Principal Component Momentum?

This post will investigate using Principal Components as part of a momentum strategy.

Recently, I ran across a post from David Varadi that I thought I’d further investigate and translate into code I can explicitly display (as David Varadi doesn’t). Of course, as David Varadi is a quantitative research director with whom I’ve done good work with in the past, I find that trying to investigate his ideas is worth the time spent.

So, here’s the basic idea: in an allegedly balanced universe, containing both aggressive (e.g. equity asset class ETFs) assets and defensive assets (e.g. fixed income asset class ETFs), that principal component analysis, a cornerstone in machine learning, should have some effectiveness at creating an effective portfolio.

I decided to put that idea to the test with the following algorithm:

Using the same assets that David Varadi does, I first use a rolling window (between 6-18 months) to create principal components. Making sure that the SPY half of the loadings is always positive (that is, if the loading for SPY is negative, multiply the first PC by -1, as that’s the PC we use), and then create two portfolios–one that’s comprised of the normalized positive weights of the first PC, and one that’s comprised of the negative half.

Next, every month, I use some momentum lookback period (1, 3, 6, 10, and 12 months), and invest in the portfolio that performed best over that period for the next month, and repeat.

Here’s the source code to do that: (and for those who have difficulty following, I highly recommend James Picerno’s Quantitative Investment Portfolio Analytics in R book.

require(PerformanceAnalytics)
require(quantmod)
require(stats)
require(xts)

symbols <- c("SPY", "EFA", "EEM", "DBC", "HYG", "GLD", "IEF", "TLT")  

# get free data from yahoo
rets <- list()
getSymbols(symbols, src = 'yahoo', from = '1990-12-31')
for(i in 1:length(symbols)) {
  returns <- Return.calculate(Ad(get(symbols[i])))
  colnames(returns) <- symbols[i]
  rets[[i]] <- returns
}
rets <- na.omit(do.call(cbind, rets))

# 12 month PC rolling PC window, 3 month momentum window
pcPlusMinus <- function(rets, pcWindow = 12, momWindow = 3) {
  ep <- endpoints(rets)

  wtsPc1Plus <- NULL
  wtsPc1Minus <- NULL
  
  for(i in 1:(length(ep)-pcWindow)) {
    # get subset of returns
    returnSubset <- rets[(ep[i]+1):(ep[i+pcWindow])]
    
    # perform PCA, get first PC (I.E. pc1)
    pcs <- prcomp(returnSubset) 
    firstPc <- pcs[[2]][,1]
    
    # make sure SPY always has a positive loading
    # otherwise, SPY and related assets may have negative loadings sometimes
    # positive loadings other times, and creates chaotic return series
    
    if(firstPc['SPY'] < 0) {
      firstPc <- firstPc * -1
    }
    
    # create vector for negative values of pc1
    wtsMinus <- firstPc * -1
    wtsMinus[wtsMinus < 0] <- 0
    wtsMinus <- wtsMinus/(sum(wtsMinus)+1e-16) # in case zero weights
    wtsMinus <- xts(t(wtsMinus), order.by=last(index(returnSubset)))
    wtsPc1Minus[[i]] <- wtsMinus
    
    # create weight vector for positive values of pc1
    wtsPlus <- firstPc
    wtsPlus[wtsPlus < 0] <- 0
    wtsPlus <- wtsPlus/(sum(wtsPlus)+1e-16)
    wtsPlus <- xts(t(wtsPlus), order.by=last(index(returnSubset)))
    wtsPc1Plus[[i]] <- wtsPlus
  }
  
  # combine positive and negative PC1 weights
  wtsPc1Minus <- do.call(rbind, wtsPc1Minus)
  wtsPc1Plus <- do.call(rbind, wtsPc1Plus)
  
  # get return of PC portfolios
  pc1MinusRets <- Return.portfolio(R = rets, weights = wtsPc1Minus)
  pc1PlusRets <- Return.portfolio(R = rets, weights = wtsPc1Plus)
  
