The post How to Lose Money Trading (and how not to) appeared first on Robot Wealth.

]]>It’s easy to lose money trading if you do certain things:

- Trade too much (paying fees and market impact on each transaction)
- Size positions too big (high volatility hurts compounding ability, and in the extreme can cause you to blow up)
- Short positive drift/risk premia

**Perhaps surprisingly, it’s actually quite hard to lose money consistently if you avoid these things.**

Why is that the case?

Because regardless of your pricing model, your prediction, or whatever, you get to * trade at market prices*.

Here’s an example to illustrate.

Imagine we can know that an asset has a fair value of $100.

You come along and decide, quite wrongly, that it’s worth $150.

But if it’s quoted $99 / $101, you can buy now at $101.

**You were totally wrong but you still bought close to fair value.**

The same mechanisms that make it hard to get an edge also make it hard for you to trade at really bad prices.

In a simple model, you might say that prices are set by:

- (risky) arbitrage and relative value in the short term
- pricing/valuation models in the long term

Both of these games are *ultra-competitive*.

It is hard to make money in the *short term* because competitive fast money playing “the arb game” chases relative value opportunities and “gets paid” to disperse the impact of large orders and other supply/demand imbalances.

It is hard to make money in the *long term* because the pricing/valuation game is so competitive that it is hard to get an edge from public information that is available to everyone else.

These things make it hard to LOSE money consistently too… **As long as you’re not trading too much, sizing too big, or fighting strong drift.**

If you are relatively small in a liquid market, you get to trade at prices set by the best at those games. This means that, in most liquid markets, the expected return from random trading is zero, less your trading costs.

**You’re equally unlikely to accidentally stumble on negative alpha as you are to stumble on positive alpha.**

What are the implications of this?

Most importantly, it’s critical to avoid the Three Mortal Sins of trading too much, sizing too big, and fighting strong drift.

Those are really the only ways you can screw up with confidence. So avoid them!

Second, type 2 errors in trading may be less harmful than type 1 errors.

Trading something with no edge doesn’t hurt you *that much* (as long as it’s not super hyperactive and you don’t trade it too big).

It has only slightly negative expected value (due to transaction costs) but it costs you in (unrewarded) p&l volatility. This perhaps offers an interesting asymmetrical opportunity.

If you are good at finding edges (on average), it can be a good idea to err on the side of trading stuff that looks marginal (and nearly everything looks marginal).

This may be especially true for edges that make economic sense, but for which there is not enough data available to run any kind of reasonable statistical analysis.

You don’t want to trade any old rubbish, but the skewed risk/reward of giving something a shot is attractive.

I sometimes see people passing up (what I suspect are) good, simple edges because they’re not 100% sure about it, or “the backtest doesn’t look that great.”

*That’s likely a problem of unrealistic expectations and lack of diversification. *Remember:

Any single edge is going to be noisy and uncertain. And the game is won not by finding a few perfect high-performing edges.

That’s asking a bit much. And it’s an overconfident bet.

Edges come and edges go. **Diversification is an operational essential**, given this uncertainty.

The game is won by:

- Avoiding the Three Mortal Sins (trading too often, sizing too big, shorting drift)
- Trading the most reliable return sources (Risk parity over various risk premia / MM if pro)
- Diversifying across many different edges

And perhaps:

- worry a little less about whether a given edge is real or “good enough”
- be OK that some things just won’t work out
- worry a little more about maximizing the probability that you always trading with a few good edges.

If you’d like to learn more about playing the games that you can win as a retail trader, consider joining Trade Like a Quant, our 6-week Bootcamp on simple, high-probability trading for the time-poor trader.

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]]>The post How to Predict Asset Prices (and how not to) appeared first on Robot Wealth.

]]>If you have some factor that you think predicts future stock returns (or similar) and you are making charts like below, then here are some tips…

You get daily SPX index prices and daily VIX close data

You align them by date and plot them on dual axes, in true RealVision style.

*“SPX tends to go down when VIX is high. I can therefore time an SPX allocation based on VIX. Let me share this on twitter”* you say.

No. Very no.

**There are two main problems with what you did:**

- The SPX price drifts. We can’t directly compare the price of SPX in 2004 with its price in 2021
- As traders, we are more interested in whether high VIX is
decreasing SPX prices, not**followed by**them.**coincident with**

We’ll deal with them in order.

First, you almost never want to be analyzing asset prices, because asset prices tend to be highly “non-stationary”.

We can’t compare them across our sample.

SPX 1000 in 2015 is not comparable to SPX 1000 in 2021 (which would be more significant)

Plotting prices is maybe how you’re used to looking at stock charts, but it’s no way to do data analysis.

If I presented something like this to my old boss he’d throw it back in my face and say:

“James, I need at least a modicum of f***ing stationarity!”

He’d then elaborate on my worth as a researcher (and human being) in ways that might appear problematic in the 2021 workplace.

But it was ultimately very helpful.

I hope you can benefit from this advice, even if you don’t have a boss like that…

So how do we get him his “modicum of stationarity”?

*An easy and effective way is to look at differences in prices (or returns) rather than prices themselves*

In this case, we’re going to look at daily log returns.

We see that returns are much more “stable” and comparable over time.

10% in 2005 is comparable to 10% in 2021.

If we plot returns as a histogram, we get the familiar “bell-shaped” distribution, with a high peak, positive mean, negative skew, and fat tails.

Now let’s turn our mind to the VIX series…

VIX is much better behaved. VIX 20 is comparable in 2005 and 2021.

The histogram of VIX values shows it to be positively skewed (occasionally we observe very large values). This is also evident from the spikes in the chart.

So we’ll leave VIX alone for now, and confront the next point.

You can probably tell by the way I’ve phrased the question, that I think this question is a bit dumb, but let’s soldier on…

We plot a scatterplot of SPX returns against the VIX level at the end of the day.

We see a weak negative relationship.

On days when the VIX closed high, we saw lower returns, on average.

*Means we might be onto something, right?*

Wrong.

“What, other than the thing I hope is true, could be causing this?”

Call yourself on your bullsh*t before someone else does.

*But first, what else do you notice about that plot? *

You should notice that the scatterplot is “noisier” and returns are more spread out for higher values of VIX.

This is because:

– we have fewer observations for very VIX

– by definition, the spread of returns is higher when volatility (VIX) is higher

We don’t have to do anything about this, other than understand it… but we can.

We can normalize our returns by their expected volatility by dividing our SPX returns by the previous day’s VIX value

Now our scatterplot looks like this (we’ve controlled for that obvious effect)

So what’s causing this – other than VIX having magic SPX direction predicting powers?

We’re looking at the relationship between SPX returns and the VIX level *at the end of that period*.

We’re looking at a coincident relationship.

