Inverse leveraged funds: The destructive effect of sucker rallies

Summary

- One can make money shorting the market using inverse leveraged funds.

- Inverse leveraged funds are not for buy-and-hold investors.

- They are risky bets, which can lead to significant gains or losses.

- One key source of risk are upward rallies. This is demonstrated through spreadsheet-based simulations.

The performance of two inverse leveraged funds

The graph below shows the performance of two popular inverse leveraged funds () during a period of a little less than 20 days in December of 2018. They are available as exchange-traded funds (ETFs). One is the ProShares UltraPro Short S&P500 (SPXU), which tends to replicate the daily performance of the S&P 500 times -3. For example, if the S&P 500 drops 1 percent in one day, the fund goes up 3 percent. The other fund on the graph is the Direxion Daily Small Cap Bear 3X ETF (TZA), which tends to replicate the daily performance of the Russell 2000 index times -3.

I owned shares of these two funds during the time period shown. As you can see from the graph, if you invested in these funds during the period shown, your investment in SPXU would have gone up 31.41 percent. The investment in TZA would have gone up 44.99 percent. This is a period of time in which the S&P 500 had gone down 8.9 percent, and the Russell 2000 had gone down 11.9 percent. So, the SPXU and TZA performed even better than expected during the period. Due to daily compounding, they provided returns over a period of a little less than 20 days that were a bit better than the daily returns; i.e., more than 3 times the drops in the reference indexes.

How one would expect things to go

The screen snapshot below is for a spreadsheet-based simulation that shows how one could expect an investment in an inverse leveraged fund to perform during a period where the S&P 500 is losing value, but with ups and downs. The cells highlighted in yellow contain the settings of the simulation, which are: (a) the initial value invested; (b) the multiplier for the inverse fund; (c) the CBOE Volatility Index (VIX), which represents the expected percentage range of movement in the S&P 500 over the following year; and (d) the bottom range for the percentage variation in the S&P 500.

The “Day % variation” is the simulated daily percentage variation in the S&P 500, calculated based on the VIX value, which was set at 50. This value of VIX suggests a highly volatile market. The “Range (top)” value is calculated based on that daily percentage variation and on the “Range (bottom)” value. Both bottom and top range values define the range of daily variation, in percentage terms, for the S&P 500. Note that the daily variation has a negative bias. This is reflected in the values under “Day % gain”, which tend to lean toward the negative end of the range.

Overall, the S&P 500 goes down 6.61 percent over a period of 20 trading days, with moves up and down throughout that period. As you can see, we are trying to be realistic in our simulation. Neither market indexes nor individual stocks go down or up in a perfectly linear fashion. At the far right we see what happens with the inverse leveraged fund. The overall cumulative percentage gain ends up being 22.08 percent. This would probably be a positive surprise for an investor. This gain is higher than 19.83 percent (3 times 6.61), which one could expect based on the daily multiplier.

The destructive effect of “sucker” rallies

The problem is that often one sees an upward rally during periods where the S&P 500 is losing value. This is the case as well with other indexes and even individual stocks during bear markets. The screen snapshot below is for a simulation where the S&P 500 is losing value over a period of 20 days, but with two 5 percent upward rallies during that period (cells highlighted in yellow). Overall, the S&P 500 goes down one half of a percent over the period. The inverse leveraged fund, instead of going up, also goes down by 4.06 percent.

In this scenario the fund has performed worse than expected. Based on the daily performance of the fund, an investor could have expected a small positive return of about 0.15 percent. The reason for the unexpected poor performance is the counter-compounding effect that the two daily 15 percent drops have on the invested value. Those two daily drops correspond to the two daily 5 percent gains in the S&P 500.

So, you can make money shorting the market using inverse leveraged funds, but the probability that you will be successful doing so is small. This is due to three main reasons: (a) the stock market goes up much more often than it goes down; (b) even during periods when the stock market is going down, there are upward rallies; and (c) once the market moves from bear to bull, it typically stays like that for a while, which can completely wipe out the original investment due to reverse compounding.

Inverse leveraged funds are not for buy-and-hold investors. They are risky bets, which can lead to significant gains or losses. On the positive side, an investor will not lose more than the initial investment with these funds. This could happen if the investor tried to replicate the performance of the fund by shorting an index ETF or trading options borrowing from a margin account.

How do exchange-traded funds (ETFs) work?

While the distinction between active and passive management sets the high-level strategy, the true "magic" of an exchange-traded fund (ETF) lies in its daily operations. Unlike mutual funds, which require managers to buy and sell securities manually to meet investor demand, ETFs utilize a streamlined "Creation and Redemption" mechanism. This process is implemented by Authorized Participants (APs)—typically large institutional entities—who exchange baskets of underlying securities for blocks of ETF shares, known as creation units. By relying on these in-kind exchanges rather than cash transactions, ETF managers can scale the fund's size without the administrative friction or trading costs associated with traditional open-end funds.

