Investing in Leveraged ETFs

Leveraged ETFs are not for long term holding, and the main reason is that the loss and recovery returns are asymmetric, coupled with the fact that large drawdowns do occur in the market regularly.

The below chart shows the profit from investing 10k in SPXL in red, and 30k in SPY in blue, with the green line showing the advantage of SPXL. No doubt the returns are better (since SPXL only uses 10k) but the total profits are actually better with 30k in SPY, with lower drawdowns.

Initial PV Final PV Profit Return Max DD Max DD Value
SPY 30000 96069 66069 220% -55.19% -32867
SPXL 10000 37865 27865 279% -93.02% -44222

The below chart shows the profit (dollar) differences between the 2 portfolios mentioned above. Increasing the time horizon makes the average return more negative, but fattening the tails to the right as well, indicating that a well-timed mid-term (2-4 years) investment in SPXL can actually beat the SPY by a large margin, but in most cases you will lose out.

As you extend the horizon, the SPXL becomes more like an OTM call option on the SPY. You're more likely to lose, but are also more likely to have an outsized gain.


Asymmetry in required returns for recovery

The asymmetry between percentage losses vs percentage gains required to recover makes a portfolio increasingly difficult to recover from larger drawdowns.

This, coupled with the nature of average daily returns and the presence of large drawdowns, combine to make leveraged ETFs unsuitable for long term holding.


Nature of returns

Ultimately it's the volatility that kills the leveraged investment PNL in the long term. The longer you hold it, the more damage it can do.

By resampling, we can find the breakeven volatility required for an ETF to guarantee a better return than the non-leveraged counterpart.

The below charts show portfolio profits using resampled returns from fitted t-dist on SPY returns, and simulated 10000 trajectories, each over 250 days. Note the cutoff at the -10k and the -30k mark - these are when portfolios get completely wiped out.

Chart 1: fitted t-dist, showing that the leveraged portfolio has a higher mean, but lower median return. On average it does better, but more times than not, it does not.

Chart 2: reducing the mean return by 50%, the comparison still stands.

Chart 3: reducing volatility by 50% really makes the leveraged portfolio shine. The less the volatility, the more certain it is to outperform.

Chart 4: increasing volatility by 100% shows that volatility is really the key in making or breaking the outperformance. Here you can see that the leveraged portfolio payoff distribution resembels an OTM call option - it is very likely to 'expire worthless' in that the entire 10k is lost.

The sampling is not entirely representative to actual markets, because there are other things to consider like autocorrelation - the simulations above only give IID returns. But it serves to identify in which cases the leveraged portfolio outperforms - in this case we know it's when volatility is lower. 


When does it pay off to hold the leveraged SPXL then?

When volatility is expected to be low.

From the previous analysis, we've seen that even with a low mean, a lower volatilty increases the likelihood of outperformance. Since mean returns are not expected to be negative in the long run, the best time to (if ever) change to a leveraged investment is when you are predicting a stable (and ideally rising) market.

Since picking the right time is not easy to do (and certainly the environment now does not warrant such a view), it's generally better to have an unleveraged portfolio - if cash is the concern, use other means, e.g. instead of 1x SPY, you can consider using options to replicate it.

Not only do you have to pick the right time to get in, you also need to pick the right time to get out, otherwise your gains can evaporate really quickly. Here are some historical performance comparisons over some periods.

This illustrates how a drawdown can set you back so bad that the following rally is not able to claw back the underperformance. Note how the leveraged portfolio did 'better' in the drawdown - this is because it started with a capital base of 10k so it was actually severely depleted, thus further losses aren't as painful in dollar terms - but this is the very same reason why it could not capitalize on the rally.

This shows how even a rally pockmarked with even light to medium severity drawdowns can cause the leverarged portfolio to underperform.

This shows how quickly the outperformance can evaporate on a medium severity drawdown. It's psychologically uncomfortable - you're amplifying your emotions for nothing.

Notice how the red only caught up with blue when the rally was really strong. Then again it quickly gave up its outperformance.

