Category: Options

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Modeling Asset Processes

Introduction

Over the last twenty five years significant advances have been made in the theory of asset processes and there now exist a variety of mathematical models, many of them computationally tractable, that provide a reasonable representation of their defining characteristics.

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While the Geometric Brownian Motion model remains a staple of stochastic calculus theory, it is no longer the only game in town.  Other models, many more sophisticated, have been developed to address the shortcomings in the original.  There now exist models that provide a good explanation of some of the key characteristics of asset processes that lie beyond the scope of models couched in a simple Gaussian framework. Features such as mean reversion, long memory, stochastic volatility,  jumps and heavy tails are now readily handled by these more advanced tools.

In this post I review a critical selection of asset process models that belong in every financial engineer’s toolbox, point out their key features and limitations and give examples of some of their applications.

Modeling Asset Processes

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Some Further Notes on Market Timing

Almost at the very moment I published a post featuring some interesting research by Glabadanidis (“Market Timing With Moving Averages”  (2015), International Review of Finance, Volume 15, Number 13, Pages 387-425 – see Yes, You Can Time the Market. How it Works, And Why), several readers wrote to point out a recently published paper by Valeriy Zakamulin, (dubbed the “Moving Average Research King” by Alpha Architect, the source for our fetching cover shot) debunking Glabadanidis’s findings in no uncertain terms:

We demonstrate that “too good to be true” reported performance of the moving average strategy is due to simulating the trading with look-ahead bias. We perform the simulations without look-ahead bias and report the true performance of the moving average strategy. We find that at best the performance of the moving average strategy is only marginally better than that of the corresponding buy-and-hold strategy.

So far, no response from Glabadanidis – from which one is tempted to conclude that Zakamulin is correct.

I can’t recall the last time a paper published in a leading academic journal turned out to be so fundamentally flawed.  That’s why papers are supposed to be peer reviewed.   But, I guess, it can happen. Still, it’s rather alarming to think that a respected journal could accept a piece of research as shoddy as Zakamulin claims it to be.

What Glabadanidis had done, according to Zakamulin, was to use the current month closing price to compute the moving average that was used to decide whether to exit the market (or remain invested) at the start of the same month.  An elementary error that introduces look-ahead bias that profoundly impacts the results.

Following this revelation I hastily checked my calculations for the SPY marketing timing  strategy illustrated in my blog post and, to my relief, confirmed that I had avoided the look-ahead trap that Glabadanidis has fallen into.  As the reader can see from the following extract from the Excel spreadsheet I used for the calculations, the decision to assume the returns for the SPY ETF or T-Bills for the current month rests on the value of the 24 month MA computed using prices up to the end of the prior month.  In other words, my own findings are sound, even if Glabadanidis’s are not, as the reader can easily check for himself.


 Excel Workbook

 

Nonetheless, despite my relief at having avoided Glabadanidis’s  blunder, the apparent refutation of his findings comes as a disappointment.  And my own research on the SPY market timing strategy, while sound as far as it goes, cannot by itself rehabilitate the concept of market timing using moving averages.  The reason is given in the earlier post.  There is a hidden penalty involved in using the market timing strategy to synthetically replicate an Asian put option, namely the costs incurred in exiting and rebuilding the portfolio as the market declines below the moving average, or later overtakes it.  In a single instance, such as the case of SPY, it might easily transpire simply by random chance that the cost of replication are far lower than the fair value of the put.  But the whole point of Glabadanidis’s research was that the same was true, not only for a single ETF or stock, but for many thousands of them.  Absent that critical finding, the SPY case is no more than an interesting anomaly.

Finally, one reader pointed out that the effect of combining a put option with a stock (or ETF) long position was to create synthetically a call option in the stock (ETF).  He is quite correct.  The key point, however, is that when the stock trades down below its moving average, the value of the long synthetic call position and the market timing portfolio are equivalent.

 

 

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Yes, You Can Time the Market. How it Works, And Why

One of the most commonly cited maxims is that market timing is impossible.  In fact, empirical evidence makes a compelling case that market timing is feasible and can yield substantial economic benefits.  What’s more, we even understand why it works.  For the typical portfolio investor, applying simple techniques to adjust their market exposure can prevent substantial losses during market downturns.