If we know anything about equity index volatility, we know that volatility expectations will tend to increase when the SPX goes down.

So it’s likely this is what we’re seeing here.

Here we plot SPX returns against the change in VIX in % points over the same period.

We see a very clear negative relationship. On days when SPX goes down, VIX tends to go up (and vice versa).

So, to what extent is this causing the effect we saw?

We can control for this by asking a better question:

“Do next day SPX returns tend to be lower, following a high VIX reading the previous day?”

We’re now starting to deal with our second problem – the coincidence thing…

So we plot vol-normalized SPX returns against the value the VIX index value at *the previous day*.

This represents something we could * almost* do in the market.

*(We can’t in reality because the VIX daily marking was, until very recently, 15 minutes after the SPX close.)*

Even though we’ve made some flattering assumptions about being able to see 15 minutes into the future, there’s little evidence pointing at a significant relationship between the VIX level and next-day SPX returns.

This shouldn’t be a surprise. The market is dominated by noise.

We’re dealing with daily data here. A scatterplot of returns vs factor is always going to be a tough ask at this scale, even for the most venerable of anomalies.

But I wanted to demonstrate that what *seems* like a clear predictive relationship if you’re looking at it sloppily, starts to look like a mass of randomness when you analyze it more carefully.

**Takeaways? **

- “Give me a modicum of f’ing stationarity” – prefer to work with returns rather than prices

- Define clearly the question you’re asking of the data

- Plot everything

- Don’t bullshit yourself… search hard for reasons outside of your pet theory.

*Want to learn more about our upcoming Bootcamp? Sign up for the waitlist – Trade like a Quant Bootcamp here*

*In this quant trading course, we concentrate on the simple things that work: the things that turn money into more money. *

*Get more content like this directly from James by following him on Twitter*

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]]>The post What P&L Swings Can I Expect as a Trader? appeared first on Robot Wealth.

]]>Many beginner traders don’t realize how variable the p&l of a high-performing trading strategy really is.

Here’s an example… I simulated ten different 5 year GBM processes with expected annual returns of 20% and annualized volatility of 10%. *(If you speak Sharpe Ratios, I’m simulating a strategy within known Sharpe 2 characteristics.)*

I plotted the path with the highest ending equity (green), median (black) and lowest (red). We know that all the paths are from exactly the same process, with the same known return distribution.

- You might think of the green line as trading a strategy with a known large edge and being lucky.
- You might think of the red line as trading a strategy with a known large edge and being unlucky.

Even when you were really lucky, you were underwater for 130 days.

When you were unlucky, you were underwater for 508 days (about 2 years)

Let that sink in: you have a strategy with a known Sharpe 2 edge, and you might reasonably expect be underwater for at least 2 years if your luck falls in the bottom decile.

**The reality of trading is even more uncertain because you never know what your edge is, see:**

We don’t simply diversify to access the well-understood vol-reducing diversification benefits.

We also because,** by spreading our bets, we decrease, the chance that we are trading without an edge****.**

* If you are serious about this game, you need to understand this dynamic deeply. *And try to structure your life, income, expenses so this level of trading p&l variance is appropriate. The “carry” of a salary, management fees, consulting work, or side gig can help you navigate this.

You can access the simulator here.

*Sign up for our upcoming Bootcamp, Trade like a Quant, here*

*Get more content like this directly from James by following him on Twitter*

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]]>The post How do I know if I have an edge? appeared first on Robot Wealth.

]]>I’ve been helping a family friend with his trading.

I’ve given him a simple systematic strategy to trade by hand.

We can plot the distribution of historic trade returns from past trading or a backtest as a histogram.

This is useful because it gives us a hint as to what the “edge” of our strategy might be – if we could ever truly *know* such a thing.

In this case, our strategy had positive mean and negative skew. *(As many things that make money tend do, regrettably)*

Now, when we make a trade, we’re really just taking a random sample from a bucket of returns.

You might think of it like we’re picking observations out of the bucket described by the histogram we just made.

*BUT….*

**The histogram doesn’t show us the true nature of the distribution of returns in the bucket – just the returns that occurred in the past.**

The “true distribution” changes with time (it is stochastic) and cannot be observed directly. We can only infer it from the past.

**So the best we can know is that, in the past, it looked like we had an edge.**

We might run rolling stats to try to observe the time-varying nature of things – but we’d be working with only a few samples and the variance of our trade return is large. So we do our best to estimate what the “true process” looks like, by inferring it from past observations and our understanding of market dynamics.

My friend has placed about 20 trades and he’s starting to try to make some distinctions based on individual trades.

“I’ve learned to exit later when momentum is in my favour” etc…

This is what humans do. They look for patterns in noise.

Ultimately, however, analysis at the individual trade level is meaningless. He’s just fitting stories to random data. Individual trade P&L carries no useful information.

Think about the trade p&l histogram we made at the start… Imagine we’re building that up trade by trade, observation by observation. **How many points would you need before it had a meaningful shape?**

It would be a lot… it would take a long time to build this histogram up block by block.

All analysis needs to be undertaken in the aggregate, ideally over as many stable observations as possible.

But everything is non-stationary (it changes with time) so our observations always arrive later than we want them to, and there are never enough of them.

**This is why trading is hard and you don’t get much feedback (on edge) from observing your own trades. **You get plenty of useful quick feedback on things such as market impact, but the data on “edge” takes forever to collect and stuff is constantly changing underneath you

You’re extremely unlikely to make much sense of this kind of probabilistic thinking by watching the market – unless you are trading extremely fast and disciplined.

**You need a quantitative approach. You need to analyze in aggregate. You need an understanding of stats**

You need a critical mind. You need to understand why something works, and track whether those conditions are still in place – so you can try to pre-empt the change in the return process.

You need to understand you can never *know* if you have an edge right now.

This is not something to be feared… this is what makes trading awesome!

You never know if you have an edge right now, but when you think you do – sample from it as much as you can in the simplest, most robust way possible.

Want to learn more about our upcoming Bootcamp? Sign up for the waitlist – Trade like a Quant Bootcamp here

In this quant trading course, we concentrate on the simple things that work: the things that turn money into more money.

Get more content like this directly from James by following him on Twitter

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]]>The post Three types of systematic strategy that “work” appeared first on Robot Wealth.

]]>Broadly, there are three types of systematic trading strategy that can “work.” In order of increasing turnover they are:

- Risk premia harvesting
- Economically-sensible, statistically-quantifiable slow-converging inefficiencies
- Trading fast-converging supply/demand imbalances

This post provides an overview of each.

Risk Premia Harvesting is typically the domain of wealth management, but it’s important to any trader who likes money.

