Seeking Volatility and Leverage

So Harry Long recently posted several articles, a couple of them all that have variations on a theme of a combination of leveraging SPY (aka SPXL), leveraging TLT (aka TMF), and some small exposure to the insanely volatile volatility indices (VXX, TVIX, ZIV, etc.), which can have absolutely insane drawdowns. Again, before anything else, a special thanks to Mr. Helmuth Vollmeier for his generosity in providing long-dated VXX and ZIV data, both of which will be leveraged for this post (in more ways than one).

In any case, here is the link to the two articles:

A Weird All-Long Strategy That Beats the S&P 500 Every Year
A Refined All-Long Strategy III

As usual, the challenge is that the exact ETFs in question didn’t exist prior to the financial crisis, giving a very handy justification as to why not to show the downsides of the strategy/strategies. From a conceptual standpoint, it’s quite trivial to realize that upon reading the articles, that when a large chunk of the portfolio consists of a leveraged SPY exposure, one is obviously going to look like a genius outperforming the SPY itself in a bull run. The question, obviously, is what happens when the market doesn’t support the strategy. If offered a 50% coin flip, with the outcome of heads winning a million dollars and being told nothing else, the obvious question to ask would be: “and what happens on tails?”

This post aims to address this for three separate configurations of the strategy.

First off, in order to create a believable backtest, the goal is to first create substitutes to the short-dated newfangled ETFs (SPXL and TMF), which will be done very simply: leverage the adjusted returns of SPY and TLT, respectively (I had to use adjusted due to the split in SPXL–normally I don’t like using adjusted data for anything, but splits sort of necessitate this evil).

Here we go:

SPXL vs. SPY:

require(quantmod)
require(PerformanceAnalytics)
require(downloader)

getSymbols("SPXL", from="1990-01-01")
spxlRets <- Return.calculate(Ad(SPXL)) #have to use adjusted due to split 
getSymbols("SPY", from="1990-01-01")
SPYrets <- Return.calculate(Ad(SPY))
spxl3SPY <- merge(spxlRets, 3*SPYrets, join='inner')
charts.PerformanceSummary(spxl3SPY)

So, the adjusted data in use for this simulation will slightly overshoot in regards to the absolute returns. That stated, it isn’t so much the returns we care about in this post (we know they’re terrific when times are good), but the drawdowns. The drawdowns are basically on top of one another, which is good.

Let’s repeat this with TMF and TLT:

getSymbols("TMF", from="1990-01-01")
TMFrets <- Return.calculate(Ad(TMF))
getSymbols("TLT", from="1990-01-01")
TLTrets <- Return.calculate(Ad(TLT))
tmf3TLT <- merge(TMFrets, 3*TLTrets, join='inner')
charts.PerformanceSummary(tmf3TLT)

The result:

> Return.annualized(tmf3TLT[,2]-tmf3TLT[,1])
                  TLT.Adjusted
Annualized Return   0.03123479

A bit more irritating, as there’s clearly a bit of discrepancy to the tune of approximately 3.1% a year in terms of annualized returns in favor of the leveraged TLT vs. the actual TMF (so if you can borrow for less than 3% a year, this may be a good strategy for you–though I’m completely in the dark about why this sort of mechanic exists–is it impossible to actually short TMF, or buy TLT on margin? If someone is more intimately familiar with this trade, let me know), so, I’m going to make like an engineer and apply a little patch to remove the bias–subtract the daily returns of the discrepancy from the leveraged adjusted TLT.

discrepancy <- as.numeric(Return.annualized(tmf3TLT[,2]-tmf3TLT[,1]))
tmf3TLT[,2] <- tmf3TLT[,2] - ((1+discrepancy)^(1/252)-1)

charts.PerformanceSummary(tmf3TLT)

Much better. Let’s save those modified TLT returns (our synthetic TMF):

modifiedTLT <- 3*TLTrets - ((1+discrepancy)^(1/252)-1)

With VXX, luckily, we simply need to compare Mr. Vollmeier’s data to Yahoo’s return data so that we can verify if two separate return streams check out.