The Background From Empirical and Theoretical Research

For the last fifty years, since the work of Paul Samuelson, the prevailing view amongst economists has been that markets are (mostly) efficient and follow a random walk. Empirical evidence to the contrary was mostly regarded as anomalous and/or unimportant economically.  Over time, however, evidence has accumulated that market effects may persist that are exploitable. The famous 1992 paper published by Fama and French, for example, identified important economic effects in stock returns due to size and value factors, while Cahart (1997) demonstrated the important incremental effect of momentum.  The combined four-factor Cahart model explains around 50% of the variation in stock returns, but leaves a large proportion that cannot be accounted for.

Other empirical studies have provided evidence that stock returns are predictable at various frequencies.  Important examples include work by Brock, Lakonishok and LeBaron (1992), Pesaran and Timmermann (1995) and Lo, Mamaysky and Wang (2000), who provide further evidence using a range of technical indicators with wide popularity among traders showing that this adds value even at the individual stock level over and above the performance of a stock index.  The research in these and other papers tends to be exceptional in term of both quality and comprehensiveness, as one might expect from academics risking their reputations in taking on established theory.  The appendix of test results to the Pesaran and Timmermann study, for example, is so lengthy that is available only in CD-ROM format.

A more recent example is the work of Paskalis Glabadanidis, in a 2012 paper entitled Market Timing with Moving Averages.  Glabadanidis examines a simple moving average strategy that, he finds, produces economically and statistically significant alphas of 10% to 15% per year, after transaction costs, and which are largely insensitive to the four Cahart factors. 

Glabadanidis reports evidence regarding the profitability of the MA strategy in seven international stock markets. The performance of the MA strategies also holds for more than 18,000 individual stocks. He finds that:

“The substantial market timing ability of the MA strategy appears to be the main driver of the abnormal returns.”

An Illustration of a Simple Marketing Timing Strategy in SPY

It is impossible to do justice to Glabadanidis’s research in a brief article and the interested reader is recommended to review the paper in full.  However, we can illustrate the essence of the idea using the SPY ETF as an example.   

A 24-period moving average of the monthly price series over the period from 1993 to 2016 is plotted in red in the chart below.

Fig1

The moving average indicator is used to time the market using the following simple rule:

if Pt >= MAt  invest in SPY in month t+1

if Pt < MAt  invest in T-bills in month t+1

In other words, we invest or remain invested in SPY when the monthly closing price of the ETF lies at or above the 24-month moving average, otherwise we switch our investment to T-Bills.

The process of switching our investment will naturally incur transaction costs and these are included in the net monthly returns.

The outcome of the strategy in terms of compound growth is compared to the original long-only SPY investment in the following chart.

Fig2

The marketing timing strategy outperforms the long-only ETF,  with a CAGR of 16.16% vs. 14.75% (net of transaction costs), largely due to its avoidance of the major market sell-offs in 2000-2003 and 2008-2009.

But the improvement isn’t limited to a 141bp improvement in annual compound returns.  The chart below compares the distributions of monthly returns in the SPY ETF and market timing strategy.

Fig3

It is clear that, in addition to a higher average monthly return, the market timing strategy has lower dispersion in the distribution in returns.  This leads to a significantly higher information ratio for the strategy compared to the long-only ETF.  Nor is that all:  the market timing strategy has both higher skewness and kurtosis, both desirable features.

Fig4

These results are entirely consistent with Glabadanidis’s research.  He finds that the performance of the market timing strategy is robust to different lags of the moving average and in subperiods, while investor sentiment, liquidity risks, business cycles, up and down markets, and the default spread cannot fully account for its performance. The strategy works just as well with randomly generated returns and bootstrapped returns as it does for the more than 18,000 stocks in the study.

A follow-up study by the author applying the same methodology to a universe of 20 REIT indices and 274 individual REITs reaches largely similar conclusions.

Why Marketing Timing Works

For many investors, empirical evidence – compelling though it may be – is not enough to make market timing a credible strategy, absent some kind of “fundamental” explanation of why it works.  Unusually, in the case of the simple moving average strategy, such explanation is possible.

It was Cox, Ross and Rubinstein who in 1979 developed the binomial model as a numerical method for pricing options.  The methodology relies on the concept of option replication, in which one constructs a portfolio comprising holdings of the underlying stock and bonds to produce the same cash flows as the option at every point in time (the proportion of stock to hold is given by the option delta).  Since the replicating portfolio produces the same cash flows as the option, it must have the same value and since once knows the price of the stock and bond at each point in time one can therefore price the option.  For those interested in the detail, Wikipedia gives a detailed explanation of the technique.

