“Make everything as simple as possible, but not simpler.” – Albert Einstein
Stock market indices are an easy and effective method for measuring overall market movement by acting as a hypothetical portfolio of an entire segment of the market. The most followed US indices include the S&P 500, Nasdaq Composite, Dow Jones Industrial Average, Russell 2000, and the Nasdaq 100. Since the 1990’s, it’s been possible to invest in the performance of these indices through ETFs like SPY, QQQ, IWM, etc. This immediately diversifies a portfolio, because the investment is spread out into holdings in hundreds of companies or more and allows an investor to make bets on entire sectors of the US economy.
The attractiveness of investing in index ETFs is simple: because these indices’ compositions are agnostic to the companies that comprise them (i.e. the S&P 500 will always be the 500 largest US-based companies by market capitalization, and no company is guaranteed a position in the index), any companies that do not survive a black swan event such as Bear-Sterns are replaced in the indices. This structure effectively guarantees that the indices will continue to create new all-time highs over the long run, taking the logical assumption that the US economy will continue to grow over the long run as well.
Following the first certainty that large-capitalization indices will increase in value over the long term, there exists the second certainty that the long-term growth will not occur uninterrupted. Every year, the stock market presents multiple tantalizing opportunities for growing investors’ portfolios: temporary drawdowns. These pullbacks can take drastically varying magnitudes, reaching as far as an 83% drawdown in the Nasdaq 100 index after the dot-com bubble collapsed in 2000. Though it took sixteen years to do so, the Nasdaq 100 eventually surpassed the March 27, 2000 high. A perfectly timed investment would have seen a 488% return over those 16 years, hence the idiom “buy the dip.”
Buying the dip is precisely the simple and elegant suggestion of this paper. With nearly guaranteed positive returns over a long investment horizon, it would be worthwhile to increase portfolio weighting into large capitalization indices during inevitable pullbacks. In order to maximize returns in these scenarios, it is recommended that these weighting increases be done via purchasing leveraged ETFs such as TQQQ, UPRO, and USD. With leveraged ETFs, there is a significant amount of volatility. Because of this, a negligible pullback in the underlying indices can result in a more significant correction in the leveraged ETFs. When the underlying indices recover and surpass their previous highs after even the most destructive bear markets, the potential returns from the leveraged ETFs will be even greater.
Taking the Nasdaq 100 during the first half of 2024 as an example, there were eight instances of temporary drawdowns with magnitudes greater than 2.5%:
For TQQQ, a 3x leveraged ETF of the Nasdaq 100 index, these same drawdowns had much larger magnitudes, presenting much more attractive investment opportunities:
Though the potential returns from perfectly timing drawdowns with the leveraged ETFs is much higher than trading with only the regular ETFs, a noticeable risk presents itself in the recovery time. For a price to return to its high after a drawdown, the gain required is the inverse of the loss. For example, a 10% loss requires a 100% ÷ (100%−10%) = 11.11% gain from the trough of the drawdown to recover the original price. With leveraged products, that drawdown becomes much larger, thus requiring a much larger burden to recover. The closer the loss gets to 100%, the faster the offsetting gain accelerates to infinity.
After sufficiently large drawdowns in the underlying indices, the leveraged ETF will not fully recover at the same time as the underlying ETF. This obviously presents a significant risk, which materializes during every bear market. An exemplary instance of this risk is the 2022 bear market. From November 22nd, 2021 through October 13th, 2022, The Nasdaq 100 index had a 37.67% drawdown. It wasn’t until December 19th, 2023 that the index had surpassed its November 2021 peak. During that same period, TQQQ experienced an 82.34% drawdown, and it still has not fully recovered that loss as of writing (661 trading days later).