Again showing how quickly outperformance evaporates and turns into underperformance.



  • It's recommended not to use leveraged ETFs for long term investment - it's better for speculating over short term horizons - arguably you can/should use calls.
  • The outperformance of leveraged ETFs can quickly evaporate - not good for psychological well-being, which is important to long term investment success.

The Effects of Timing your Investments

Below are some visualizations that help to give a sense of to what degree does timing affect the final returns for a particular asset (in this case, index).

A larger and/or more uniform area of colour indicate that timing is not that important, whereas a very small area of different colour (especially blues) indicate that you could only have achieved the highest returns if you invested in the right time.

For the SPY, the areas of highest returns are only achievable if you invested during either of the 2 recent crises (2000 and 2008), and held it until today (end Aug 2020). The similar shades of dark blue show that the 2008 crisis wiped out most of the gains achieved investing in 2000-2008, such that investing in 2008 yields similar returns as investing in 2000.

A dark vertical bar of red at the 2008 area also show that any investment prior to 2008 would have achieved pretty much nothing if exited at that time.

The difference in QQQ is much more pronounced - the highest returns could only have been achieved if you invested in the trough of the 2000 crash.

For the below ETFs representing China and Singapore, investing early was the key to achieving the best returns - see how the blues are in horizontal swathes near the top instead of localized ones as per the SPY and QQQ.

Finally, Bitcoin. Because of the wider range of returns, I've truncated returns above 400% - here all represented by the darkest blue. Early adopters have it the best, but note the red patch near the top left, indicating how they had to suffer severe drawdowns too.

I am not recommending that you should or should not time the market - this simply shows that for some investments, timing plays a huge role in determining whether you make average returns or not. It may be seen one way as "since the odds are against me, I might as well settle for average returns", or "since the rewards of beating the market are so great, I should strive to get the timing right".

*ETF prices and returns are dividend-adjusted

Investing in stocks – better than holding cash?

While it is true that investing in equities yield better returns than holding cash, it does not mean that you will always do better investing than doing nothing.

When factoring in the realities of how people invest (not speaking about biases /flaws but simply how life works), the returns of stocks do not translate as well to investors' portfolios.

The main reason is that people tend to quote stock market returns (e.g. 150% gain from 10 years ago), but rarely do investors dump in their full investable amount in one shot. Rather, they slowly accrue investable cash over time, and they can only decide at that time how they want to deploy that cash.

Below I've simulated 3 portfolios: (1) a buy-on-the-dip strategy, (2) using dollar-cost averaging, and (3) simply not investing the cash.

Each start out with 10k investable cash, and accrue $50 of investable cash every trading day (≈ setting aside 1k each month to invest). The investable instrument is the S&P index.

For simplicity, dividends are not included in the returns, and this is offset by the cash portfolio not being invested in bonds. One of the reasons for simplicity is that this is not meant to be a research piece on how we should invest, but rather just to give a sense of what investing looks like in reality, with an appreciation of its worst-of-times where being fully invested over 15 years can approach the gains obtained by simply doing nothing (can you stomach that?).


Summary of findings:

  1. For the past 30 years, the difference between being invested vs doing nothing is only evident in the 12-year super bull run of 2009-2020
  2. Before that (from 1990 to 2008) any gains were largely wiped out by the downturns of the 2000 and 2008 (depending on when you started)
  3. DCA introduces more risk because it stays fully invested throughout, but yields better total returns; the Sharpe however is slightly lower than the buy-the-dip strategy (but the different is not big and retail investors like us rarely care for such a small difference in Sharpe; total returns to us is more of a priority)
  4. Comparing dollar-cost-averaging and buy-the-dip: in very bad downturns (2008), the decades of gains using the DCA can be easily wiped out, and strategy total returns can be the same as BTD
  5. Depending on when you started, the drawdowns have different impact (how much strategies 1 and 2 loses compared to the all-cash portfolio)

What this means:

  • Widen your range of expectations for future market returns (next 30 years), as we don't know if we can get the same 12-year bull run we had. Be prepared that investment returns may not be as good for the next 20 years or so.
  • There is no universal strategy that is better - see below charts to get a sense of the variabiliy of 'which strategy is better' - see how starting at different times can change your conclusions. That's just one variable; others are: initial capital, how to BTD, and most importantly what is the magnitude of the next bull run.
  • Stay invested anyway - the degree to that (full DCA or BTD) is up to you -  your psychological comfort and anticipated circumstances



  • Start with $10,000 cash, immediately invest to the target equity ratio (e.g. 70% equity)
  • Daily inflow of $50; if DCA, invest immediately, if not, save it for the next dip
  • If actual equity ratio is higher than target equity ratio, wait for next market recovery (makes new all-time-highs) to unwind (sell) equity positions at a rate of 0.1% of entire equity portfolio every day, and stop unwinding if market dips down again (back to buying mode)
  • Charts start at 1990, 1995, 2000, and 2005


Grey line: dollar-cost-averaging strategy
Black line: total portfolio value of equities (blue) and cash (dark green)
Lime green line: cash-only portfolio

From 1990

Notice how all 3 strategies go back to square 1 in 2008

From 1995

Now, both equity strategies fare worse than cash in 2008 just because we started 5 years late

From 2000

A worse picture

From 2005

Needles to show starting at 2010 - would have been spectacular

The January Effect – Part 2

Continuing from Part 1

Comparing between strategies

S2 strategy invests in months {1,3,4,7,10,11,12} and yields better Sharpe and higher total return than the benchmark. It also has less negative skew.

S1 invests in only 4 months of the year {3,4,11,12} and so the total profit is much lower. The Sharpe does not improve, but the skew is significantly improved – it is now positive.

S1b squeezes out a little more total return by shorting month 9, giving us less of a max DD, but does not improve on the Sharpe nor the skew, so it might not be worth the effort.

Because this is an active method, the number of trades needed is proportional to the number of months. S2: 7, S1: 4, and S1b: 5.

Active method equity curves

Using the active method, we can see that the curve is significantly smoother than the benchmark, especially for S1 strategies.

Passive method

The passive method is what we normally do in real life – a hypothetical growth of $1. We do not rebalance the amount, but simply let it grow. The percentage returns are compounded, not simply added as per previous method.

Conservative strategies (like S1) are penalized because they tend to miss out on some of the compounding gains accrued in bull runs. This makes a sizeable difference in the long run.

The passive strategy comparisons show that S2 allows us to beat the benchmark, with slightly lower SD and drawdown measures.

S1 strategies are far superior in terms of Sharpe, but don’t eke out as much of a profit. To solve that, use leverage.

Using leverage of 1.5x, we can get the S1 strategies to beat the the total return of S2 and the benchmark, with somewhat similar SD and drawdown.


However, implementation is not so simple – we will need to find a way to get the 1.5x monthly return of the index, and keep compounding it. It’s not as easy to implement as S2.



Following a simple strategy like S2 can give us better total and risk-adjusted returns than the benchmark.

Continue reading "The January Effect – Part 2"

The January Effect

Many have heard of January effect in stock markets - stocks generally go up in January. Here we take a look at this phenomenon and see if it still persists.

Below are the results for the S&P 500 for 1951 to 2018 using monthly simple percentage returns

It shows that while the mean return is indeed positive, there are many other months with higher mean returns. Might as well call it the January-and-March-and-April-and-July-and-November-and-December-effect.

What's more important is that the Sharpe of the other (Mar, Apr, Jul, Nov, Dec) months are higher.

The only advantage that January has is that it is the only month with a positive skew, albeit very slight.

Below are the return distributions for each month.

We are also interested in the smoothness of the equity curve, and whether the strategy is robust through time.

Below we can note the following observations:

  • The January effect lost its effect from 2000 onwards
  • Mar, Apr, Nov, Dec are remarkably good month
  • Sep is consistently bad
  • Oct (while having the reputation for worst declines) is still on a general up trend

In the next part, we will look at implementing a market timing strategy that invests only in certain months, and see how it fares against the benchmark.