We can apply the concept of option replication to construct something very close the MA market timing strategy, as follows.  Consider what happens when the ETF falls below the moving average level.  In that case we convert the ETF portfolio to cash and use the proceeds to acquire T-Bills.  An equivalent outcome would be achieved by continuing to hold our long ETF position and acquiring a put option to hedge it.  The combination of a long ETF position, and a 1-month put option with delta of -1, would provide the same riskless payoff as the market timing strategy, i.e. the return on 30-day T-Bills.  An option in which the strike price is based on the average price of the underlying is known as an Arithmetic Asian option.    Hence when we apply the MA timing strategy we are effectively constructing a dynamic portfolio that replicates the payoff of an Arithmetic Asian protective put option struck as (just above) the moving average level.

Market Timing Alpha and The Cost of Hedging

None of this explanation is particularly contentious – the theory behind option replication through dynamic hedging is well understood – and it provides a largely complete understanding of the way the MA market timing strategy works, one that should satisfy those who are otherwise unpersuaded by arguments purely from empirical research.

There is one aspect of the foregoing description that remains a puzzle, however.  An option is a valuable financial instrument and the owner of a protective put of the kind described can expect to pay a price amounting to tens or perhaps hundreds of basis points.  Of course, in the market timing strategy we are not purchasing a put option per se, but creating one synthetically through dynamic replication.  The cost of creating this synthetic equivalent comprises the transaction costs incurred as we liquidate and re-assemble our portfolio from month to month, in the form of bid/ask spread and commissions.  According to efficient market theory, one should be indifferent as to whether one purchases the option at a fair market price or constructs it synthetically through replication – the cost should be equivalent in either case.  And yet in empirical tests the cost of the synthetic protective put falls far short of what one would expect to pay for an equivalent option instrument.  This is, in fact, the source of the alpha in the market timing strategy.

According to efficient market theory one might expect to pay something of the order of 140 basis points a year in transaction costs – the difference between the CAGR of the market timing strategy and the SPY ETF – in order to construct the protective put.  Yet, we find that no such costs are incurred.

Now, it might be argued that there is a hidden cost not revealed in our simple study of a market timing strategy applied to a single underlying ETF, which is the potential costs that could be incurred if the ETF should repeatedly cross and re-cross the level of the moving average, month after month.  In those circumstances the transaction costs would be much higher than indicated here.  The fact that, in a single example, such costs do not arise does not detract in any way from the potential for such a scenario to play out. Therefore, the argument goes, the actual costs from the strategy are likely to prove much higher over time, or when implemented for a large number of stocks.

All well and good, but this is precisely the scenario that Glabadanidis’s research addresses, by examining the outcomes, not only for tens of thousands of stocks, but also using a large number of scenarios generated from random and/or bootstrapped returns.  If the explanation offered did indeed account for the hidden costs of hedging, it would have been evident in the research findings.

Instead, Glabadanidis concludes:

“This switching strategy does not involve any heavy trading when implemented with break-even transaction costs, suggesting that it will be actionable even for small investors.”

Implications For Current Market Conditions

As at the time of writing, in mid-February 2016, the price of the SPY ETF remains just above the 24-month moving average level.  Consequently the market timing strategy implies one should continue to hold the market portfolio for the time being, although that could change very shortly, given recent market action.

Conclusion

The empirical evidence that market timing strategies produce significant alphas is difficult to challenge.  Furthermore, we have reached an understanding of why they work, from an application of widely accepted option replication theory. It appears that using a simple moving average to time market entries and exits is approximately equivalent to hedging a portfolio with a protective Arithmetic Asian put option.

What remains to be answered is why the cost of constructing put protection synthetically is so low.  At the current time, research indicates that market timing strategies consequently are able to generate alphas of 10% to 15% per annum.

References

  1. Brock, W., Lakonishok, J., LeBaron, B., 1992, “Simple Technical Trading Rules and the Stochastic Properties of Stock Returns,” Journal of Finance 47, pp. 1731-1764.
  2. Carhart, M. M., 1997, “On Persistence in Mutual Fund Performance,” Journal of Finance 52, pp. 57–82.