  # combine them
  combine <-na.omit(cbind(pc1PlusRets, pc1MinusRets))
  colnames(combine) <- c("PCplus", "PCminus")
  
  momEp <- endpoints(combine)
  momWts <- NULL
  for(i in 1:(length(momEp)-momWindow)){
    momSubset <- combine[(momEp[i]+1):(momEp[i+momWindow])]
    momentums <- Return.cumulative(momSubset)
    momWts[[i]] <- xts(momentums==max(momentums), order.by=last(index(momSubset)))
  }
  momWts <- do.call(rbind, momWts)
  
  out <- Return.portfolio(R = combine, weights = momWts)
  colnames(out) <- paste("PCwin", pcWindow, "MomWin", momWindow, sep="_")
  return(list(out, wtsPc1Minus, wtsPc1Plus, combine))
}


pcWindows <- c(6, 9, 12, 15, 18)
momWindows <- c(1, 3, 6, 10, 12)

permutes <- expand.grid(pcWindows, momWindows)

stratStats <- function(rets) {
  stats <- rbind(table.AnnualizedReturns(rets), maxDrawdown(rets))
  stats[5,] <- stats[1,]/stats[4,]
  stats[6,] <- stats[1,]/UlcerIndex(rets)
  rownames(stats)[4] <- "Worst Drawdown"
  rownames(stats)[5] <- "Calmar Ratio"
  rownames(stats)[6] <- "Ulcer Performance Index"
  return(stats)
}

results <- NULL
for(i in 1:nrow(permutes)) {
  tmp <- pcPlusMinus(rets = rets, pcWindow = permutes$Var1[i], momWindow = permutes$Var2[i])
  results[[i]] <- tmp[[1]]
}
results <- do.call(cbind, results)
stats <- stratStats(results)

After a cursory look at the results, it seems the performance is fairly miserable with my implementation, even by the standards of tactical asset allocation models (the good ones have a Calmar and Sharpe Ratio above 1)

Here are histograms of the Calmar and Sharpe ratios.

PCCalmarHistogram
PCSharpeHistogram

These values are generally too low for my liking. Here’s a screenshot of the table of all 25 results.

PCresultsTable.PNG

While my strategy of choosing which portfolio to hold is different from David Varadi’s (momentum instead of whether or not the aggressive portfolio is above its 200-day moving average), there are numerous studies that show these two methods are closely related, yet the results feel starkly different (and worse) compared to his site.

I’d certainly be willing to entertain suggestions as to how to improve the process, which will hopefully create some more meaningful results. I also know that AllocateSmartly expressed interest in implementing something along these lines for their estimable library of TAA strategies, so I thought I’d try to do it and see what results I’d find, which in this case, aren’t too promising.

Thanks for reading.

NOTE: I am networking, and actively seeking a position related to my skill set in either Philadelphia, New York City, or remotely. If you know of a position which may benefit from my skill set, feel free to let me know. You can reach me on my LinkedIn profile here, or email me.

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A Review of James Picerno’s Quantitative Investment Portfolio Analytics in R

This is a review of James Picerno’s Quantitative Investment Portfolio Analytics in R. Overall, it’s about as fantastic a book as you can get on portfolio optimization until you start getting into corner cases stemming from large amounts of assets.

Here’s a quick summary of what the book covers:

1) How to install R.

2) How to create some rudimentary backtests.

3) Momentum.

4) Mean-Variance Optimization.

5) Factor Analysis

6) Bootstrapping/Monte-Carlo simulations.

7) Modeling Tail Risk

8) Risk Parity/Vol Targeting

9) Index replication

10) Estimating impacts of shocks

11) Plotting in ggplot

12) Downloading/saving data.

