Abstract

This paper will examine portfolio returns using long-term relative strength and long-term momentum as the only criteria for investment decisions. It will compare various portfolios using quarterly RSI readings as the sole gauge for long-term relative strength and will use the S&P 500 monthly RSI reading for its long-term momentum parameter. The results suggest that long-term relative strength and the S&P 500 long-term momentum are both useful for investment criteria.

Introduction

The academic literature is dominated by fundamental analysis. Fundamental analysis itself is built on a handful of foundational concepts. Seemingly most academics and academic institutions have accepted these concepts and their assumptions as fundamentally true.

This, in turn, has affected the belief of most market participants. Many professional market participants aspire to beat passive “buy and hold” investing where investors will buy index funds with low management fees. It is quite challenging to beat indexing over the long term and many people believe this is due to the efficient market hypothesis (EMH), especially when accounting for management fees as outlined by Eugene Fama and Kenneth French. Furthermore, many fundamentalists believe technical analysis has no merit as the efficient market hypothesis debunked all technical analysis theory decades ago. This paper will explore the foundational concepts of modern portfolio theory and whether using long-term relative strength and long-term momentum can provide superior returns compared to passive investing.

Foundational Concepts and Literature Review

Efficient Market Hypothesis

Eugene Fama mainstreamed the efficient market hypothesis into the financial literature. He hypothesized that there are three levels of market efficiency – weak form, semi-strong form, and strong form efficient markets. Many market participants believe that financial markets, especially liquid, information rich markets, are weak form efficient. Weak form efficient markets, in theory, accurately discount all historical stock pricing information. This means that all past stock prices are accurately reflected in a security’s current price and therefore no edge can be gained from using it to invest for the future. As technical analysis uses mainly pricing historical information, it would not be useful for investing in markets that are weak form efficient. Much of the empirical evidence on the efficient market hypothesis was focused on finding serial correlation of a stock’s price over a time- series. The evidence showed there was little, if any, correlation between a stock’s past change in price and a future change in price; therefore, markets were weak form efficient. After conducting serial correlation research on stocks in the Dow Jones Index from the late 1950’s to the mid 1960’s, Fama concluded there was only very slight dependence or it was non-existent.

Capital Asset Pricing Model

The capital asset pricing model (CAPM) is closely linked to the efficient market hypothesis. CAPM hypothesizes that markets have a security market line whereby securities will be accurately priced given their risk and the only way to beat the market is to take on more risk. CAPM identifies systematic and unsystematic risk as the two types of risk in the market. This model implies that market participants cannot beat the market while taking on less risk or, said another way, market participants cannot beat the market on an absolute and risk-adjusted basis.

Modern Portfolio Theory

Modern portfolio theory (MPT) is the practical application of the above theories. MPT was also built on Harry Markowitz’s portfolio selection research. His research argued that investors should consider expected returns and variance which he outlined as the “E-V rule”. The E-V rule implies that the right kind of diversification is needed in portfolio selection. The diversification outlined advocates for buying securities that aren’t highly correlated to an investors existing portfolio to reduce overall risk. MPT is the practice of buying diversified market indexes in accordance with Markowitz’s portfolio selection criteria and CAPM to eliminate unsystematic risk.

The above frameworks tie together in their belief that markets are efficient, that active investing cannott beat passive investing over the long term, and that market participants cannot avoid systematic risk. Interestingly, one pillar of CAPM and modern portfolio theory is their reliance on correlation when selecting securities in a portfolio. This is interesting because correlation is a technical indicator since it does not consider intrinsic value. On one hand EMH and CAPM suggest that technical analysis is futile, and on the other hand, technical analysis is a foundational element in the application of both theories.

Correlations in Bear Markets

In recent years, more research has been done on systematic risk, or what this author colloquially refers to as “macro risk”. Longin and Solnik researched market correlations in 2000 and they concluded that correlations increase in bear markets, but that correlations don’t increase in bull markets which partially nullifies the potential benefit of diversification. Correlations approaching one are what caused this author to refer to the risk as macro risk because the macro environment was evidently poor making it so that harsh bear markets are a poor time to be invested in any stocks. Longin and Solnik’s research suggest that a market timing system could be useful for investors as market timing and avoiding bear markets could provide more downside protection than diversification as the benefit of diversification is greatly reduced in a bear market.