A *risk premium* is the excess return you might expect over and above risk-free cashflows for taking on certain unattractive risks. *Equity Risk Premium*, for example, is how you say *“Stonks, they go up”* if you work for Blackrock (though, they’re really referring to the extent to which they “go up” * more than *an equivalent less risky thing).

The basics of risk premia harvesting are:

- Intentionally expose your portfolio to diverse
**sources of risk that tend to be rewarded**(noting that not all risks are rewarded) - Manage risk sensibly so no risk dominates at any time
- Be patient and chill (the hardest part for most)

A very simple example of such a risk premia harvesting strategy is the 60/40 stock/bond portfolio.

More balanced implementations include Bridgewater’s All-Weather portfolio and Risk Parity strategies generally, which attempt to equalize risk across assets or sources of risk premia.

Doing useful things like providing liquidity in a highly stressed market, or making a two-sided market at all times is also arguably risk premia harvesting since you’re taking on the risk of getting run over by those who can choose when to trade.

Risk premia harvesting is something nearly every trader should do. In fact, we like to treat it as the foundation of a serious independent trading operation, to which other edges and strategies can be added over time.

Active traders need to be aware of risk premia too. For example, if you’re shorting stocks, you’re facing a big hurdle in the form of the equity risk premium. You need to be right over and above the expected drift in the asset. On the other hand, if you’re long stocks in an active strategy, there’s a decent chance you’ll make money even if your reason for getting into the position was wrong.

*It’s better to play easy games than hard ones, and it’s nice to still make money when you’re wrong. *

These are **noisy** tendencies for assets to trade too cheap or expensive at certain times due to behavioral or structural effects. Examples include momentum effects, seasonal regularities, and effects due to indexing inclusion/exclusion. We can probably lump style factors (momentum, value, carry, quality, low vol) and most medium frequency statistical arbitrage approaches in this bucket too.

This stuff tends to be noisy and slow to converge, so you have to analyze it in aggregate over large data sets.

It also means that your P&L is very slow to converge to expected returns – which can be challenging to sit through.

So to trade these edges effectively we need:

- To understand why the inefficiency would persist.
- Faster converging metrics around what we’re exploiting so we’re not the last to know when the inefficiency disappears.
- Patience and discipline to keep swinging the bat – you have to let the noisy edge play out over a large number of bets.

Useful sources for finding these trades include:

*Expected Returns*, Antti Ilmanen*Efficiently Inefficient*, Lasse Pedersen*Positional Option Trading*, Euan Sinclair**(which literally gives you stuff to trade)***Active Portfolio Management,*Grinhold and Kahn

Generally, these edges are less reliable than risk premia harvesting and fast-converging flow effects that we’ll discuss below.

In my experience, independent traders usually spend too much time on these edges, and too little on risk premia harvesting.

This stuff is the bread-and-butter of proprietary trading firms.

Short term supply and demand imbalances create dislocations in prices which fast traders can “disperse” by trading against them and offsetting risk elsewhere.

These trades are conceptually simple and economically sound. For example, I might buy futures on Shanghai INE and buy a similar contract cheaper on Singapore SGX for a profit (after costs).

That’s a simple arb, but it carries risks because we can’t trade instantaneously. Generally, we’re doing riskier trades than this simple arb, that we expect to work out on average.

Often, these trades involve looking to buy cheap and sell high based on simple relative-value models, the assumption being that deviations from (relative) fair value will converge. So trading models in this space are less about predicting the future (as per 2, above) and more about extrapolating the present (Q vs P).

Advantages of these trades include:

- They’re easy to understand and economically simple
- They converge fast to expected returns. You know quickly when your model is out or you don’t have an edge anymore. They fit nicely with Kris Abdelmessih’s “measurement and normalization” paradigm

The disadvantages of these trades are that they are capital constrained and require significant investment in infrastructure and staff.

Whilst this area isn’t practical for “home gamers”, the lessons here are crucial for a good understanding of the market.

Systematic trading strategies that “work” can be grouped into three categories:

- Risk premia harvesting
- Slow converging inefficiencies based on economic or structural effects
- Fast converging inefficiencies based on deviation from some notion of relative fair value

Independent traders should, generally, start off by focusing on (1), over time add a little of (2), but not as much of this as (1), and dig into (3) to understand and appreciate the efficiency of the markets.

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]]>The post Exporting Zorro Data to CSV appeared first on Robot Wealth.

]]>Earlier versions of Zorro used to ship with a script for converting market data in Zorro binary format to CSV. That script seems to have disappeared with the recent versions of Zorro, so I thought I’d post it here.

When you run this script by selecting it and pressing [Test] on the Zorro interface, you are asked to select a Zorro market data file to convert to CSV format. Zorro then does the conversion for you and writes the data to Zorro/History/Export.csv.

// convert a .t6 or .t1 file to .csv //#define ASCENDING #define MAX_RECORDS 10000 string Target = "History\\Export.csv"; int point(int Counter) { if(0 == Counter % 10000) { if(!wait(0)) return 0; printf("."); } return 1; } function main() { file_delete(Target); string Source = file_select("History","T1,T6\0*.t1;*.t6\0\0"); if(strstr(Source,".t6")) { T6 *Ticks = file_content(Source); int Records = file_length(Source)/sizeof(T6); printf("\n%d records..",Records); #ifdef MAX_RECORDS Records = min(Records,MAX_RECORDS); #endif #ifdef ASCENDING int nTicks = Records; while(--nTicks) #else int nTicks = -1; while(++nTicks < Records) #endif { T6 *t = Ticks+nTicks; file_append(Target,strf("%s,%.5f,%.5f,%.5f,%.5f\n", strdate("%Y-%m-%d %H:%M:%S",t->time), (var)t->fOpen,(var)t->fHigh,(var)t->fLow,(var)t->fClose)); if(!point(nTicks)) return; } } else if(strstr(Source,".t1")) { T1 *Ticks = file_content(Source); int Records = file_length(Source)/sizeof(T1); printf("\n%d records..",Records); #ifdef MAX_RECORDS Records = min(Records,MAX_RECORDS); #endif #ifdef ASCENDING int nTicks = Records; while(--nTicks) #else int nTicks = -1; while(++nTicks < Records) #endif { T1 *t = Ticks+nTicks; file_append(Target,strf("%s,%.5f\n", strdate("%Y-%m-%d %H:%M:%S",t->time),(var)t->fVal)); if(!point(nTicks)) return; } } printf("\nDone!"); }

By default, the data is written in descending order (newest data first). If you want ascending order instead, uncomment the line `#define ASCENDING`

.

As you can see, this script works with Zorro version 2.30:

This script is useful if you want to convert a single market data file. But it’s a little cumbersome if you want to convert the entire market data history of a ticker since Zorro splits that data into separate files by year (except for end-of-day data – that all goes into a single file).