This structural design offers a significant advantage: superior tax efficiency. (See figure below. Source: State Street Global Advisors.) Because the manager is exchanging securities in-kind with an AP rather than selling them on the open market, the fund avoids triggering capital gains taxes at the fund level. This allows the ETF to shed low-cost-basis shares through the redemption process, effectively raising the portfolio's average cost basis and shielding investors from the "tax drag" common in mutual fund portfolios. For the end investor, this means taxes are generally only realized upon the personal sale of their own shares, not as a result of the manager’s internal rebalancing.

Furthermore, the ETF structure creates a self-regulating pricing loop through arbitrage. Because ETF shares trade on secondary exchanges like stocks, their price can occasionally drift away from the fund’s Net Asset Value (NAV). When a premium or discount appears, APs are incentivized to step in: they buy the cheaper asset and sell the more expensive one until the price equilibrium is restored. This constant monitoring ensures that an ETF’s market price remains tightly tethered to the value of its underlying holdings, providing investors with reliable liquidity even during periods of heightened market volatility.

The asymmetric danger of short selling in a high-value market

The fundamental risk profile of short selling is defined by a harsh mathematical asymmetry. When you go "long" on a stock, your downside is strictly defined: the most you can lose is the 100% you initially invested, as a share price cannot drop below zero. Conversely, shorting flips this safety net on its head. Because there is no theoretical limit to how high a stock price can climb, a short seller’s potential losses are effectively infinite. You are contractually obligated to buy back those shares eventually to return them to the lender, regardless of whether the price has doubled, tripled, or surged by a factor of ten.

This unlimited risk is often realized through the "domino effect" known as a short squeeze. (See figure below. Data source: Board of Governors of the US Federal Reserve System; Chicago Board Options Exchange; via FRED.) When a heavily shorted security begins to rise unexpectedly, it triggers a panicked feedback loop. Short sellers, seeing their capital evaporate, rush to buy back shares to "cover" their positions and mitigate further damage. This sudden wave of buying pressure—ironically coming from those who bet against the stock—drives the price even higher. As the price climbs, it hits the "stop-loss" orders of more short sellers, forcing them to buy as well, which creates a self-fulfilling prophecy of rapidly escalating prices that can decouple entirely from the company's actual value.

Compounding these market dynamics is the structural danger of using margin. Shorting is rarely done with pure cash; it is an inherently leveraged move using borrowed funds. As the stock price rises against you, your collateral shrinks relative to the size of the position, often triggering a "margin call." At this stage, your broker may demand an immediate cash infusion to keep the trade open. If you cannot meet this requirement, the broker maintains the legal right to execute a "forced buy-in," closing your position at the current market price without your consent. This locks in your losses at what might be the worst possible moment. Understanding these mechanics is vital in the current climate, where an elevated VIX indicates high volatility and a highly-priced market leaves little room for error.

Understanding the "warp" in long-term Treasuries

A common point of confusion for many investors is the distinction between average maturity and effective duration, two metrics that are often used interchangeably but serve very different roles in a portfolio. Average maturity represents the weighted average of the time remaining until the bonds in a fund reach their final payment date. Effective duration, however, measures the fund's actual price sensitivity to interest rate changes. For a fund like the Vanguard Long-Term Treasury ETF (VGLT), this gap is significant. As of early 2026, VGLT carries a weighted average maturity of approximately 21.90 years, yet its effective duration sits lower at roughly 14.10 years. (See figure below. Data source: Vanguard.) This occurs because the semi-annual coupon payments "shorten" the economic life of the investment, meaning you recover your capital faster than the final maturity date suggests.

The primary reason to understand the difference between these measures is to predict how your principal will react to a changing rate environment. The mathematical relationship is inverse: when interest rates go down, the principal value of the bond fund goes up. Using VGLT’s current effective duration of 14.10 as a guide, we can quantify this "warp" in value. If the 10-year and 30-year Treasury yields were to drop by 1% (100 basis points), the share price of VGLT would be expected to rise by approximately 14.10%. This leveraged-like sensitivity is exactly why long-term Treasuries are favored by those looking to hedge against economic slowdowns, as the price appreciation can be substantial during a "flight to safety."

This distinction is the cornerstone of sophisticated bond investing and the reason why this post is important. If an investor looks only at the 21.9-year maturity of VGLT, they might overestimate the time their capital is locked away or the immediate volatility of the fund. Conversely, failing to account for the 14.10 duration means ignoring the precise tool used to calculate risk. By understanding that effective duration is the "speedometer" of one’s bond portfolio’s price movement, one can better position their assets to benefit from shifting yields rather than being caught off guard by them. (Disclosure: the author owns VGLT shares at the time of this writing.)

The AI capex super-cycle: A math problem for the S&P 500

The scale of investment in artificial intelligence by S&P 500 companies—specifically the "hyperscalers" like Microsoft, Alphabet, and Meta—has reached levels that are historically unprecedented. (See figure below. Data source: Goldman Sachs.) For the 2026 fiscal year, collective capital expenditures for these firms are now forecasted to hit a staggering $674 billion, up from roughly $400 billion in 2025. To put that in perspective, this spending represents about 2.2% of U.S. GDP, a figure that is more than four times the investment level seen as recently as 2023. We are witnessing an infrastructure "arms race" that dwarfs the historical buildouts of the interstate highway system and the moon landing combined.