All in all, the book teaches the reader many fantastic techniques to get started doing some basic portfolio management using asset-class ETFs, and under the assumption of ideal data–that is, that there are few assets with concurrent starting times, that the number of assets is much smaller than the number of observations (I.E. 10 asset class ETFs, 90 day lookback windows, for instance), and other attributes taken for granted to illustrate concepts. I myself have used these concepts time and again (and, in fact, covered some of these topics on this blog, such as volatility targeting, momentum, and mean-variance), but in some of the work projects I’ve done, the trouble begins when the number of assets grows larger than the number of observations, or when assets move in or out of the investable universe (EG a new company has an IPO or a company goes bankrupt/merges/etc.). It also does not go into the PortfolioAnalytics package, developed by Ross Bennett and Brian Peterson. Having recently started to use this package for a real-world problem, it produces some very interesting results and its potential is immense, with the large caveat that you need an immense amount of computing power to generate lots of results for large-scale problems, which renders it impractical for many individual users. A quadratic optimization on a backtest with around 2400 periods and around 500 assets per rebalancing period (days) took about eight hours on a cloud server (when done sequentially to preserve full path dependency).

However, aside from delving into some somewhat-edge-case appears-more-in-the-professional-world topics, this book is extremely comprehensive. Simply, as far as managing a portfolio of asset-class ETFs (essentially, what the inimitable Adam Butler and crew from ReSolve Asset Management talk about, along with Walter’s fantastic site, AllocateSmartly), this book will impart a lot of knowledge that goes into doing those things. While it won’t make you as comfortable as say, an experienced professional like myself is at writing and analyzing portfolio optimization backtests, it will allow you to do a great deal of your own analysis, and certainly a lot more than anyone using Excel.

While I won’t rehash what the book covers in this post, what I will say is that it does cover some of the material I’ve posted in years past. And furthermore, rather than spending half the book about topics such as motivations, behavioral biases, and so on, this book goes right into the content that readers should know in order to execute the tasks they desire. Furthermore, the content is presented in a very coherent, English-and-code, matter-of-fact way, as opposed to a bunch of abstract mathematical derivations that treats practical implementation as an afterthought. Essentially, when one buys a cookbook, they don’t get it to read half of it for motivations as to why they should bake their own cake, but on how to do it. And as far as density of how-to, this book delivers in a way I think that other authors should strive to emulate.

Furthermore, I think that this book should be required reading for any analyst wanting to work in the field. It’s a very digestible “here’s how you do X” type of book. I.E. “here’s a data set, write a backtest based on these momentum rules, use an inverse-variance weighting scheme, do a Fama-French factor analysis on it”.

In any case, in my opinion, for anyone doing any sort of tactical asset allocation analysis in R, get this book now. For anyone doing any sort of tactical asset allocation analysis in spreadsheets, buy this book sooner than now, and then see the previous sentence. In any case, I’ll certainly be keeping this book on my shelf and referencing it if need be.

Thanks for reading.

Note: I am currently contracting but am currently on the lookout for full-time positions in New York City. If you know of a position which may benefit from my skills, please let me know. My LinkedIn profile can be found here.

A Different Way To Think About Drawdown — Geometric Calmar Ratio

This post will discuss the idea of the geometric Calmar ratio — a way to modify the Calmar ratio to account for compounding returns.

So, one thing that recently had me sort of annoyed in terms of my interpretation of the Calmar ratio is this: essentially, the way I interpret it is that it’s a back of the envelope measure of how many years it takes you to recover from the worst loss. That is, if a strategy makes 10% a year (on average), and has a loss of 10%, well, intuition serves that from that point on, on average, it’ll take about a year to make up that loss–that is, a Calmar ratio of 1. Put another way, it means that on average, a strategy will make money at the end of 252 trading days.

But, that isn’t really the case in all circumstances. If an investment manager is looking to create a small, meager return for their clients, and is looking to make somewhere between 5-10%, then sure, the Calmar ratio approximation and interpretation makes sense in that context. Or, it makes sense in the context of “every year, we withdraw all profits and deposit to make up for any losses”. But in the context of a hedge fund trying to create large, market-beating returns for its investors, those hedge funds can have fairly substantial drawdowns.