Here’s a script for converting the entire history of a ticker from Zorro format to CSV:

//Export selected asset history to CSV function run() { StartDate = 20060101; LookBack = 0; BarPeriod = 1; string Format = ifelse(assetType(Asset) == FOREX, "\n%04i-%02i-%02i %02i:%02i, %.5f, %.5f, %.5f, %.5f", "\n%04i-%02i-%02i %02i:%02i, %.1f, %.1f, %.1f, %.1f"); char FileName[40]; sprintf(FileName,"History\\%s.csv",strx(Asset,"/","")); // remove slash from forex pairs if(is(INITRUN)) file_write(FileName,"Date,Open,High,Low,Close",0); else file_append(FileName,strf(Format, year(),month(),day(),hour(),minute(), round(priceOpen(),0.1*PIP), round(priceHigh(),0.1*PIP), round(priceLow(),0.1*PIP), round(priceClose(),0.1*PIP))); }

This one takes the ticker selected in Zorro’s asset dropdown box and writes its entire history to Zorro/History/ticker.csv. Again, you can see it works with Zorro 2.30:

If you want to import that data into R as an `xts`

object, the following snippet will do the trick:

`Data <- xts(read.zoo("ticker.csv", tz="UTC", format="%Y-%m-%d %H:%M", sep=",", header=TRUE))`

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]]>The post Evolving Thoughts on Data Mining appeared first on Robot Wealth.

]]>Several years ago, I wrote about some experimentation I’d done with data mining for predictive features from financial data. The article has had several tens of thousands of views and nearly 100 comments.

I *think* the popularity of the article lay in its demonstration of various tools and modeling frameworks for doing data mining in R (it didn’t generate any alpha, so it can’t have been that). To that end, I’ve updated the data, code, and output, and added it to our GitHub repository. You can view the updated article here and find the code and data here.

Re-reading the article, it was apparent that my thinking had moved on quite significantly in just a few short years.

Back when I originally wrote this article, there was a commonly held idea that a newly-hyped approach to predictive modeling known as *machine learning* could discern predictive patterns in market data. A quick search on SSRN will turn up dozens of examples of heroic attempts at this very thing, many of which have been downloaded thousands of times.

Personally, I spent more hours than I care to count on this approach. And while I learned an absolute ton, I can also say that *nothing* that I trade today emerged from such a data-mining exercise. A large scale data mining exercise *contributed* to *one* of our strategies, but it was supported by a ton of careful analysis.

Over the years since I first wrote the article, a realisation has dawned on me:

Trading is very hard, and these techniques don’t really help that much with the hardest part.

I think, in general, the trading and investment community has had a similar awakening.

*OK, so what’s the “hardest part” of trading?*

Operational issues of running a trading business aside, the hardest part of trading is maximising the probability that the edges you trade continue to pay off in the future.

Of course, we can never be entirely sure about anything in the markets. They change. Edges come and go. There’s always anxiety that an edge isn’t really an edge at all, that it’s simply a statistical mirage. There is uncertainty everywhere.

Perhaps the most honest goal of the quantitative researcher is to **reduce this uncertainty as far as reasonably possible.**

Unfortunately (or perhaps fortunately, if you take the view that if it were easy, everyone would do it), reducing this uncertainty takes a lot of work and more than a little market nouse.

In the practical world of our own trading, we do this in a number of ways centred on detailed and careful analysis. Through data analysis, we try to answer questions like:

- Does the edge make sense from a structural, economic, financial, or behavioural perspective?
- Is there a reason for it to exist that I can explain in terms of taking on risk or operational overhead that others don’t want, or providing a service?
- Is it stable through time?
- Does it show up in the assets that I’d expect it to, given my explanation for why it exists?
- What else could explain it? Have I isolated the effect from things we already know about?
- What other edges can I trade with this one to diversify my risk?

In the world of machine learning and data mining, “reducing uncertainty” involves accounting for data mining bias (the tendency to eventually find things that look good if you look at enough combinations). There are statistical tests for data-mining bias, which, if being generous, offer plausible-sounding statistical tools for validating data mining efforts. However, I’m not here to be generous to myself and can admit that the appeal of such tools, at least for me, lay in the promise of avoiding the really hard work of careful analysis. *I don’t need to do the analysis, because a statistical test can tell me how certain my edge is!*

But what a double-edged sword such avoidance turns out to be.

If you’ve ever tried to trade a data-mined strategy, regardless of what your statistical test for data-mining bias told you, you know that it’s a constant battle with your anxiety and uncertainty. Because you haven’t done the work to understand the edge, it’s impossible to just leave it alone. You’re constantly adjusting, wondering, and looking for answers *after the* *fact*. It turns into an endless cycle – and I’ve *personally *seen it play out at all levels from beginner independent traders through to relatively sophisticated and mature professional trading firms.

The real tragedy about being on this endless cycle is that it short-circuits the one thing that is most effective at reducing uncertainty, at least at the level of your overall portfolio – finding new edges to trade.

This reality leads me to an approach for adding a new trade to our portfolio:

- Do the work to reduce the uncertainty to the extent possible. You don’t want to trade just
*anything*, you want to trade high-probability edges that you understand deeply. - Trade it at a size that can’t hurt you at the portfolio level if you’re wrong – and we will all be wrong from time to time.
- Leave it alone and go look for something else to trade.

The third point is infinitely more palatable if you’ve done the work and understand the things you’re already trading.

Having said all that, I’m not about to abandon machine learning and other statistical tools. They absolutely have their place, but it’s worth thinking about the relative importance of what to concentrate on and what we spend our time on.

At one extreme, we might think that market insight and quantitative analysis (what we’d call “feature engineering” in machine learning speak) is the most important thing and that we should spend all our time there.

However, the problem with this approach is that there are effective and well-understood techniques (for example PCA, lasso regression, and others) that will very much help with modeling and analysis. Understanding these tools well enough to know what they are and when they might help greatly enhances your effectiveness as a quantitative researcher.

On the other extreme, we might think that spending all our time on machine learning, data mining and statistical tests is appropriate. This is akin to owning a top-notch toolkit for servicing a car, but not knowing anything about cars, and leads to the endless cycle of patching things up mentioned above.

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]]>The post Are Cheap Stocks Expensive? A Simple Equity Factor Analysis Walkthrough appeared first on Robot Wealth.

]]>I have been sharing examples of simple real-time trading research on my Twitter account.

I do this kind of thing a lot in the training program of our trading group – and I’m sharing in the hope that it might also help a wider audience.

Here’s a piece of analysis I did recently on a really simple factor that appeared to be predictive of relative equity returns.

Shall we do some analysis on a *really dumb* factor which might predict relative returns in stocks?