#get long VXX -- thank you so much, Mr. Helmuth Vollmeier
download("https://dl.dropboxusercontent.com/s/950x55x7jtm9x2q/VXXlong.TXT", 
         destfile="longVXX.txt") #requires downloader package
VXXlong <- read.csv("longVXX.txt", stringsAsFactors=FALSE)
VXXlong <- xts(VXXlong[,2:5], order.by=as.Date(VXXlong$Date))
VXXrets <- Return.calculate(Cl(VXXlong)) #long data only has close

getSymbols("VXX", from="1990-01-01")
vxxYhooRets <- Return.calculate(Ad(VXX))
vxx2source <- merge(VXXrets, vxxYhooRets, join='inner')
charts.PerformanceSummary(vxx2source) #identical

And the result:

No discrepancies here whatsoever. So once again, I am very fortunate to have experienced readers commenting on this blog.

So, with this in mind, let’s attempt to recreate the equity curve of the first strategy, which consists of 50% SPXL, 45% TMF, and 5% VXX.

rSPY_TLT_VXX <- cbind(3*SPYrets, modifiedTLT, VXXrets)
rSPY_TLT_VXX <- rSPY_TLT_VXX[!is.na(rSPY_TLT_VXX[,3]),]
colnames(rSPY_TLT_VXX) <- c("SPY", "TLT", "VXX")

strat <- Return.rebalancing(R = rSPY_TLT_VXX, weights = c(.5, .45, .05), 
                            rebalance_on = "years", geometric=TRUE)
stratAndSPY <- merge(strat, SPYrets, join='inner')
charts.PerformanceSummary(stratAndSPY["2009-04-16::"])

About there.

One other note, on a purely mechanical issue: when using the

geometric = TRUE

argument with R, when creating synthetic leverage, you cannot create it in the actual

weights

argument, or it will leverage your capital at every rebalancing period, giving you obviously incorrect results. Furthermore, these results were achieved using geometric = TRUE in two places: one in the Return.rebalancing argument (which implies reinvesting the capital), and then once again when calling the PerformanceAnalytics functions. Essentially, the implication of this is reinvesting all gains at the rebalancing period, and not touching any position no matter what. Used inappropriately, this will create results that border on the optimistic.

Now that we’ve replicated the general shape and pattern of the original equity curve, let’s look at this strategy on a whole.

charts.PerformanceSummary(stratAndSPY)

If you just look at the top chart, it looks pretty amazing, doesn’t it? Now look at the bottom chart. Not only is there a massive drawdown, but there’s a massive spike up, and then *another* massive, larger drawdown. Imagine what would have happened to someone who didn’t follow this strategy to the letter. Get out at the very worst moment, get back in after a run-up, and then get hit *again*.

Here are the usual statistics I use:

> Return.annualized(stratAndSPY)
                  portfolio.returns SPY.Adjusted
Annualized Return         0.2305339   0.07937642
> maxDrawdown(stratAndSPY)
               portfolio.returns SPY.Adjusted
Worst Drawdown         0.4901882    0.5518672
> SharpeRatio.annualized(stratAndSPY)
                                portfolio.returns SPY.Adjusted
Annualized Sharpe Ratio (Rf=0%)         0.9487574    0.3981902

An annualized Sharpe just shy of 1, using adjusted data, with a CAGR/max drawdown ratio of less than one half, and a max drawdown far beyond the levels of acceptable (even 20% may be too much for some people, though I’d argue it’s acceptable over a long enough time frame provided it’s part of a diversified portfolio of other such uncorrelated strategies).