Relative Strength

Robert Levy, adding to the work of Benjamin F. King Jr.’s unpublished PhD dissertation, was the first person to bring the concept of relative strength into the mainstream literature. He didn’t dispute serial correlation, which EMH, CAPM, and MPT all rely on, however, he researched if relative strength could provide investors an edge and therefore show that the above frameworks, while useful, might not be entirely robust. Relative strength, also known as cross-sectional momentum, compares two securities or sectors and notes which one was stronger than the other over a given timeframe.

Robert Levy researched stocks according to recent strength and put them in groups based on their relative strength. His research examined stocks over a 26-week period. He concluded that stocks among the top decile far outperformed stocks that were in the bottom decile over the same period. The stocks in the top decile averaged a 9.6% increase over the 26-week period while stocks in the bottom decile averaged 2.9% over the 26- week period. His empirical testing suggested the concept of relative strength had merit and could serve as a tool for outperforming the market. Levy also implied that examining serial correlation alone might not preclude the existence of underlying dependencies in the stock market. This suggests that even though stocks abide by a random walk movement, it does not invalidate certain forms of technical or statistical analysis, in particular relative strength. Levy’s research and assertions were the basis for this paper.

System Design and Results

This system was designed to further explore Levy’s findings and to examine if a simple technical system could beat passive investing. This paper will also briefly explore one long- term momentum parameter and whether it can be used as a type of macro (systematic) risk gauge. Modern portfolio theory states that investors should rebalance their portfolios on a quarterly basis so that excess growth from one index is sold and invested in index funds that didn’t appreciate as much (rebalancing) – the opposite will be done for this system. Depending on which type of portfolio is being tested, the system will concentrate funds every quarter in the weakest or strongest sectors. The quarterly relative strength index (RSI) readings will be used to rank each of the original nine SPDR sectors from strongest to weakest starting from the 2nd quarter of 2002 through the end of September 2021. This paper focused on the original nine sectors because they were created in late 1998 and had the most quarterly RSI data. The nine sectors that were included in the testing are materials (XLB), energy (XLE), financials (XLF), industrials (XLI), technology (XLK), consumer staples (XLP), utilities (XLU), health care (XLV), and consumer discretionary (XLY). Their first quarterly RSI readings were available at the end of June 2002 and the final recording was taken at the end of September 2021. The sectors will be ranked according to the previous quarter’s RSI reading meaning the RSI reading at the end of Q1 will determine the sectors selected for Q2 of that year and so on.

In all, eight different portfolios will be tested. The first six portfolios will not include the long-term momentum parameter (macro/systematic risk gauge). The long-term momentum parameter will be added to the last two portfolios to gauge its effect on performance. The long-term momentum parameter will be used to gauge the health of the broad market.

The long-term momentum parameter is the monthly RSI reading on the S&P 500. When the S&P 500 finishes a month below the 50 level on the monthly RSI, the entire portfolio will be sold and moved into bonds. Vanguard’s Total Bond Market Index Fund, VBMFX, was used as the bond security for the portfolios. When the monthly RSI closes a month above 50, the portfolio will stay or be invested in the prescribed sectors. The long-term momentum parameter is a simple, practical approach to mitigate damage done in bear markets where correlations move to one and diversification has limited benefit. This system only uses one indicator and applies it into two different ways.

The results for the eight portfolios are below. The timeframe for all portfolio’s will be from July 2002 until the end of September 2021, except for portfolio SPY-LTM which will have its timeframe in its explanation. The funds will be reallocated at the close of the last trading day in every quarter.

Portfolio 1-WK

Allocating all portfolio funds in the single weakest SPDR sector according to the quarterly RSI reading. Reallocating is done every quarter to allocate in the weakest sector.

