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

Shiller P/E and Market Performance (1/1/1929 to 4/30/2014)

  • Shiller P/E and S&P 500 Over Time
  • Low Shiller P/Es, on average, are followed by bull markets over long cycles.
    • The figure to the right plots the Shiller P/E over time (left axis) and the S&P 500 return series over time (right axis).
    • Log scale.
1
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

 Opportunity Costs

Given a Shiller P/E starting point, what do subsequent 3-year stock and bond returns look like?

  • Low valuation implies higher expected future stock returns, on average.
  • Bonds are fairly stable across equity valuation regimes, but also see a boost during the cheapest market environments.
2
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request. The figure plots different Shiller P/E regimes (X-axis). For example, “15-16” represents all historical samples when the S&P 500 was priced between a 15 and a 16 Shiller P/E. Compound annual growth rates (CAGR) are presented on the Y-axis. All CAGRs are calculated over 3-year periods. We test periods ranging from 1 to 5 years and find similar results.

Given a Shiller P/E starting point, what do subsequent 3-year Sharpe ratios look like?

  • Stocks show a relationship between risk-adjusted returns and valuation, but the correlation is not as strong as Shiller P/E level and 3-yr CAGR (chart above).
  • Bonds have strong risk-adjusted returns across equity valuation regimes, to include the extreme cheap and extreme expensive equity valuation regimes (bonds actually outperform at the extremes).
3
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request. The figure plots different Shiller P/E regimes (X-axis). For example, “15-16” represents all historical samples when the S&P 500 was priced between a 15 and a 16 Shiller P/E. Sharpe ratios are presented on the Y-axis. All Sharpes are calculated over 3-year periods. We test periods ranging from 1 to 5 years and find similar results.

Digging deeper into extremely cheap markets

The figure below plots the Shiller P/E over time (left axis) and the S&P 500 return series over time (right axis). We highlight prominent valuation troughs with red circles. In the analysis that follows we examine the detailed performance data for stocks and bonds.

4
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.
S&P Statistics Summary

The following table contains the statistics for various Shiller PE regimes (each column represents a red circle above).

5
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.
LTR Statistics Summary

The following table contains the statistics for various Shiller PE regimes (each column represents a red circle above).

6
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.
Conclusion on Opportunity Costs

On  Sharpe ratio basis, stocks outperform in the 49-52, 74-77,  and the 09-12 bear markets.
On  Sortino ratio basis (MAR = 5%), stocks outperform in the 49-52, 74-77, 82-85, and the 09-12 bear markets.

Stocks AND bonds are interesting during cheap equity markets.

Diversification

Given a trough Shiller P/E starting point, what does a diversified allocation between stocks and bonds do for the investor?

The common story is that cheap stock markets warrant a wholesale move into equities.

50/50 Statistics Summary (50% equity; 50% 10-year bonds)

7
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

60/40 Statistics Summary (60% equity; 40% 10-year bonds)

8
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.
Conclusion on Diversification

Diversified stock/bond portfolios following trough Shiller P/E events typically outperform single position portfolios in either stocks or bonds independently.

  • Diversification always matters

Real Equity Premium

Absolute valuation metrics may not precisely capture the benefit/cost  to holding risk. In other words, a P/E of 20x doesn’t mean anything in a vacuum.

Any first year finance student will tell you that expected equity returns will roughly equal the risk-free rate plus an equity premium. Why anchor on the risk-free rate and why add an equity premium? Well, the risk-free rate is what you get in your checking account–so that is the baseline we should all expect from ANY asset class. Next, ask yourself, Who would hold risky equity if there was no extra kick in performance over stashing the cash in the checking account?…that is the equity premium…the extra return we get for taking on risk.

Understanding the “RF +equity premium concept” helps us better understand why absolute valuation levels may not capture true equity market valuations. For example a P/E of 10 (a 10% earnings yield) with a 10-year yield of 15% may imply an expensive equity market (-5% equity premium) relative to a situation where the P/E is 20x (5% earnings yield) and the 10-year yield is 1% (+4% equity premium). The P/E in the second scenario signals “expensive,” but on a equity premium basis, stocks are cheap relative to the scenario where the P/E is 10.

We test how stocks and bond perform during different Real Equity Premium periods, where Real Equity Premium = 1/CAPE [Earnings Yield] – Real 10-year yields (Note: CAPE is already in “real” terms).

The figure below plots the Shiller P/E, or cyclically-adjusted P/E (CAPE), over time (right axis) and the Real Equity Premium (1/CAPE – Real Treasury Yield) (left axis). Extreme spread events are highlighted with red circles.

9
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

Real Equity Premiums tend to roughly correspond with trough Shiller P/Es, but not always (e.g., 1947)

Real Equity Premium Performance Characteristics

Given a Real Equity Premium starting point, what do subsequent 3-year returns look like?