“Are cheap stocks expensive?”

A research thread

— Robot James (@therobotjames) November 12, 2020

Options on stocks with a low share price tend to be overpriced.

Equity options (at 100 shares a pop) are quite big for a small retail trader. So we might say there is excess retail demand for options on cheap stocks – which would result in them being overpriced.

The AMZN share price is $3k+. There are Robinhooders who can’t afford a single stock.

Do we see the same effect in Stocks as we do in the options?

I’m going to analyze this in R – using datasets from the Robot Wealth research lab.

My raw price data looks like this:

I have daily OHLC for every stock that appeared in the Russell 1000 index over the last 20 years. (Whether it still exists or not)

- The OHLC points are adjusted for splits and dividends.
- The unadjusted_close price is the price the stock actually closed on that day
- If the stock didn’t trade that day we still have a row. It has
`volume = 0`

- If the stock was not in the index that day then
`is_universe = 0`

I don’t need daily data. I’m trying to answer a pretty dumb question here. So let’s keep things simple.

I’m going to just get snapshots of the prices on the last day of each calendar year.

Always keep stuff simple for yourself. At the start of a piece of analysis, you’re just trying to quickly disprove an idea. Most ideas are bad and the market is super-efficient. So make life easy, move fast, and disprove fast.

Borrowing the language of machine learning for my trivial analysis (because it’s precise) I now need to prepare:

- the target (the thing I am trying to predict)
- the feature (the thing I hope is predictive)

My (raw) target is going to be the log returns of the stock over a year

My (raw) feature is going to be the unadjusted close price of the stock at the end of the previous year.

Here I calculate the feature and target and align them in a single data set:

I’ve calculated those for all the stocks, including on days when those stocks weren’t in the Russell 1000 index.

So now I filter out the days when the stock wasn’t in the index and days when a given stock didn’t trade (due to a trading halt or similar)

Always assume you’ve screwed it up. Check. Here I spot check on TSLA.

Looks good.

- The feature is just the unadjusted close at the end of the year.
- The target is the log returns over the next year.

Now we’re ready to do some scaling and sorting.

We don’t want to work with the raw feature. We’re looking to answer a very broad question here, and large numbers are our friends.

So we want to sort and group our data so we can aggregate it effectively.

We’ll scale our feature by sorting each stock into one of 10 buckets each year

- Bucket 1 will contain the stocks in the index with the lowest (unadjusted) share price that year
- Bucket 10 will contain the stocks in the index with the highest (unadjusted) share price that year

We call these deciles if we are fancy. I usually call them buckets.

To understand what that has done we plot a histogram of all our feature observations and colour it by the bucket it ended up in..

Now we’ve reduced our raw feature to 10 buckets. That will be helpful.

Our next task is to think about scaling the target.

We’re really more interested in * relative* (rather than absolute) returns:

So we “de-mean” the target by subtracting the mean returns of all stocks that year from the yearly returns for each stock in our universe.

The data now look like this. I’ve highlighted the scaled feature (`bucket`

) and target (`demeaned_target`

.)

Now we want to see if the really low priced stuff that ended up in bucket 1 had lower returns than the really high priced stuff that ended up in bucket 10.

So we take our observations, group by bucket and plot the mean of next years (de-meaned) returns for each bucket.

Interestingly… we do appear to see – at least over the whole sample – the annual return of the cheap stocks is significantly (6-7%) lower than the returns of the more expensive stocks.

*I haven’t lost interest yet…*

So let’s create one of those plots for each of the 22 years in the sample.

We want to get a feel for whether we see this pattern consistently.

Looks quite consistent… The relative shapes of 2000/2001 and 2007/2008 are interesting and point to this effect likely having some explanatory variable we already know about such as a beta / size / reversion effect…

Let’s not worry about that yet… move fast and loop back.

To make this thing more readable i’m going to group into groups of about 3 years and plot them.

Woah there 2017-2019… makes me wonder whether I’ve introduced some bias *(or my unadjusted close is correct)*. Something to look at.

To complete our superficial analysis, let’s plot a cumulative return time series of a strategy that goes long the 10% with the highest share price and the 0% with the lowest share price.

Long bucket 10, short bucket 1

Very interesting… I’m quite surprised at the results of this… I thought I would find nothing. Or at, least, an incredibly noisy effect.

Two main things to do now

- Get more acquainted with unadjusted close data to ensure it’s correct and I’m not introducing helpful bias

2 Try to isolate this from any other casual factors we already know about (size, reversion from big moves, beta effect)

There is a * suggestion* that cheaper stocks are expensive.

You think you’ve identified a new, useful predictive factor for trading…

But is it really new? Or just another way of looking at something you already know about?

How might you tell? Here are some simple ways…

A research thread https://t.co/q9ga3S6zbd

— Robot James (@therobotjames) November 27, 2020

We know that a low stock price doesn’t actually * cause *future returns to be lower. That would be silly.

But we thought that stocks with very low share prices may be attractive to a low capitalized seeker of stock returns – whose marginal demand may bid up these stocks.

This is *plausible*. And we *would like *it to be true (cos then we’ve found a new effect we might harness.) But we can’t always get what we want.

So we must ask: **“Is this something we already know about?”**

Economic intuition comes before statistics.

*What do we already know about that might be causing this?*

Well, it is well known that high volatility assets tend to have very poor long-run returns.You can read about this in Antti Ilmanen’s Expected Returns here…

We suspect high vol assets are attractive to those who like lotterylike “YOLO” payoffs or who dislike leverage or can’t access it easily. This creates excess demand for highly volatile stocks, which makes them more expensive, which makes their future expected returns lower.

So do stocks with lower share prices tend to underperform simply because they tend to be more volatile stocks? Or is there something else going on? Let’s look…

First, we calculate a volatility factor – which will just be the annualised volatility of the stock over the last 252 trading days (1 year).

I’m using the same dataset as in the linked thread at the top…

Now we want to answer the question:

Do stocks with low share price also tend to be high volatility stocks (and vice versa)?

A scatterplot is a useful tool for this. For each yearly stock observation plot its past volatility on the y-axis and the log share price on the x-axis.

It’s quite clear that stocks with low share prices tend to be higher volatility stocks. This suggests what we are seeing could well be a high-volatility effect.

Now we want to see if our share price effect goes away if we control for the high volatility effect.

First, let’s look at the volatility effect itself. We sort all our annual stock observations into deciles by rising volatility and plot the mean of their log returns the following year. It’s pretty clear the high vol stuff tends to have crappy returns.

What if we filter out the highly volatile stuff from our analysis?

If we only look at the stuff that appears in volatility deciles 1-8, do we still see any “signal” in our share price factor? Do lower volatility stocks with low share prices still have worse returns?