This risk is unavoidable and problematic for investors, except when using a sufficiently-long time horizon such that the leveraged ETF’s long-term growth eventually surpasses the long-term growth of the underlying index. Because the underlying index is effectively guaranteed to continue growing in perpetuity, there will be a point at which the leveraged ETF outperforms the underlying index. Returning to historical examples, the stock market crash in the last quarter of 2018 shows the extent to which patience with leverage is rewarded. The Nasdaq 100 index underwent a 23.42% drawdown into the end of 2018. During the same period, TQQQ drew down 58.52%. The Nasdaq 100 recovered in 136 trading days, while TQQQ took 278 trading days to do the same. However, as of writing, TQQQ has returned 354.95% since the October 2018 peak, and the NADAQ 100 had a 167.08% return. While the latter is still remarkable, it pales in comparison to the outsized returns that leveraged ETFs offer in the long run. And over an even longer horizon, the difference in returns continues to compound into an irresistible investment. Since TQQQ’s inception, the Nasdaq 100 is up a commendable 1,052%, but TQQQ is up an unbelievable 20,193%. To put it into another perspective, a $10,000 investment in the Nasdaq 100 at the inception of TQQQ would be worth $115,200. That $10,000 invested instead in TQQQ would be worth $2,029,300.
In the interest of implementing at least a modicum of risk management, accepting smaller but still market-beating returns over a long time horizon, this paper proposes mainly holding regular ETFs of large capitalization indices, with conversion of a small percentage of those holdings into leveraged versions of the regular ETFs after drawdowns of the underlying index above a certain magnitude. The purpose of this methodology is to “buy the dip” while keeping a high percentage of holdings deployed at all times. This is because all of the capital that would be used for initiating investments during a dip would not have to come from cash reserves that drag down a fund’s potential returns outside of the few opportunities to make these dip investments. Rather, the capital comes from already-deployed capital, and simply applies leverage to that already-deployed capital to provide outsized returns during recovery periods.
A hypothetical example structure for this methodology would be a fund starting with $100 million AUM. It then puts that capital into the SPY ETF. Every time that SPY draws down 2.5%, 1% of the SPY holdings will be converted into a position in UPRO, a 3x leveraged ETF of the S&P 500. Then, whenever a UPRO position recovers to a 20% return, it is converted back into an SPY position. This structure does not provide the outsized gains that a full investment in UPRO position would, but it does drastically reduce the volatility of the fund’s value while still outperforming the benchmark S&P 500 over the long run.
Using this methodology across the past 10 years results in a 263% gain compared to the benchmark S&P 500’s gain of 186%. From Figure 2, it is very apparent that the leveraged weighting methodology does have more volatility, and it takes a significant amount of time before the methodology can distinguish itself from the underlying index. However, given that significant amount of time, it does indeed outperform the benchmark quite handily: an annualized return of 13.76% compared to the benchmark 11.08%.
The beauty of this system is in its simplicity. There is nothing fancy, no trend reversal predictions, and no consideration of technical or fundamental market forces. A truly elegant solution to the problem of beating the market: leveraging the dip. Another elegant aspect to this methodology is that it is also easily adjustable to suit the risk appetite of the person implementing it. At the risk of holding onto a more volatile position for a longer period of time, one can increase the required return for closing the UPRO position to, say, 30%, 50%, etc. At the risk of directly increasing the portfolio’s volatility, one can increase the percentage of SPY holdings to convert into a UPRO position. And with these higher risks comes better long-term performance. A graph showing the sensitivity of portfolio performance to each of the variables is presented in Table 3 below:
From Table 3, one might come to the obvious conclusion that taking larger positions in UPRO and holding onto them for longer will be the most effective investment scheme. Thus, the best strategy would be to simply buy-and-hold UPRO instead of SPY. For a fund manager, that would simply be out of the question, because the volatility would be much too high for LPs to tolerate. As pointed out previously, these leveraged ETFs can have annual returns as low as -85%. While an individual investor would view it as a temporary setback in a larger picture of outsized gains, hedge funds are expected to maintain low volatility while still achieving above-benchmark returns. It should be noted that meeting these expectations should also be a focus for individual investors.