  3. Fama, E. F., French, K. R., 1992, “The Cross-Section of Expected Stock Returns,” Journal of Finance 47(2), 427–465
  4. Glabadanidis, P., 2012, “Market Timing with Moving Averages”, 25th Australasian Finance and Banking Conference.
  5. Glabadanidis, P., 2012, “The Market Timing Power of Moving Averages: Evidence from US REITs and REIT Indexes”, University of Adelaide Business School.
  6. Lo, A., Mamaysky, H., Wang, J., 2000, “Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation,” Journal of Finance 55, 1705–1765.
  7. Pesaran, M.H., Timmermann, A.G., 1995, “Predictability of Stock Returns: Robustness and Economic Significance”, Journal of Finance, Vol. 50 No. 4
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Investing in Leveraged ETFs – Theory and Practice

Summary

Leveraged ETFs suffer from decay, or “beta slippage.” Researchers have attempted to exploit this effect by shorting pairs of long and inverse leveraged ETFs.

The results of these strategies look good if you assume continuous compounding, but are often poor when less frequent compounding is assumed.

In reality, the trading losses incurred in rebalancing the portfolio, which requires you to sell low and buy high, overwhelm any benefit from decay, making the strategies unprofitable in practice.

A short levered ETF strategy has similar characteristics to a short straddle option position, with positive Theta and negative Gamma, and will experience periodic, large drawdowns.

It is possible to develop leveraged ETF strategies producing high returns and Sharpe ratios with relative value techniques commonly used in option trading strategies.

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Decay in Leveraged ETFs

Leveraged ETFs continue to be much discussed on Seeking Alpha.

One aspect in particular that has caught analysts’ attention is the decay, or “beta slippage” that leveraged ETFs tend to suffer from.

Seeking Alpha contributor Fred Picard in a 2013 article (“What You Need To Know About The Decay Of Leveraged ETFs“) described the effect using the following hypothetical example:

To understand what is beta-slippage, imagine a very volatile asset that goes up 25% one day and down 20% the day after. A perfect double leveraged ETF goes up 50% the first day and down 40% the second day. On the close of the second day, the underlying asset is back to its initial price:

(1 + 0.25) x (1 – 0.2) = 1

And the perfect leveraged ETF?

(1 + 0.5) x (1 – 0.4) = 0.9

Nothing has changed for the underlying asset, and 10% of your money has disappeared. Beta-slippage is not a scam. It is the normal mathematical behavior of a leveraged and rebalanced portfolio. In case you manage a leveraged portfolio and rebalance it on a regular basis, you create your own beta-slippage. The previous example is simple, but beta-slippage is not simple. It cannot be calculated from statistical parameters. It depends on a specific sequence of gains and losses.

Fred goes on to make the point that is the crux of this article, as follows:

At this point, I’m sure that some smart readers have seen an opportunity: if we lose money on the long side, we make a profit on the short side, right?

Shorting Leveraged ETFs

Taking his cue from Fred’s article, Seeking Alpha contributor Stanford Chemist (“Shorting Leveraged ETF Pairs: Easier Said Than Done“) considers the outcome of shorting pairs of leveraged ETFs, including the Market Vectors Gold Miners ETF (NYSEARCA:GDX), the Direxion Daily Gold Miners Bull 3X Shares ETF (NYSEARCA:NUGT) and the Direxion Daily Gold Miners Bear 3X Shares ETF (NYSEARCA:DUST).

His initial finding appears promising:

Therefore, investing $10,000 each into short positions of NUGT and DUST would have generated a profit of $9,830 for NUGT, and $3,900 for DUST, good for an average profit of 68.7% over 3 years, or 22.9% annualized.

At first sight, this appears to a nearly risk-free strategy; after all, you are shorting both the 3X leveraged bull and 3X leveraged bear funds, which should result in a market neutral position. Is there easy money to be made?

Source: Standford Chemist

Not so fast! Stanford Chemist applies the same strategy to another ETF pair, with a very different outcome:

“What if you had instead invested $10,000 each into short positions of the Direxion Russell 1000 Financials Bullish 3X ETF (NYSEARCA:FAS) and the Direxion Russell 1000 Financials Bearish 3X ETF (NYSEARCA:FAZ)?

The $10,000 short position in FAZ would have gained you $8,680. However, this would have been dwarfed by the $28,350 loss that you would have sustained in shorting FAS. In total, you would be down $19,670, which translates into a loss of 196.7% over three years, or 65.6% annualized.