Citadel–one of the gold standards of the hedge fund industry, had a drawdown of more than 50% during the financial crisis, and of course, there was https://www.reuters.com/article/us-usa-fund-volatility/exclusive-ljm-partners-shutting-its-doors-after-vol-mageddon-losses-in-u-s-stocks-idUSKCN1GC29Hat least one fund that blew up in the storm-in-a-teacup volatility spike on Feb. 5 (in other words, if those guys were professionals, what does that make me? Or if I’m an amateur, what does that make them?).

In any case, in order to recover from such losses, it’s clear that a strategy would need to make back a lot more than what it lost. Lose 25%? 33% is the high water mark. Lose 33%? 50% to get back to even. Lose 50%? 100%. Beyond that? You get the idea.

In order to capture this dynamic, we should write a new Calmar ratio to express this idea.

So here’s a function to compute the geometric calmar ratio:

require(PerformanceAnalytics)

geomCalmar <- function(r) {
  rAnn <- Return.annualized(r)
  maxDD <- maxDrawdown(r)
  toHighwater <- 1/(1-maxDD) - 1
  out <- rAnn/toHighwater
  return(out)
}

So, let's compare how some symbols stack up. We'll take a high-volatility name (AMZN), the good old S&P 500 (SPY), and a very low volatility instrument (SHY).

getSymbols(c('AMZN', 'SPY', 'SHY'), from = '1990-01-01')
rets <- na.omit(cbind(Return.calculate(Ad(AMZN)), Return.calculate(Ad(SPY)), Return.calculate(Ad(SHY))))
compare <- rbind(table.AnnualizedReturns(rets), maxDrawdown(rets), CalmarRatio(rets), geomCalmar(rets))
rownames(compare)[6] <- "Geometric Calmar"
compare

The returns start from July 31, 2002. Here are the statistics.

                           AMZN.Adjusted SPY.Adjusted SHY.Adjusted
Annualized Return             0.3450000   0.09110000   0.01940000
Annualized Std Dev            0.4046000   0.18630000   0.01420000
Annualized Sharpe (Rf=0%)     0.8528000   0.48860000   1.36040000
Worst Drawdown                0.6525491   0.55189461   0.02231459
Calmar Ratio                  0.5287649   0.16498652   0.86861760
Geometric Calmar              0.1837198   0.07393135   0.84923475

For my own proprietary volatility trading strategy, a strategy which has a Calmar above 2 (interpretation: finger in the air means that you make a new equity high every six months in the worst case scenario), here are the statistics:

> CalmarRatio(stratRetsAggressive[[2]]['2011::'])
                Close
Calmar Ratio 3.448497
> geomCalmar(stratRetsAggressive[[2]]['2011::'])
                     Close
Annualized Return 2.588094

Essentially, because of the nature of losses compounding, the geometric Calmar ratio will always be lower than the standard Calmar ratio, which is to be expected when dealing with the geometric nature of compounding returns.

Essentially, I hope that this gives individuals some thought about re-evaluating the Calmar Ratio.

Thanks for reading.

NOTES: registration for R/Finance 2018 is open. As usual, I’ll be giving a lightning talk, this time on volatility trading.

I am currently contracting and seek network opportunities, along with information about prospective full time roles starting in July. Those interested in my skill set can feel free to reach out to me on LinkedIn here.

The New Short Volatility Instrument Landscape

This post will discuss the consequences of ProShares’ decision to change the investment objective of SVXY, and possible alternatives that various investors can use to try and create an identical exposure if their strategy calls for such an instrument.

So, to begin with, Proshares recently decided to make SVXY http://www.proshares.com/news/proshare_capital_management_llc_plans_to_reduce_target_exposure_on_two_etfs.htmlhalf the ETF it used to be, and overnight, no less. While I myself do not trade options, following some traders on twitter, a few of them got badly burned. In any case, for the purpose of taking near-curve short-vol positions, this renders SVXY far less attractive as far as my proprietary trading strategy goes, as well as others like it.