A compelling result from this conversion methodology is that the portfolio can outperform the buy-and-hold UPRO strategy, though not by much. Over the 10-year period analyzed in this paper, UPRO grew 768.17%, which was beat by a few variable combinations of the conversion strategy. This is because the strategy involves purchasing large amounts of UPRO shares well below their previous highs and sells them after achieving benchmark-beating returns.
Presenting the results from a different view helps to add nuance to the decision of what combination of variables would be the most attractive. In Figure 3, the performance of each return threshold is grouped by position size:
At a 1% position size, the returns increase linearly with return threshold, so choosing to only convert 1% of SPY holdings at each 2.5% drawdown would simply be most interested in selecting the 50% return threshold for reconverting the UPRO position back into SPY. However, at all other position sizes, a pattern of decreasing marginal benefit with increasing return thresholds introduces more nuance to the decision.
The most attractive option is the 30% return threshold for all position sizes greater than 1%. At the 30% return threshold, the portfolio performances are always much larger than those for the 25% return threshold, and the trend does not decelerate noticeably from increasing the return threshold from 25% to 30%. However, above the 30% return threshold, the deceleration in returns becomes quite noticeable. At higher position sizes, the marginal change to performance with increasing return thresholds even turns negative. This indicates that the 30% return threshold is the highest threshold at which increasing marginal performance can justifiably offset the increased marginal risk from a higher return threshold.
Another attractive option would appear to be the 50% return threshold, as it bucks the trend of rounding off portfolio performances with increasing return thresholds. However, this anomalous behavior may be attributable to a small number of instances in which, for lack of a better term, the trade was lucky. This would make replicating similar performances improbable, and it would be inadvisable to expect that, going forward, using the 50% return threshold would not follow the same pattern befalling the other return thresholds above 30%. The purpose of developing this strategy is to reduce the influence that luck plays in timing tops and bottoms as much as possible, and to instead take advantage of lower prices agnostic of timing. An obvious delineation from an observable trend should therefore be ignored, and instead the decision for setting the return threshold is based on that observable trend – decreasing marginal performance after the 30% return threshold.
With the return threshold set to 30%, attention is focused on selecting the position size. For this decision, there is not a distinguishable ideal point in the portfolio performance chart like there is for the return threshold. Instead, the better option would be a more personal decision based on risk tolerance. Risk, in this case, is volatility of the portfolio performance, which is measured as beta. Beta is calculated as the covariance of the portfolio’s performance relative to that of the underlying index divided by the variance of the underlying index returns. A good way to understand beta is:
A beta greater than 1 indicates higher volatility relative to the benchmark.
A beta greater than 0 but less than 1 indicates lower volatility relative to the benchmark.
A beta less than 0 indicates inverse action relative to the benchmark.
During Q1 2024, UPRO had a beta of 2.98. This is to be expected, because it is a 3x leveraged ETF of the S&P 500, and it indicates that UPRO is about 3 times as volatile as the S&P 500. Figure 4 presents the beta for each of the position size options used in Table 3 corresponding to the 30% return threshold. Naturally, the beta increases proportionally with position size. With its near linearity, it is useful to also examine the ratio of performance-to-beta, so it is also presented in Figure 4 below:
From Figure 4, it is apparent that the performance-to-beta ratio peaks at a 7% position size. At this size, the hypothetical portfolio return would be 683% (22.85% annualized) with a beta of 2.101, meaning that over the 10-year period, the strategy would outperform the S&P 500 benchmark by 2.73-fold with a little over twice the volatility. That extra volatility results in a 53.69% maximum drawdown during the 2022 bear market, much larger than the 34.10% maximum drawdown that the S&P 500 experienced during 2022. The performance of a fund using this strategy over the past 10 years is graphed in [Figre] below:
Though this strategy is simple and elegant, it does unfortunately come with the curse of high reward at the cost of high risk. The strategy will never be able to outperform the market every year. As mentioned earlier, however, with a sufficiently long investment horizon, this strategy is almost guaranteed to outperform the benchmark, and quite handedly as well.