No free lunch there.

The Rebalancing Issue

Stanford Chemist puts his finger on one of the key issues: rebalancing. He explains as follows:

So what happened to the FAS-FAZ pair? Essentially, what transpired was that as the underlying asset XLF increased in value, the two short positions became unbalanced. The losing side (short FAS) ballooned in size, making further losses more severe. On the other hand, the winning side (short FAZ) shrunk, muting the effect of further gains.

To counteract this effect, the portfolio needs to be rebalanced. Stanford Chemist looks at the implications of rebalancing a short NUGT-DUST portfolio whenever the market value of either ETF deviates by more than N% from its average value, where he considers N% in the range from 10% to 100%, in increments of 10%.

While the annual portfolio return was positive in all but one of these scenarios, there was very considerable variation in the outcomes, with several of the rebalanced portfolios suffering very large drawdowns of as much as 75%:

Source: Stanford Chemist

The author concludes:

The results of the backtest showed that profiting from this strategy is easier said than done. The total return performances of the strategy over the past three years was highly dependent on the rebalancing thresholds chosen. Unfortunately, there was also no clear correlation between the rebalancing period used and the total return performance. Moreover, the total return profiles showed that large drawdowns do occur, meaning that despite being ostensibly “market neutral”, this strategy still bears a significant amount of risk.

Leveraged ETF Pairs – Four Case Studies

Let’s press pause here and review a little financial theory. As you recall, it is possible to express a rate of return in many different ways, depending on how interest is compounded. The most typical case is daily compounding:

R = (Pt – Pt-1) / Pt

Where Pt is the price on day t, and Pt-1 is the price on day t-1, one day prior.

Another commonly used alternative is continuous compounding, also sometimes called log-returns:

R = Ln(Pt) – Ln(Pt-1)

Where Ln(Pt) is the natural log of the price on day t, Pt

When a writer refers to a rate of return, he should make clear what compounding basis the return rate is quoted on, whether continuous, daily, monthly or some other frequency. Usually, however, the compounding basis is clear from the context. Besides, it often doesn’t make a large difference anyway. But with leveraged ETFs, even microscopic differences can produce substantially different outcomes.

I will illustrate the effect of compounding by reference to examples of portfolios comprising short positions in the following representative pairs of leveraged ETFs:

  • Direxion Daily Energy Bull 3X Shares ETF (NYSEARCA:ERX)
  • Direxion Daily Energy Bear 3X Shares ETF (NYSEARCA:ERY)
  • Direxion Daily Gold Miners Bull 3X ETF
  • Direxion Daily Gold Miners Bear 3X ETF
  • Direxion Daily S&P 500 Bull 3X Shares ETF (NYSEARCA:SPXL)
  • Direxion Daily S&P 500 Bear 3X Shares ETF (NYSEARCA:SPXS)
  • Direxion Daily Small Cap Bull 3X ETF (NYSEARCA:TNA)
  • Direxion Daily Small Cap Bear 3X ETF (NYSEARCA:TZA)

The findings in relation to these pairs are mirrored by results for other leveraged ETF pairs.

First, let’s look the returns in the ETF portfolios measured using continuous compounding.

Source: Yahoo! Finance

The portfolio returns look very impressive, with CAGRs ranging from around 20% for the short TNA-TZA pair, to over 124% for the short NUGT-DUST pair. Sharpe ratios, too, appear abnormally large, ranging from 4.5 for the ERX-ERY short pair to 8.4 for NUGT-DUST.

Now let’s look at the performance of the same portfolios measured using daily compounding.

Source: Yahoo! Finance

It’s an altogether different picture. None of the portfolios demonstrate an attract performance record and indeed in two cases the CAGR is negative.

What’s going on?

Stock Loan Costs

Before providing the explanation, let’s just get one important detail out of the way. Since you are shorting both legs of the ETF pairs, you will be faced with paying stock borrow costs. Borrow costs for leveraged ETFs can be substantial and depending on market conditions amount to as much as 10% per annum, or more.

In computing the portfolio returns in both the continuous and daily compounding scenarios I have deducted annual stock borrow costs based on recent average quotes from Interactive Brokers, as follows:

  • ERX-ERY: 14%
  • NUGT-DUST: 16%
  • SXPL-SPXS: 8%
  • TNA-TZA: 8%

It’s All About Compounding and Rebalancing

The implicit assumption in the computation of the daily compounded returns shown above is that you are rebalancing the portfolios each day. That is to say, it is assumed that at the end of each day you buy or sell sufficient quantities of shares of each ETF to maintain an equal $ value in both legs.