Now, the claim is that this strategy consistently beats the S&P 500 year after year? That can also be tested.

diff <- stratAndSPY[,1] - stratAndSPY[,2]
diffAndModTLT <- cbind(diff, modifiedTLT)
charts.PerformanceSummary(diffAndModTLT)

Essentially, I shorted the SPY against the strategy (which would simply mean still long the SPY, except at 50% instead of 150%), and this is the result, in comparison to the 3x leveraged TLT (and cut down by the original discrepancy on a daily level)

So even after shorting the SPY and its massive drawdown away, one is still left with what amounts to a diluted TMF position, which has its own issues. Here are the three statistics, once again:

> Return.annualized(diffAndModTLT)
                  portfolio.returns TLT.Adjusted
Annualized Return         0.1181923    0.1356003
> maxDrawdown(diffAndModTLT)
               portfolio.returns TLT.Adjusted
Worst Drawdown         0.3930016    0.6348332
> SharpeRatio.annualized(diffAndModTLT)
                                portfolio.returns TLT.Adjusted
Annualized Sharpe Ratio (Rf=0%)         0.4889822    0.3278975

In short, for a strategy that markets itself on beating the SPY, shorting the SPY against it costs more in upside than is gained on the downside. Generally, anytime I see an article claiming “this strategy does really well against benchmark XYZ”, my immediate intuition is: “so what does the equity curve look like when you short your benchmark against your strategy?” If the performance deteriorates, that once again means some tough questions need asking. That stated, the original strategy handily trounced the SPY benchmark, and the difference trounced the leveraged TLT. Just that my own personal benchmark is an annualized return over max drawdown of 1 or more (meaning that even the worst streak can be made up for within a year’s time–or, more practically, that generally, you don’t go a year without getting paid).

Let’s move on to the second strategy. In this instance, it’s highly similar–50% SPXL (3x SPY), 40% TMF (3x TLT), and 10% TVIX (2x VXX). Again, let’s compare synthetic to actual.

getSymbols("TVIX", from="1990-01-01")
TVIXrets <- Return.calculate(Ad(TVIX))
vxxTvix <- merge(2*VXXrets, TVIXrets, join='inner')
charts.PerformanceSummary(vxxTvix) #about identical

We’re in luck. This chart is about identical, so no tricks necessary.

The other two instruments are identical, so we can move straight to the strategy.

First, let’s replicate an equity curve:

rSPY_TLT_VXX2 <- cbind(3*SPYrets, modifiedTLT,  2*VXXrets)
rSPY_TLT_VXX2 <- rSPY_TLT_VXX2[!is.na(rSPY_TLT_VXX2[,3]),]

stratTwo <- Return.rebalancing(R=rSPY_TLT_VXX, weights = c(.5, .4, .1), rebalance_on="years", geometric=TRUE)
stratTwoAndSPY <- merge(stratTwo, SPYrets, join='inner')
charts.PerformanceSummary(stratTwoAndSPY["2010-11-30::"], geometric=TRUE)

General shape and pattern of the strategy’s equity curve achieved. What does it look like since the inception of the original VIX futures?

charts.PerformanceSummary(stratTwoAndSPY)

Very similar to the one before. Let’s look at them side by side.

bothStrats <- merge(strat, stratTwo, join='inner')
colnames(bothStrats) <- c("strategy one", "strategy two")
charts.PerformanceSummary(bothStrats)

First of all, let’s do a side by side comparison of the three statistics:

> Return.annualized(bothStrats)
                  strategy one strategy two
Annualized Return    0.2305339    0.2038783
> maxDrawdown(bothStrats)
               strategy one strategy two
Worst Drawdown    0.4901882    0.4721624
> SharpeRatio.annualized(bothStrats)
                                strategy one strategy two
Annualized Sharpe Ratio (Rf=0%)    0.9487574    0.9075242

The second strategy seems to be strictly worse than the first. If we’d short the second against the first, essentially, it’d mean we have a 15% exposure to TLT, and a -15% exposure to VXX. For a fun tangent, what does such a strategy’s equity curve look like?

stratDiff <- bothStrats[,1] - bothStrats[,2]
charts.PerformanceSummary(stratDiff)

With the following statistics:

> Return.annualized(stratDiff)
                  strategy one
Annualized Return   0.02606221
> maxDrawdown(stratDiff)
[1] 0.1254502
> SharpeRatio.annualized(stratDiff)
                                strategy one
Annualized Sharpe Ratio (Rf=0%)    0.8544455