So we:

- filter out all the high vol stocks (vol_bucket <= 8)
- plot the mean log return for each share price bucket for the remaining low and moderate volatility stocks.

**And it no longer looks interesting!**

Once we’ve controlled for the high volatility effect, the share price doesn’t seem to have anything interesting to add.

As often happens in the markets, it’s unlikely we’re going to get what we want here. **It’s likely we just found another proxy for volatility.**

Now, let’s try isolating the high vol stuff. Does the share price allow us to discriminate between high vol stuff with better (less bad?) returns?

Nope. Doesn’t seem to be anything there either!

At this point, I think we can say that it’s very likely the share price effect we saw isn’t that interesting by itself – it’s really just a proxy for the volatility / “betting-against-beta” effect we already knew about.

Such is the way it goes!

The good news is we understand the effect better now. The less good news is it’s likely just another crude way of looking at something we already knew about.

Here’s a simple recipe of sorts for doing this kind of thing:

- Use economic intuition to identify what else might explain the effect
- Proxy that other thing as a factor
- Look at the relationship between the two factors (scatterplot is good)
- Control for one effect (as best you can) and see if the other factor still explains returns

Economic intuition and simple exploratory data analysis should always be your first port of call.

Don’t rush into running regressions or the like without asking some good simple questions of the data first. You’ll get much more insight this way.

Stocks with low share prices tend to underperform those with higher share prices.

Unfortunately, this doesn’t look to be a unique factor. It appears to be almost entirely explained by the fact that stocks with low share prices tend to be higher volatility stocks (a known “betting-against-beta” factor.)

The post Are Cheap Stocks Expensive? A Simple Equity Factor Analysis Walkthrough appeared first on Robot Wealth.

]]>The post Trading FX using Autoregressive Models appeared first on Robot Wealth.

]]>I’m a big fan of Ernie Chan’s quant trading books: *Quantitative Trading*, *Algorithmic Trading,* and *Machine Trading*. There are some great insights in there, but the thing I like most is the simple but thorough treatment of various edges and the quant tools you might use to research and trade them. Ernie explicitly states that the examples in the books won’t be tradable, but they’ve certainly provided fertile ground for ideas.

In *Machine Trading*, there is an FX strategy based on an autoregressive model of intraday price data. It has a remarkably attractive pre-cost equity curve, and since I am attracted to shiny objects, I thought I’d take a closer look.

An autoregressive (AR) model is a time-series multiple regression where:

- the predictors are past values of the time series
- the target is the next realisation of the time series

If we used a single prior value as the only predictor, the AR model would be called an AR(1) and it would look like:

y_t = \beta_0 + \beta_1 y_{t-1} + \epsilon_t (the \beta‘s are the regression coefficients)

If we used two prior values, it would be called an AR(2) model and would look like:

y_t = \beta_0 + \beta_1 y_{t-1} + \beta_2 y_{t-2} + \epsilon_t `

You get the picture.

Ernie says that

“Time-series techniques are most useful in markets where fundamental information and intuition are either lacking or not particularly useful for short-term predictions. Currencies … fit this bill.”

He built an AR(p) model for AUD/USD minutely prices (spot, I assume), using Bayesian Information Criterion to find the optimal p. He used data from July 24 2007 to August 12 2014 to find p and the model coefficients:

He used an out-of-sample data set from August 12 2014 to August 3 2015 to generate the following (pre-cost) backtest:

If we were to use an AR(p) model of prices to predict future prices, what are we assuming?

Essentially, that past prices are correlated with future prices, to the extent that they contain tradable information.

The first part of that seems perfectly reasonable. After all, a very good place to start predicting tomorrow’s price would be today’s price. The latter part of that however is fairly heroic. Such a naive forecast is obviously not going to help much when it comes to making profitable trades. If we could forecast returns on the other hand…now that would be a useful thing!

Most quants will tell you that price levels can’t contain information that is predictive in a useful way, and that instead, you need to focus on the process that manifests those prices – namely, returns. **Building a time series model on prices feels a bit like doing technical analysis… albeit with a more interesting tool than a trend line.**

Anyway, let’s put that aside for now and dig in.

If we’re going to use an AR model, then a reasonable place to start would be figuring out if we have an AR process. For that, we can use the `acf`

function in R:

Our minutely price series is indeed very strongly autocorrelated, as we’d expect. We have a lot of data (I used minutely data from 2009 – 2020), and of course, the price from one minute ago looks a lot like the price right now.

We can use the partial autocorrelation function (`pacf`

) to get a handle on how many lags we might need to build an AR model.

A partial autocorrelation is the correlation of a variable and a lagged version of itself *that isn’t explained by correlations of previous lags.* Essentially, it prevents information explained by prior lags from leaking into subsequent lags.

That makes it a useful way to identify the number of lags to use in your AR model – if there is a significant partial correlation at a lag, then that lag has some explanatory power over your variable and should be included. Indeed, you find that the partial correlation values correspond to the coefficients of the AR model.

Here are the partial autocorrelations with the lag-0 correlation removed:

This is interesting. If our price data were a random walk, we’d expect no lags of the PACF plot to be significant. Here, we have many lags having significant autocorrelation – is our price series weakly stationary, or does it drift?

Here’s a random walk simulation and the resulting PACF plot for comparison:

# random walk for comparison n <- 10000 random_walk <- cumsum(c(100, rnorm(n))) data.frame(x = 1:(n+1), y = random_walk) %>% ggplot(aes(x = x, y = y)) + geom_line() + theme_bw() p <- pacf(random_walk, plot = FALSE) plot(p[2:20])

Here’s a plot of the random walk:

And the PACF plot (again, with the lag-0 correlation removed):

Returning to the PACF plot of our price data, Ernie’s choice of 10 lags for his AR model looks reasonable (those partial correlation values translate to the coefficients of the AR model), but the data also suggests that going as far back as 15 lags is OK too.

It would be interesting to see how that PACF plot changes through time. Here it is separately for each year in our data set:

# annual pacfs annual_partials <- audusd %>% mutate(year = year(timestamp)) %>% group_by(year) %>% # create a column of date-close dataframes called data nest(-year) %>% mutate( # calculate acf for each date-close dataframe in data column pacf_res = purrr::map(data, ~ pacf(.x$close, plot = F)), # extract acf values from pacf_res object and drop redundant dimensions of returned lists pacf_vals = purrr::map(pacf_res, ~ drop(.x$acf)) ) %>% # promote the column of lists such that we have one row per lag per year unnest(pacf_vals) %>% group_by(year) %>% mutate(lag = seq(0, n() - 1)) signif <- function(x) { qnorm((1 + 0.95)/2)/sqrt(sum(!is.na(x))) } signif_levels <- audusd %>% mutate(year = year(timestamp)) %>% group_by(year) %>% summarise(significance = signif(close)) annual_partials %>% filter(lag > 0, lag <= 20) %>% ggplot(aes(x = lag, y = pacf_vals)) + geom_segment(aes(xend = lag, yend = 0)) + geom_point(size = 1, colour = "steelblue") + geom_hline(yintercept = 0) + facet_wrap(~year, ncol = 3) + geom_hline(data = signif_levels, aes(yintercept = significance), colour = 'red', linetype = 'dashed')

Those partial correlations do look quite stable… But remember, we’re not seeing any information about returns here – we’re only seeing that recent prices are correlated with past prices.