In the case of continuously compounded returns the assumption you are making is that you maintain an equal $ value in both legs of the portfolio at every instant. Clearly that is impossible.

Ok, so if the results from low frequency rebalancing are poor, while the results for instantaneous rebalancing are excellent, it is surely just a question of rebalancing the portfolio as frequently as is practically possible. While we may not be able to achieve the ideal result from continuous rebalancing, the results we can achieve in practice will reflect how close we can come to that ideal, right?

Unfortunately, not.

Because, while we have accounted for stock borrow costs, what we have ignored in the analysis so far are transaction costs.

Transaction Costs

With daily rebalancing transaction costs are unlikely to be a critical factor – one might execute a single trade towards the end of the trading session. But in the continuous case, it’s a different matter altogether.

Let’s use the SPXL-SPXS pair as an illustration. When the S&P 500 index declines, the value of the SPXL ETF will fall, while the value of the SPXS ETF will rise. In order to maintain the same $ value in both legs you will need to sell more shares in SPXL and buy back some shares in SPXS. If the market trades up, SPXL will increase in value, while the price of SPXS will fall, requiring you to buy back some SPXL shares and sell more SPXS.

In other words, to rebalance the portfolio you will always be trying to sell the ETF that has declined in price, while attempting to buy the inverse ETF that has appreciated. It is often very difficult to execute a sale in a declining stock at the offer price, or buy an advancing stock at the inside bid. To be sure of completing the required rebalancing of the portfolio, you are going to have to buy at the ask price and sell at the bid price, paying the bid-offer spread each time.

Spreads in leveraged ETF products tend to be large, often several pennies. The cumulative effect of repeatedly paying the bid-ask spread, while taking trading losses on shares sold at the low or bought at the high, will be sufficient to overwhelm the return you might otherwise hope to make from the ETF decay.

And that’s assuming the best case scenario that shares are always available to short. Often they may not be: so that, if the market trades down and you need to sell more SPXL, there may be none available and you will be unable to rebalance your portfolio, even if you were willing to pay the additional stock loan costs and bid-ask spread.

A Lose-Lose Proposition

So, in summary: if you rebalance infrequently you will avoid excessive transaction costs; but the $ imbalance that accrues over the course of a trading day will introduce a market bias in the portfolio. That can hurt portfolio returns very badly if you get caught on the wrong side of a major market move. The results from daily rebalancing for the illustrative pairs shown above indicate that this is likely to happen all too often.

On the other hand, if you try to maintain market neutrality in the portfolio by rebalancing at high frequency, the returns you earn from decay will be eaten up by transaction costs and trading losses, as you continuously sell low and buy high, paying the bid-ask spread each time.

Either way, you lose.

Ok, what about if you reverse the polarity of the portfolio, going long both legs? Won’t that avoid the very high stock borrow costs and put you in a better position as regards the transaction costs involved in rebalancing?

Yes, it will. Because, you will be selling when the market trades up and buying when it falls, making it much easier to avoid paying the bid-ask spread. You will also tend to make short term trading profits by selling high and buying low. Unfortunately, you may not be surprised to learn, these advantages are outweighed by the cost of the decay incurred in both legs of the long ETF portfolio.

In other words: you can expect to lose if you are short; and lose if you are long!

An Analogy from Option Theory

To anyone with a little knowledge of basic option theory, what I have been describing should sound like familiar territory.

Being short the ETF pair is like being short an option (actually a pair of call and put options, called a straddle). You earn decay, or Theta, for those familiar with the jargon, by earning the premium on the options you have sold; but at the risk of being short Gamma – which measures your exposure to a major market move.

Source: Interactive Brokers

You can hedge out the portfolio’s Gamma exposure by trading the underlying securities – the ETF pair in this case – and when you do that you find yourself always having to sell at the low and buy at the high. If the options are fairly priced, the option decay is enough, but not more, to compensate for the hedging cost involved in continuously trading the underlying.

Conversely, being long the ETF pair is like being long a straddle on the underling pair. You now have positive Gamma exposure, so your portfolio will make money from a major market move in either direction. However, the value of the straddle, initially the premium you paid, decays over time at a rate Theta (also known as the “bleed”).