Investing in the single weakest sector vastly underperformed passive investing on an absolute and risk-adjusted basis. All risk measures were well below passive investing’s risk measures and 1-WK’s CAGR trailed by over 8%. The Sharpe ratio of .14 showed significant underperformance as the portfolio didn’t have much upside to make up for its standard deviation while the Sortino ratio of .20 shows 1-WK had significant drawdowns compared to passive investing. The Treynor ratio also trailed passive investing significantly coming in at 2.65. Evidently, it does not always pay to be a contrarian.

The below tables compare the annual returns for 1-WK and SPY.

Portfolio 1-WK had eight negative years and 12 positive years over the tested period. In contrast, SPY had 3 negative years and 17 positive years. Portfolio 1-WK’s average negative year was -20.09% while its average positive year was 21.09%. SPY’s average negative year was -17.12% and its average positive year was 15.90%. Portfolio 1-WK outperformed SPY in seven years and underperformed SPY in 13 years.

Portfolio 2-WK:

Allocating all portfolio funds in the two weakest SPDR sectors according to the quarterly RSI reading. The portfolio will be allocated in two equal parts at the start of each quarter based on last quarter’s reading.

The addition of diversifying into the 2nd weakest sector markedly improved results compared to being entirely allocated in the weakest sector, however, it still underperformed passive investing on an absolute and risk-adjusted basis. Investing 50% each in the two weakest sectors improved all risk measures compared to portfolio 1-WK. The Sharpe ratio improved from .14 to .38, the Sortino ratio improved from .20 to .55, and the Treynor ratio improved from 2.65 to 6.43. This amount of improvement from the last portfolio suggests that the weakest sector can significantly impair an investors portfolio if they have too much exposure to it.

The below tables compare the annual returns for 2-WK and SPY.

Portfolio 2-WK had six negative years and 14 positive years over the tested period. Portfolio 2-WK’s average negative year was -15.46% while its average positive year was 19.30%. Portfolio 2-WK outperformed SPY in eight years and underperformed SPY in 12 years.

Portfolio 3-WK:

Allocating all portfolio funds in the three weakest SPDR sectors according to the quarterly RSI reading. The portfolio will be allocated in three equal parts at the start of each quarter based on last quarter’s reading.

Adding a third layer of diversification again improved the results. The portfolio’s CAGR improved to 7.95% compared to 7.02% for portfolio 2-WK. This portfolio, while it still underperformed passive investing, had improved risk measures across the board compared to portfolio 2-WK. The Sharpe ratio improved from .38 to .44, the Sortino ratio improved from .55 to .65, and the Treynor ratio improved from 6.43 to 7.02. Given all three portfolios where all funds were concentrated in some variation of the weakest 3 sectors underperformed passive buy and hold investing on an absolute and risk-adjusted basis over the near 20-year period, it is reasonable to conclude that relentlessly buying the weakest sectors is an inferior strategy compared to passive investing. It is also interesting that the results incrementally improved as more funds were allocated in relatively stronger, albeit still weak, sectors.

The below tables compare the annual returns for 3-WK and SPY.

Portfolio 3-WK had five negative years and 15 positive years over the tested period. Portfolio 3-WK’s average negative year was -14.33% while its average positive year was 17.20%. Portfolio 3-WK outperformed SPY in ten years and underperformed SPY in ten years.

Portfolio 3-STR:

Allocating all portfolio funds in the three strongest SPDR sectors according to the quarterly RSI reading. The portfolio will be allocated in three equal parts at the start of each quarter based on last quarter’s reading.

Portfolio 3-STR outperformed SPY by .76% per year on an absolute basis. Its risk-adjusted performance also outperformed passive investing. This is the first portfolio where it outperformed passive investing on an absolute and risk-adjusted basis. Accordingly, 3-STR was the first portfolio where annualized alpha was positive. 3-STR also outperformed in all risk-adjusted ratios. Portfolio 3-STR saw the Sharpe ratio increase from .44 to .70 compared to 3-WK. Also, the Sortino ratio increased from .65 to 1.02 and the Treynor ratio increased from 7.02 to 11.34.