My gut feel is that this represents the noisy mean reversion you tend to see in FX at short time scales. Take a look at this ACF plot of minutely *returns* (not prices):

ret_acf <- acf(audusd %>% mutate(returns = (close - dplyr::lag(close))/dplyr::lag(close)) %>% select(returns) %>% na.omit() %>% pull(), lags = 20, plot = FALSE ) plot(ret_acf[2:20], main = 'ACF of minutely returns')

There are clearly some significant negative autocorrelations when we view things through the lens of returns. Any method of trading that negative autocorrelation would show results like Ernie’s backtest – including AR models and dumber-seeming technical analysis approaches. At least, in a world without transaction costs.

I think we can make the following assumptions:

- There is nothing special about the last ten minutely prices
- This is not going to be something we can trade, particularly under retail spot FX trading conditions.

But let’s not get caught up with inconvenient assumptions and press on with some simulations…

Here’s the game plan:

- Fit an AR(10) model on a big chunk of data
- Simulate a trading strategy that uses that model for its predictions on unseen data

I’ll use R to fit the AR(10) model. I’ll use Zorro to simulate the profit and loss of a strategy that traded on the basis of that model’s predictions. In the simulation, I’ll use Zorro’s R bridge to execute an R function that returns the step-ahead prediction given the last ten prices. Here’s a tutorial for setting up Zorro’s R bridge if you’d like to follow along.

First, here’s how to fit the AR(10) model in R (I have my AUD/USD prices in a dataframe indexed by `timestamp`

):

# fit an AR model ar <- arima( audusd %>% filter(timestamp < "2014-01-01") %>% select(close) %>% pull(), order = c(10, 0, 0) )

Here we use the `arima`

function from the `stats`

package and specify an order of `(10, 0, 0)`

. Those numbers correspond to the number of autoregressive terms, the degree of differencing, and the number of moving average terms, respectively. Specifying zero for the latter two results in an AR model.

Here are the model coefficients:

ar$coef # ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 ar9 ar10 # 0.9741941564 0.0228922865 0.0019821879 -0.0073977641 0.0045880720 0.0072364966 -0.0047513598 0.0003852733 -0.0048944003 0.0057283039 # intercept # 0.6692288336

Next, here’s an R function for generating predictions from an AR model:

# fit an AR model and return the step-ahead prediction # can fit a new model or return predictions given an existing set of coeffs and new data # params: # series: data to use to fit model or to predict on # fixed: either NA or a vector of coeffs of same length as number of model parameters # usage: # fit a new model an return next prediction: series should consist of the data to be fitted, fixed should be NA # fit_ar_predict(audusd$close[1:100000], order = c(10, 0, 0)) # predict using an existing set of coeffs: series and fixed should be same length as number of model parameters # fit_ar_predict(audusd$close[100001:100010], order = c(10, 0, 0), fixed = ar$coef) fit_ar_predict <- function(series, order = 10, fixed = NA) { if(sum(is.na(fixed)) == 0) { # make predictions using static coefficients # arima(series, c(1, 0, 0)) fits an AR(1) predict(arima(series, order = c(order, 0, 0), fixed = fixed), 1)$pred[1] } else { # fit a new model predict(arima(series, order = c(order, 0, 0)), 1)$pred[1] } }

If you supply the `fixed`

parameter (corresponding to the model coefficients), the function returns the step-ahead prediction given the values in `series`

. The length of `series`

needs to be the same as`order`

, and the length of `fixed`

needs to be `order + 1`

to account for the intercept term.

If you don’t supply the `fixed`

parameter, the function will fit an AR(order) model on the data in `series`

and return the step-ahead prediction.

Save this file in Zorro’s Strategy folder.

Finally, here’s the Zorro code for running the simulation given our model parameters derived above (no transaction costs):

#include <r.h> function run() { set(PLOTNOW); setf(PlotMode, PL_FINE); StartDate = 2014; EndDate = 2015; BarPeriod = 10; LookBack = 10; MaxLong = MaxShort = 1; MonteCarlo = 0; if(is(INITRUN)) { // start R and source the kalman iterator function if(!Rstart("ar.R", 2)) { print("Error - can't start R session!"); quit(); } } asset("AUD/USD"); Spread = Commission = RollLong = RollShort = Slippage = 0; // generate reverse price series (the order of Zorro series is opposite what you'd expect) vars closes = rev(series(priceClose())); // model parameters int order = 10; var coeffs[11] = {0.9793975109, 0.0095665978, 0.0025503174, 0.0013394797, 0.0060263045, -0.0023060104, -0.0022220192, 0.0006940781, 0.0011942208, 0.0037558386, 0.9509437891}; //note 1 extra coeff - intercept if(!is(LOOKBACK)) { // send function argument values to R Rset("order", order); Rset("series", closes, order); Rset("fixed", coeffs, order+1); // compute AR prediction and trade var pred = Rd("fit_ar_predict(series = series, order = order, fixed = fixed)"); printf("\nCurrent: %.5f\nPrediction: %.5f", priceClose(), pred); if(pred > priceClose()) enterLong(); else if(pred < priceClose()) enterShort(); } }

Now, since we’re calling out to R once every minute for a new prediction, this simulation is going to take a while. Let’s just run it for a couple of years out of sample while we go make a cocktail…

Here’s the result:

Which is quite consistent with Ernie’s pre-cost backtest (noting differences due to slightly different historical data periods and modeling software. Also note that Zorro’s percent return calculation is based on the assumption that you invest the minimum amount in order to avoid a margin call in the backtest – hence why it looks astronomically large in this case).

Unfortunately, this is a massively hyperactive strategy that is going to get killed by costs. You can see in the Zorro backtest that the average pre-cost profit per trade is only 0.1 pip. That’s going to make your FX broker extremely pleased.

Transaction costs are a major problem, so let’s start there.

If we saw evidence of partial autocorrelation at longer time horizons, we could potentially slow the strategy down such that it traded less frequently and held on to positions for longer.