Source: Interactive Brokers

You can offset the bleed by performing what is known as Gamma trading. When the market trades up your portfolio delta becomes positive, i.e. an excess $ value in the long ETF leg, enabling you to rebalance your position by selling excess deltas at the high. Conversely, when the market trades down, your portfolio delta becomes negative and you rebalance by buying the underlying at the current, reduced price. In other words, you sell at the high and buy at the low, typically making money each time. If the straddle is fairly priced, the profits you make from Gamma trading will be sufficient to offset the bleed, but not more.

Typically, the payoff from being short options – being short the ETF pair – will show consistent returns for sustained periods, punctuated by very large losses when the market makes a significant move in either direction.

Conversely, if you are long options – long the ETF pair – you will lose money most of the time due to decay and occasionally make a very large profit.

In an efficient market in which securities are fairly priced, neither long nor short option strategy can be expected to dominate the other in the long run. In fact, transaction costs will tend to produce an adverse outcome in either case! As with most things in life, the house is the player most likely to win.

Developing a Leveraged ETF Strategy that Works

Investors shouldn’t be surprised that it is hard to make money simply by shorting leveraged ETF pairs, just as it is hard to make money by selling options, without risking blowing up your account.

And yet, many traders do trade options and often manage to make substantial profits. In some cases traders are simply selling options, hoping to earn substantial option premiums without taking too great a hit when the market explodes. They may get away with it for many years, before blowing up. Indeed, that has been the case since 2009. But who would want to be an option seller here, with the market at an all-time high? It’s simply far too risky.

The best option traders make money by trading both the long and the short side. Sure, they might lean in one direction or the other, depending on their overall market view and the opportunities they find. But they are always hedged, to some degree. In essence what many option traders seek to do is what is known as relative value trading – selling options they regard as expensive, while hedging with options they see as being underpriced. Put another way, relative value traders try to buy cheap Gamma and sell expensive Theta.

This is how one can thread the needle in leveraged ETF strategies. You can’t hope to make money simply by being long or short all the time – you need to create a long/short ETF portfolio in which the decay in the ETFs you are short is greater than in the ETFs you are long. Such a strategy is, necessarily, tactical: your portfolio holdings and net exposure will likely change from long to short, or vice versa, as market conditions shift. There will be times when you will use leverage to increase your market exposure and occasions when you want to reduce it, even to the point of exiting the market altogether.

If that sounds rather complicated, I’m afraid it is. I have been developing and trading arbitrage strategies of this kind since the early 2000s, often using sophisticated option pricing models. In 2012 I began trading a volatility strategy in ETFs, using a variety of volatility ETF products, in combination with equity and volatility index futures.

I have reproduced the results from that strategy below, to give some indication of what is achievable in the ETF space using relative value arbitrage techniques.

Source: Systematic Strategies, LLC

Source: Systematic Strategies LLC

Conclusion

There are no free lunches in the market. The apparent high performance of strategies that engage systematically in shorting leveraged ETFs is an illusion, based on a failure to quantify the full costs of portfolio rebalancing.

The payoff from a short leveraged ETF pair strategy will be comparable to that of a short straddle position, with positive decay (Theta) and negative Gamma (exposure to market moves). Such a strategy will produce positive returns most of the time, punctuated by very large drawdowns.

The short Gamma exposure can be mitigated by continuously rebalancing the portfolio to maintain dollar neutrality. However, this will entail repeatedly buying ETFs as they trade up and selling them as they decline in value. The transaction costs and trading losses involved in continually buying high and selling low will eat up most, if not all, of the value of the decay in the ETF legs.

A better approach to trading ETFs is relative value arbitrage, in which ETFs with high decay rates are sold and hedged by purchases of ETFs with relatively low rates of decay.

An example given of how this approach has been applied successfully in volatility ETFs since 2012.

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Quant Strategies in 2018

Quant Strategies – Performance Summary Sept. 2018

The end of Q3 seems like an appropriate time for an across-the-piste review of how systematic strategies are performing in 2018.  I’m using the dozen or more strategies running on the Systematic Algotrading Platform as the basis for the performance review, although results will obviously vary according to the specifics of the strategy.  All of the strategies are traded live and performance results are net of subscription fees, as well as slippage and brokerage commissions.