To justify this massive $600 billion-plus annual burn, the earnings of these S&P 500 giants will need to grow at an extraordinary clip over the next few years. For the current level of AI investment to generate a positive return on invested capital (ROIC), AI-driven revenues would need to scale to approximately $2 trillion annually by 2030. Currently, actual AI-related revenue for these firms is estimated to be in the neighborhood of only $20 billion to $40 billion. This implies that the market is banking on a 100-fold increase in top-line AI contribution within just four to five years to keep pace with the depreciation and operating costs of the hardware being installed today.

From a structural and historical standpoint, this "hockey stick" growth requirement is bordering on the mathematically impossible. While the S&P 500 is currently projected to grow earnings per share (EPS) by roughly 12% to 14% in 2026, those gains are largely driven by cost-cutting and existing software margins, not yet by a massive influx of AI-native profits. When you factor in the short three-to-five-year useful life of AI chips compared to traditional industrial infrastructure, the "earn-back" hurdle becomes so high that even a "goldilocks" economy may not be enough to prevent a significant valuation correction.

What is the impact of the price of oil on an inflation measure that excludes the price of oil? A look at the Core PCE

A recent econometric analysis covering the volatile period from late 2020 to late 2025 reveals a striking paradox in how we measure inflation. Utilizing WarpPLS () to conduct a nonlinear robust path analysis, we found that the association between Brent Crude oil prices and the Core Personal Consumption Expenditures (PCE) price index stands at a remarkable 0.78. Perhaps most significantly, the WarpPLS Nonlinear Bivariate Causality Direction Ratio (NLBCDR) suggests a causal link, indicating that fluctuations in oil prices are likely a primary driver of the Core PCE’s movement. This challenges the conventional wisdom of inflation tracking, as it suggests that oil prices account for approximately 60 percent of the variance in a metric specifically designed to exclude energy costs.

The nature of this relationship is distinctly nonlinear, characterized by a strong correlation that eventually hits a ceiling. Within the price range of approximately $54 to $105 per barrel, the linear association (correlation) between Brent Crude and Core PCE is a high 0.91. In this range, a $1 increase in the price of oil is associated with a 0.08 increase in Core PCE inflation. However, once oil prices exceed the $105 threshold, the relationship turns flat, suggesting a diminishing marginal impact on core inflationary pressures at very high oil price levels. This "warped" relationship explains why core inflation can feel so tethered to the gas pump during moderate price climbs, yet appears decoupled during historically high oil spikes.

These findings necessitate a fundamental re-thinking of the Core PCE measure as a tool for monetary policy. If "Core" inflation is intended to strip out volatile elements to reveal the underlying price trend, its 60 percent dependency on oil—one of the very elements it seeks to exclude—suggests that energy costs are far more "sticky" and systemic than previously assumed. For investors and policymakers, this means that Core PCE may not be a very reliable measure of domestic demand, but rather a lagging reflection of energy-driven supply chain costs. Understanding this nonlinear dependency is crucial for anticipating Fed shifts in an era of energy transition.

The looming trap for American banks: Why financial stability demands Fed intervention

The American banking sector currently faces an unprecedented level of interest rate risk that threatens the fundamental solvency of traditional lending models. After a decade of suppressed volatility, the rapid transition to a higher-rate environment has left many institutions holding vast portfolios of low-yield, long-duration assets—primarily Treasuries and mortgage-backed securities—that have suffered significant mark-to-market losses. Unlike the liquidity crises of the past, the current systemic fragility is rooted in a duration mismatch where the cost of liabilities (deposits) has adjusted upward far more rapidly than the yield on legacy assets, compressing net interest margins and eroding capital buffers across the industry.

This precarious position is the direct result of a unique "perfect storm" in the debt markets: a prolonged era of ZIRP (Zero Interest Rate Policy) overlapping with an un-inverted yield curve. During the low-rate years, banks were incentivized to "reach for yield" by extending duration. The curve then inverted, and now, as the yield curve moves toward a more "normal" upward slope—not through a drop in short-term rates, but through a "bear steepener" where long-term yields rise—the market value of those long-term holdings is cratering. This transition from an inverted curve to a positive slope is historically where the most acute financial accidents occur, as the "hidden" duration risk in bank portfolios is suddenly forced into the light by market pricing.

Consequently, the Federal Reserve is approaching a pivot point where its dual mandate of price stability and maximum employment may be eclipsed by its implicit third mandate: financial stability. To prevent a systemic de-leveraging event or a wave of technical insolvencies, the Fed will likely be forced to initiate a targeted form of Quantitative Easing (QE) specifically at the long end of the curve. By becoming the "buyer of last resort" for long-dated paper, the Fed can cap long-term yields, effectively engineering a ceiling on duration losses for the banking system. While this may complicate the inflation fight, the alternative—a disorderly collapse of bank balance sheets—is a risk the central bank cannot afford to take.