  • Future stocks appear to have a relationship between Real Equity Premium, but the correlation is weak.
  • There is no clear pattern between Real Equity Premium and future bond returns.
10
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request. The figure plots different Real Yield regimes (X-axis). For example, “7-7.5” represents all historical samples when the 1/CAPE – 10-Year Treas was priced between a 7% and a 7.5%. Compound annual growth rates (CAGR) are presented on the Y-axis. All CAGRs are calculated over 3-year periods. We test periods ranging from 1 to 5 years and find similar results.

Given a Real Equity Premium starting point, what do subsequent 3-year returns look like?

  • Future stocks appear to have a relationship between Real Equity Premium, but the correlation is weak.
  • There is no clear pattern between Real Equity Premium and future bond or stock returns.
11
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

Real Equity Premium Performance Characteristics–Details at Trough Real Equity Premium

S&P Statistics Summary

The following table contains the statistics for various Real Equity Premium regimes (each column represents a red circle above).

13
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.
LTR Statistics Summary
14
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.
50/50 Statistics Summary
15
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.
 Conclusions on Real Equity Premium
  • High Real Yield periods predict high spreads in CAGRs between stocks and bonds.
  • On a risk-adjusted basis stocks tend to outperform bonds
  • Diversified portfolios—in contrast to the results for low absolute Shiller P/E event–do not always outperform all-in stock bets.
    • Diversification is less valuable and targeted bets may be warranted during high Real Equity Premium periods.

Overall Conclusions

  • Bonds perform well across different valuation periods–to include extreme low valuation periods.
  • We should stay diversified during low absolute valuation periods.
  • We might want to tactically shift towards equity during high Real Equity Premium periods.
  • The results highlight a lot of noise and variation in the data. Identifying a “silver bullet” for tactical asset allocation is impossible…but good luck trying.

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Definitions of common statistics used in our analysis are available here (towards the bottom)




About the Author

Wesley R. Gray, Ph.D.

After serving as a Captain in the United States Marine Corps, Dr. Gray received a PhD, and was a finance professor at Drexel University. Dr. Gray’s interest in entrepreneurship and behavioral finance led him to found Alpha Architect. Dr. Gray has published three books: EMBEDDED: A Marine Corps Adviser Inside the Iraqi Army, QUANTITATIVE VALUE: A Practitioner’s Guide to Automating Intelligent Investment and Eliminating Behavioral Errors, and DIY FINANCIAL ADVISOR: A Simple Solution to Build and Protect Your Wealth. His numerous published works has been highlighted on CBNC, CNN, NPR, Motley Fool, WSJ Market Watch, CFA Institute, Institutional Investor, and CBS News. Dr. Gray earned an MBA and a PhD in finance from the University of Chicago and graduated magna cum laude with a BS from The Wharton School of the University of Pennsylvania.


  • Rian Weber

    Very interesting topic. On a related note, have you done any research on the Shiller Barclays CAPE US Core Sector Index? Uses CAPE ratios for the underlying US equity sectors to arrive at a portfolio. Historical performance looks quite strong but not a long track record. Below is a link to the ETN website that was created.

    https://barxis.barcap.com/US/7/en/details.app?instrumentId=174066

  • I consider sector allocations based on valuations/momentum/X-factor as a noisy way of doing individual security selection based on valuations/momentum/X-factor. When you back-out the “sector allocations” based on buying the x % cheapest stocks and compare those allocations to buying the x % cheapest sectors you typically find that the security selection version outperforms. In analogy terms, sector-level allocation systems are like axes, security-level allocation systems are like scalpels.

    Of course, investing is simple, but not easy…one also needs to consider tracking error, and thus, career risk…

    Anyway, to answer your question: Yes, I am very familiar with the index (which actually has a momentum element interestingly enough) and I think it is pretty dang cool…but I’ve seen cooler…

  • siamond

    Good topic. It is quite clear that a 3-years horizon is mostly unpredictable though. Even the PE doesn’t really help for such short horizon (cf. the roaring 90s). It would be good to see more analysis related to a longer horizon (10 or 15 years).

  • longer horizons generate similar conclusions

  • siamond

    Well, I actually ran the numbers. The S&P500 Earnings Yield (1/CAPE) provides a fairly decent prediction (Correlation=0.64; R2=0.4) over 15 years of actual returns for 1881 to now. And the correlation is better in the past 50 years. This does seem somewhat actionable, either as such or as TAA decisions relying on an equity premium, wouldn’t you agree?

  • try it in a system that actually allocates and compare that to buy and hold or long term MA. Let me know what you find

  • siamond

    I did… Although I have a good dose of skepticism about the findings… Check your e-mail… 😉