The below tables compare the annual returns for 3-STR and SPY.

Portfolio 3-STR had three negative years and 17 positive years over the tested period. Portfolio 3-STR’s average negative year was -18.55% while its average positive year was 17.25%. Portfolio 3-STR outperformed SPY in 12 years and underperformed SPY in eight years.

Portfolio 2-STR:

Allocating all portfolio funds in the two strongest SPDR sectors according to their quarterly RSI readings. The portfolio will be allocated in two equal parts at the start of each quarter based on last quarter’s reading.

Portfolio 2-STR outperformed passive investing on an absolute and risk-adjusted basis. 2- STR’s CAGR was 1.64% more than SPY with superior risk-adjusted ratios. 2-STR had a positive annualized alpha of 3.13% and saw the Sharpe, Sortino, and Treynor ratios modestly improve from portfolio 3-STR. The Sharpe ratio improved from .70 to .73, the Sortino ratio improved from 1.02 to 1.10, and the Treynor ratio improved from 11.34 to 12.93. Interestingly, the standard deviation increased from 14.56% to 15.04% compared to 3-STR. This is the first portfolio that invested incrementally more in relative strength and had its standard deviation increase. All previous increments saw the standard deviation decrease.

The below tables compare the annual returns for 2-STR and SPY.

Portfolio 2-STR had three negative years and 17 positive years over the tested period. Portfolio 2-STR’s average negative year was -16.71% while its average positive year was 17.68%. Portfolio 2-STR outperformed SPY in 12 years and underperformed SPY in eight years.

Portfolio 1-STR:

Allocating all portfolio funds in the strongest SPDR sector according to the quarterly RSI reading. Reallocating is done every quarter to allocate in the strongest sector.

Portfolio 1-STR significantly outperformed SPY over the 19 year and 3-month period. 1-STR’s CAGR was an impressive 14.38% which was 4.34% higher than passive investing. 1-STR outperformed passive investing on all risk-adjusted ratios. Additionally, all risk-adjusted ratios improved compared to portfolio 2-STR – the Sharpe ratio improved from .73 to .80, the Sortino ratio improved from 1.10 to 1.24, and the Treynor ratio improved 12.93 to 17.42. Portfolio 1-STR had an annualized alpha of 6.55%. Portfolio 1-STR saw its standard deviation increase from 15.04% to 17.17% compared to portfolio 2-STR.

All six portfolios that strictly allocated according to the previous quarter’s relative strength index, which is historical information, incrementally improved as the allocation was increasingly concentrated in relative strength.

The below tables compare the annual returns for 1-STR and SPY.

Portfolio 1-STR had two negative years and 18 positive years over the tested period. Portfolio 1-STR’s average negative year was -22.28% while its average positive year was 19.38%. Portfolio 1-STR outperformed the SPY in half of the years.

Portfolio SPY-LTM:

Allocating all portfolio funds in SPDR’s S&P 500 ETF, SPY, if long-term momentum is positive (monthly RSI above 50). All funds will be moved to VBMFX, Vanguard’s bond index, when long-term momentum is negative (monthly RSI close below 50). For this comparison, the timeline will be from January 1999 to September 2021.

Portfolio SPY-LTM outperformed SPY on an absolute and risk-adjusted basis. SPY-LTM had an annualized alpha of 4.44% and outperformed on all risk ratios.

Starting this comparison at the beginning of 1999 biases this timeframe toward portfolio SPY-LTM as the long-term momentum parameter will allow it to miss most the bear market from 2000-2002. This paper will also examine a timeframe that is biased towards passive investing compared to this timeframe.

The below tables compare the annual returns for SPY-LTM and SPY.

Portfolio SPY-LTM had four negative years and 19 positive years over the tested period. Portfolio SPY-LTM outperformed SPY in four years, underperformed SPY in six years, and performed the same as SPY in 13 years.