Volatility Strategies

Those waiting for the hammer to fall on option premium collecting strategies will have been disappointed with the way things have turned out so far in 2018.  Yes, February saw a long-awaited and rather spectacular explosion in volatility which completely destroyed several major volatility funds, including the VelocityShares Daily Inverse VIX Short-Term ETN (XIV) as well as Chicago-based hedged fund LJM Partners (“our goal is to preserve as much capital as possible”), that got caught on the wrong side of the popular VIX carry trade.  But the lack of follow-through has given many volatility strategies time to recover. Indeed, some are positively thriving now that elevated levels in the VIX have finally lifted option premiums from the bargain basement levels they were languishing at prior to February’s carnage.  The Option Trader strategy is a stand-out in this regard:  not only did the strategy produce exceptional returns during the February melt-down (+27.1%), the strategy has continued to outperform as the year has progressed and YTD returns now total a little over 69%.  Nor is the strategy itself exceptionally volatility: the Sharpe ratio has remained consistently above 2 over several years.

Hedged Volatility Trading

Investors’ chief concern with strategies that rely on collecting option premiums is that eventually they may blow up.  For those looking for a more nuanced approach to managing tail risk the Hedged Volatility strategy may be the way to go.  Like many strategies in the volatility space the strategy looks to generate alpha by trading VIX ETF products;  but unlike the great majority of competitor offerings, this strategy also uses ETF options to hedge tail risk exposure.  While hedging costs certainly acts as a performance drag, the results over the last few years have been compelling:  a CAGR of 52% with a Sharpe Ratio close to 2.

F/X Strategies

One of the common concerns for investors is how to diversify their investment portfolios, especially since the great majority of assets (and strategies) tend to exhibit significant positive correlation to equity indices these days. One of the characteristics we most appreciate about F/X strategies in general and the F/X Momentum strategy in particular is that its correlation to the equity markets over the last several years has been negligible.    Other attractive features of the strategy include the exceptionally high win rate – over 90% – and the profit factor of 5.4, which makes life very comfortable for investors.  After a moderate performance in 2017, the strategy has rebounded this year and is up 56% YTD, with a CAGR of 64.5% and Sharpe Ratio of 1.89.

Equity Long/Short

Thanks to the Fed’s accommodative stance, equity markets have been generally benign over the last decade to the benefit of most equity long-only and long-short strategies, including our equity long/short Turtle Trader strategy , which is up 31% YTD.  This follows a spectacular 2017 (+66%) , and is in line with the 5-year CAGR of 39%.   Notably, the correlation with the benchmark S&P500 Index is relatively low (0.16), while the Sharpe Ratio is a respectable 1.47.

Equity ETFs – Market Timing/Swing Trading

One alternative to the traditional equity long/short products is the Tech Momentum strategy.  This is a swing trading strategy that exploits short term momentum signals to trade the ProShares UltraPro QQQ (TQQQ) and ProShares UltraPro Short QQQ (SQQQ) leveraged ETFs.  The strategy is enjoying a banner year, up 57% YTD, with a four-year CAGR of 47.7% and Sharpe Ratio of 1.77.  A standout feature of this equity strategy is its almost zero correlation with the S&P 500 Index.  It is worth noting that this strategy also performed very well during the market decline in Feb, recording a gain of over 11% for the month.

Futures Strategies

It’s a little early to assess the performance of the various futures strategies in the Systematic Strategies portfolio, which were launched on the platform only a few months ago (despite being traded live for far longer).    For what it is worth, both of the S&P 500 E-Mini strategies, the Daytrader and the Swing Trader, are now firmly in positive territory for 2018.   Obviously we are keeping a watchful eye to see if the performance going forward remains in line with past results, but our experience of trading these strategies gives us cause for optimism.

Conclusion:  Quant Strategies in 2018

There appear to be ample opportunities for investors in the quant sector across a wide range of asset classes.  For investors with equity market exposure, we particularly like strategies with low market correlation that offer significant diversification benefits, such as the F/X Momentum and F/X Momentum strategies.  For those investors seeking the highest risk adjusted return, option selling strategies like the Option Trader strategy are the best choice, while for more cautious investors concerned about tail risk the Hedged Volatility strategy offers the security of downside protection.  Finally, there are several new strategies in equities and futures coming down the pike, several of which are already showing considerable promise.  We will review the performance of these newer strategies at the end of the year.

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