Here are some rough PACF charts of what that might look like. First, using ten-minutely data:

# 10-minute partials partial <- pacf( audusd %>% mutate(minute = minute(timestamp)) %>% filter(minute %% 10 == 0) %>% select(close) %>% pull(), lags = 20, plot = FALSE) plot(partial[2:20], main = 'Ten minutely PACF')

Next, hourly:

# hourly partials partial <- pacf( audusd %>% mutate(minute = minute(timestamp)) %>% filter(minute == 0) %>% select(close) %>% pull(), lags = 20, plot = FALSE) plot(partial[2:20], main = 'Hourly PACF')

Finally, at the daily resolution:

# daily partials partial <- pacf( audusd %>% mutate(hour = hour(timestamp)) %>% filter(hour == 0) %>% select(close) %>% pull(), lags = 20, plot = FALSE) plot(partial[2:20], main = 'Daily PACF')

There’s a pattern emerging there, with fewer and fewer significant partial correlations as we increase the resolution.

We can try an AR(10) model using ten-minutely data. Follow the same procedure above, where we calculate the coefficients in R, then hard-code them in our Zorro script. This gives the following result:

We managed to triple our average cost per trade, but it’s still not going to come close to covering costs.

At this point, it’s becoming quite clear (if it wasn’t already) that this is a very marginal trade, no matter how you cut it. However, some other things that might be worth considering include:

- If we assumed that our predictions were both useful in terms of magnitude as well as direction, we could implement a prediction threshold such that we would trade only when the prediction is a certain distance from the current price.
- It would be reasonable to think that when volatility is higher, price tends to move further. To the extent that an edge exists, it will be larger as a percent of costs the larger the volatility. Since volatility is somewhat predictable (at least in a noisy sense), we might be able to improve the average profit per trade by simply not trading when we think volatility is going to be low.
- Finally, we may want to try re-fitting the model at regular intervals. To check if that’s a useful thing to do, you could look for evidence of persistence of model coefficients. That is, are the model coefficients estimated over one window similar to those fitted over the next window? You can backtest this approach using the Zorro and R scripts above – simply don’t pass the
`fixed`

parameter from Zorro and think about how much data you want in your fitting window.

Fitting an autoregressive model to historical prices of FX was a fun exercise that yielded a surprising result: namely, the deviation of the price series from the assumption of a random walk. The analysis suggests that short-term mean reversion of FX exists, but is unlikely to be something we can trade effectively.

When we think about what the strategy is really doing, it’s merely trading mean-reversion around a recent price level. It’s unlikely that the ten AR lags are doing anything more nuanced than trading a noisy short-term reversal effect that could probably be harnessed in a more simple and effective way. For example, we could very likely get a similar result with less fuss by looking to fade extreme moves in the short term.

Maybe there *are *sophisticated and important interdependencies between those ten lags, but I don’t think we should assume that there are. In any event, no matter how we trade this effect, it’s unlikely to yield profit after costs.

The post Trading FX using Autoregressive Models appeared first on Robot Wealth.

]]>The post Tesla’s inclusion in the S&P 500 – Is there a trade? appeared first on Robot Wealth.

]]>The S&P index committee recently announced that Tesla, already one of the biggest stocks listed in the country, would be included in the S&P 500.

Here’s the press release:

Due to TSLA’s size, it was widely expected to have entered the S&P 500 index much earlier – but S&P has some discretionary criteria it applies to ensure that the index is an effective measure of the larger stocks in the market. I suspect they worried that TSLA’s recent parabolic move was unsustainable.

TSLA’s inclusion in the index is going to be a big deal because TSLA is so big. The S&P 500 is a market capitalization-weighted index. If prices stay roughly the same, then TSLA will represent over 1% of the index – putting it near the top 10 on its inclusion.

Now, there’s a lot of money that is tracking that index. On the rebalance date these indexers will need to:

- buy a lot of TSLA shares
- sell a lot of shares stocks that are not TSLA.

Finger in the air, we’re talking $50 – $80 billion dollars (ish) worth of rebalancing trading that will need to occur around December 21st.

Due to the sheer size of the rebalance, S&P is seeking feedback on whether the index should be rebalanced in two tranches, or all in one go.

Certainly, we know there’s going to be a large amount of rebalance trading going on. Could that generate dislocations that may be tradeable?

Quite possibly… though maybe not in immediately obvious ways.

Everybody knows that everyone knows there will be significant demand for TSLA stock on the rebalance. So, on the S&P announcement, the stock price of TSLA jumped about 13%. Markets are forward-looking like that, you see. They don’t wait for permission.

Anything obvious gets “priced in” pretty quick. But an understanding of over-reaction/under-reaction dynamics, trader constraints, and some statistical analysis can sometimes uncover noisy inefficiencies around these kinds of events.

Early studies such as The S&P 500 Index Effect in Continuous Time: Evidence from Overnight, Intraday and Tick-By-Tick Stock Price Performance by Brooks and Ward suggested that:

- Any excess returns for the index joiner were mostly incorporated in the price overnight after the announcement date
*(which, of course, is untradeable)* - There were still some excess returns realized in the period from the first day after the announcement up to the event
- There were consistent intraday trading patterns around the announcement event, suggesting inefficient front-running flows which may be exploited
*(for example, see the image below which shows the cumulative intraday abnormal performance on the day after the stock has been added to the index.)*

Of course, time passes and the market continues to become more efficient. Banks and end-users develop more sophisticated rebalancing algorithms. The world moves onwards and upwards.

In a more recent paper, The Diminished Effect of Index Rebalances, Konstantina Kappou finds no tradeable abnormal returns between the announcement and the index rebalance dates. This suggests that market participants have become more effective in pre-positioning themselves for such an event, and indexers have become more sophisticated in avoiding market impact on rebalancing.

However – they do find what appear to be tradeable patterns on and after the index inclusion date.

In particular, using data between 2002 and 2013 (and a total of 276 index inclusions) the author finds highly significant excess returns for the stock on the first day it is included in the index (see green box) – which reverse thereafter.

Now – I’ve done no work to validate this. And I don’t intend to. (One has to prioritize one’s efforts.)

But this research suggests:

- If you’re looking to buy TSLA to harvest abnormal returns prior to the inclusion date, then you’re probably too late.
- But you may look to add TSLA exposure ahead of its first day of trading in the index and reduce it at the end of the day.
- Or, if you’re feeling fruity, you may look to short TSLA against the index at the end of the day and hold for a month or so.

At best these kinds of trades are marginal. You’re never going to get rich trading stuff like this.

Do your own analysis and trade small. S&P rebalancing in two tranches may change the dynamics here. If that happens then look into it and see if you can figure out a way you might be able to exploit the dynamics.

The post Tesla’s inclusion in the S&P 500 – Is there a trade? appeared first on Robot Wealth.

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