Basically, a 1 to 5 annualized return to max drawdown ratio. In short, this may be how a lot of mediocre managers go out of business–see an idea that looks amazing, leverage it up, then have one short period of severe underperformance, where everything goes wrong for a small amount of time (EG equity market-neutral quant meltdown of August 2007, flash crash, etc.), and then a whole fund keels over. In fact, these spikes of underperformance are the absolute worst type of phenomena that can happen to many systematic strategies, since they trigger the risk-exit mechanisms, and then recover right before the strategy can make it back in.

Finally, we have our third strategy, which introduces one last instrument–ZIV. Here’s the specification for that strategy:

30% SPXL
30% ZIV
30% TMF
10% TVIX

Again, let’s go through the process and get our replicated equity curve.

download("https://www.dropbox.com/s/jk3ortdyru4sg4n/ZIVlong.TXT", destfile="longZIV.txt")
ZIVlong <- read.csv("longZIV.txt", stringsAsFactors=FALSE)
ZIVlong <- xts(ZIVlong[,2:5], order.by=as.Date(ZIVlong$Date))
ZIVrets <- Return.calculate(Cl(ZIVlong))

strat3components <- cbind(3*SPYrets, ZIVrets, modifiedTLT, 2*VXXrets)
strat3components <- strat3components[!is.na(strat3components[,4]),]
stratThree <- Return.rebalancing(strat3components, weights=c(.3, .3, .3, .1), rebalance_on="years", geometric=TRUE)
stratThreeAndSPY <- merge(stratThree, SPYrets, join='inner')
chart.TimeSeries(log(cumprod(1+stratThreeAndSPY["2010-11-30::"])))

With the resulting equity curve replication:

And again, the full-backtest equity curve:

charts.PerformanceSummary(stratThreeAndSPY)

To put it together, let’s combine all three strategies, and the SPY.

threeStrats <- merge(bothStrats, stratThree, join='inner')
threeStratsSPY <- merge(threeStrats, SPYrets, join='inner')
colnames(threeStratsSPY)[3] <- "strategy three"
charts.PerformanceSummary(threeStratsSPY)

stats <- data.frame(cbind(t(Return.annualized(threeStratsSPY))*100, 
               t(maxDrawdown(threeStratsSPY))*100, 
               t(SharpeRatio.annualized(threeStratsSPY))))
stats$returnToDrawdown <- stats[,1]/stats[,2]

The resultant equity curve:

The resultant statistics:

> stats
               Annualized.Return Worst.Drawdown Annualized.Sharpe.Ratio..Rf.0.. returnToDrawdown
strategy.one           23.053387       49.01882                       0.9487574        0.4702967
strategy.two           20.387835       47.21624                       0.9075242        0.4317970
strategy three         15.812291       39.31843                       0.8019835        0.4021597
SPY.Adjusted            7.937642       55.18672                       0.3981902        0.1438325

In short, all of them share the same sort of profile–very strong annualized returns, even scarier drawdowns, Sharpe ratios close to 1 (albeit using adjusted data), and return to drawdown ratios slightly less than .5 (also scary). Are these complete strategies on their own? No. Do they beat the S&P 500? Yes. Does it make sense that they beat the S&P 500? Considering that two of these configurations have a greater than 100% market exposure, and the direction of the equity markets tends to be up over time (at least over the period during which the VIX futures traded), then this absolutely makes sense. Should one short the S&P against these strategies? I wouldn’t say so.

One last thing to note–the period over which these strategies were tested (inception of VIX futures) had no stagflation, and the Fed’s QE may be partially (or a great deal) responsible for the rise in the equity markets since the crisis. If the market declines as a result of the fed raising rates (which it inevitably will have to at some point), these strategies might be seriously hurt, so I’d certainly advise a great deal of caution, even going forward.

In any case, for better or for worse, here are a few strategies from SeekingAlpha, replicated to as far as synthetic data is available.

Thanks for reading.