Portfolio SPY-LTM:

The allocations will be the same as above except the timeframe will be from July 2002 to September 2021.

SPY-LTM underperformed SPY on an absolute basis but outperformed SPY on a risk- adjusted basis over this timeframe. As noted above, this timeframe begins near the end of 2000-2002 bear market so passive investing does not see a sizeable decline at the beginning of the timeframe. SPY-LTM was still invested in bonds at the beginning of this timeframe and didn’t invest in equities until the November 2003, so this timeframe is biased towards passive investing.

The below tables compare the annual returns for SPY-LTM and SPY.

Portfolio SPY-LTM had two negative years and 18 positive years over the tested period. Portfolio SPY-LTM’s average negative year was -3.75% while its average positive year was 11.30%. Portfolio SPY-LTM outperformed SPY in two years, underperformed SPY in six years, and performed the same as SPY in 12 years.

Portfolio 1-STR-LTM:

Allocating all portfolio funds in the strongest SPDR sector according to the quarterly RSI reading while the S&P 500’s monthly RSI reading closes above 50. If the S&P 500’s monthly RSI reading closes below 50, the portfolio will be allocated in bonds. This comparison will use the timeframe of July 2002 to September 2021.

Portfolio 1-STR-LTM utilizes the long-term momentum / macro risk parameter to signal when to invest in bonds. It was invested in bonds at the start of this timeframe and didn’t invest into equities until November 2003. 1-STR-LTM outperformed SPY by 4.32% per year on an absolute basis and significantly outperformed on a risk-adjusted basis. Although it is not displayed above, this portfolio had a skew of 0 which is atypical for a portfolio. 1-STR- LTM had significant annualized alpha at 9.66% with a lower standard deviation and only .47 correlation to the US market. Portfolio 1-STR-LTM had a lower annual return of .02% compared to 1-STR by itself, however, its risk-adjusted returns significantly improved compared to 1-STR – the Sharpe ratio improved from .80 to .96, the Sortino ratio improved from 1.24 to 1.64, and the Treynor ratio improved from 17.42 to 29.57.

The below tables compare the annual returns for 1-STR-LTM and SPY.

Portfolio 1-STR-LTM had one negative year and 19 positive years over the tested period. Portfolio 1-STR-LTM’s lone negative year was -9.39% while its average positive year was 15.73%. Portfolio 1-STR-LTM outperformed SPY in 11 years and underperformed SPY in nine years.

The long-term momentum parameter was added to all six original portfolios, but the data will not be included for the sake of brevity. The additional parameter improved the absolute and risk-adjusted performance for all portfolios outside of 1-STR where it only improved the risk-adjusted return. Portfolio 1-WK saw the largest improvement in absolute return as it moved to bonds and avoided a significant drawdown during the great financial crisis. The other four portfolios CAGR’s improved as well as they also moved to bonds and avoided much of the GFC. Most portfolios saw a noticeable improvement with risk- adjusted returns except for portfolio 1-WK which only saw modest improvements in its risk- adjusted returns. Portfolio 1-WK-LTM still had a 58% drawdown as XLE, which was the weakest sector and was therefore the sole investment in 1-WK-LTM, markedly declined during the 2020 covid crash as the long-term momentum parameter didn’t trigger before the Covid crash. This 58% drawdown in 2020 for 1-WK-LTM was the reason why the portfolio only had modest improvements in its risk-adjusted performance compared to portfolio 1-WK.

Implications and Discussion

Combined Portfolio Performance Metrics

All portfolios that invested exclusively in the weakest sectors as judged by their last quarter’s RSI reading underperformed SPY on an absolute and risk-adjusted basis. On the other hand, all portfolios that invested exclusively in the strongest sectors outperformed SPY on an absolute and risk-adjusted basis. The data shows that as the portfolios incrementally invested more in relatively strong sectors all risk ratios improved. It is reasonable to conclude that as the portfolios invested incrementally more in relative strength, they saw relatively smaller drawdowns and relatively larger rallies. The standard deviation is the only risk indicator that didn’t increase incrementally along with relative strength exposure portfolio, however, all portfolios that invested in relative strength had lower standard deviations than all portfolios that invested in relative weakness.

SPY-LTM outperformed passive investing from 1999 to the end of September 2021, however, it underperformed passive investing from July 2002 to the end of September 2021. SPY-LTM outperformed passive investing on a risk-adjusted basis on both timeframes. Additionally, when the broad market long-term momentum indicator was combined with 1-STR, it significantly increased risk-adjusted returns for 1-STR-LTM. The results were inconclusive as to whether long-term momentum can beat passive investing, however, the results suggest that monitoring and acting on the long-term momentum of the broad market is effective for reducing risk. This ties into Longin and Solnik’s conclusion that correlations in the stock market increase in bear markets so the risk-reward profile for most equities is poor in bear markets. Consequently, investors should avoid these periods of poor risk-adjusted returns and significant volatility.

Combined Annual Return Data

Portfolios that allocated more in relative strength saw a larger number of positive years and fewer negative years. The number of positive years increased sequentially as portfolios allocated more to the stronger sectors. Over and underperformance was a different story. The portfolios that allocated the most in relative weakness underperformed more during the tested period compared to SPY, but 1-STR didn’t outperform SPY during the majority of the tested period. Similarly, 1-STR-LTM only outperformed SPY in 11 of the 20 years. Portfolios 2-STR and 3-STR outperformed SPY in 12 of the 20 years, but they experienced more negative years than 1-STR and their average positive year’s return were also less than 1-STR’s average positive year.

The above data further shows that the long-term momentum parameter was useful for preventing large drawdowns. SPY-LTM and 1-STR-LTM had the lowest average negative returns of all portfolios tested. This is consistent with Longin and Solnik’s assertion that correlations approach 1 in bear markets; the long-term momentum parameter was effective at reducing drawdowns in bear markets where no sectors escaped the broad selling in equities. However, the long-term momentum parameter also forced portfolios to be invested in bonds during the early stages of new bull markets so portfolios that used the LTM parameter missed those periods of strong returns.

The data is clear in that investing in relative strength provides superior absolute and risk- adjusted returns compared to passive investing. This supports Robert Levy’s claim that serial correlation alone, or lack thereof, does not necessarily mean markets are weak-form efficient and that markets may still have underlying dependencies. These results suggest EMH, CAPM, and the security market line aren’t strictly accurate portrayals of markets even though they are useful, profound frameworks. The results have similar implications for modern portfolio theory in that the theory is useful and perhaps is the best investing method for the majority of market participants, but that it is beatable over the long term.

It is important to highlight the simplicity of this system. This system only uses one indicator in two different ways over two timeframes. Some readers might be skeptical of a portfolio management system that only uses one indicator to beat the market over the long term, especially one that has an annualized alpha of 9.66%; however, the relative strength index has been applied in ways that are consistent with existing research on relative strength, gauge the broad market strength, and quantify which sectors of the market have been the strong strongest. Essentially, it is not the indicator itself that provides superior returns, but the concept of relative strength that allows for superior returns. Many market participants believe technical indicators or trading rules are static and rigid. This is a flawed view of technical analysis as the foundational concepts are more important than rigid investing rules. This paper was written to test long-term relative strength and long-term momentum, but it also shows that technical indicators can be used in a multitude of ways and that they don’t have static, rigid applications.

Conclusion

The above evidence and near 20-year testing period show that using long-term relative strength and long-term momentum can significantly outperform passive investing on an absolute and risk-adjusted basis. Historical relative strength information provides investors with a measurable edge and can show investors where the best risk and reward opportunities lie. These results are consistent with existing research on relative strength.

The results of the six portfolios showed that investing more in relatively strong sectors improved results with each increment. Adding a long-term momentum parameter to gauge broad market health can also improve risk-adjusted performance by markedly decreasing drawdowns and volatility.

Lastly, the results showed a soundly applied, simple technical system could beat passive investing over the long-term; simplicity might be the ultimate form of sophistication.

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