Essentially, while this turns SVXY into a “safer” buy and hold instrument, in my opinion, it turns it into a worse instrument. Considering that SVXY’s annual fee is 139 bps, traders now pay Proshares 139 bps just to keep half their capital in cash–capital which could have been invested in other strategies, or simply manually kept on the sidelines. Essentially, this is an attempt on Proshares’ part to idiot-proof a product that should not be used by “idiots” in the first place. However, in the battle between entities to idiot-proof a product, and the universe to create a better idiot, it’s a safe bet to bet on the universe creating a better idiot.

So what does this mean going forward in terms of alternatives to replace XIV and SVXY? Well, I’m at a bit of a loss. While my institutional client (whose crowdfund I am a part of) can short VXX, (and rebalance daily) for other individuals out there (such as myself in my own PA), they may not be able to short shares of VXX, and it may become hard to borrow (although a 50% position short TVIX, or 66% in short UVXY will also obtain the same exposure, again, rebalanced daily, but let’s assume similar constraints), and the borrowing cost may increase. A couple of alternatives are XIVH and the new VMIN, which hasn’t specified its exact new formulation, but to my understanding after a long conversation with Scott Acheychek of REXshares
, a formulation using the term structure futures (that currently are unavailable from the CBOE, but since the implied volatility term structure is at dangerous levels at this point, it’s not problematic yet) that is similar to ZIV except using the 2nd through 6th month instead of 4th through 7th is somewhere in the ballpark.

In any case, let’s look at some alternatives.

As one of my strategy subscribers was kind enough to send me some synthetic XIVH history, I’ll use that (no replication available unless said subscriber wants to post a link for readers to download. If not, I recommend reaching out to Vance Harwood for his replication).

In any case, here’s a fantastic post by Vance Harwood on how XIVH works. I won’t attempt to paraphrase that post, because I think Vance’s explanations of the products in the vol space are in a class of their own, and someone looking for secondhand information would be doing themselves a disservice not to read Vance’s work with regards to learning about the various options available in the vol space.

In any case, let’s compare.

For the record, here’s an updated function to compute the “back of the envelope new VMIN”, which works exactly like ZIV does, except with dr/dt on month 2, and 1-dr/dt on month 6, and a 25% weighting between 2+6, then 3, 4, 5 constant.

syntheticXIV <- function(termStructure, expiryStructure, contractQty = 1) {
  
  # find expiry days
  zeroDays <- which(expiryStructure$C1 == 0)
  
  # dt = days in contract period, set after expiry day of previous contract
  dt  nrow(expiryStructure)] <- nrow(expiryStructure)
  dtXts <- expiryStructure$C1[dt,]
  
  # create dr (days remaining) and dt structure
  drDt <- cbind(expiryStructure[,1], dtXts)
  colnames(drDt) <- c("dr", "dt")
  drDt$dt <- na.locf(drDt$dt)
  
  # add one more to dt to account for zero day
  drDt$dt <- drDt$dt + 1
  drDt <- na.omit(drDt)
  
  # assign weights for front month and back month based on dr and dt
  wtC1 <- drDt$dr/drDt$dt
  wtC2 <- 1-wtC1
  
  # realize returns with old weights, "instantaneously" shift to new weights after realizing returns at settle
  # assumptions are a bit optimistic, I think
  valToday <- termStructure[,1] * lag(wtC1) + termStructure[,2] * lag(wtC2)
  valYesterday <- lag(termStructure[,1]) * lag(wtC1) + lag(termStructure[,2]) * lag(wtC2)
  syntheticRets <- (valToday/valYesterday) - 1
  
  # on the day after roll, C2 becomes C1, so reflect that in returns
  zeroes <- which(drDt$dr == 0) + 1 
  zeroRets <- termStructure[,1]/lag(termStructure[,2]) - 1
  
  # override usual returns with returns that reflect back month becoming front month after roll day
  syntheticRets[index(syntheticRets)[zeroes]] <- zeroRets[index(syntheticRets)[zeroes]]
  syntheticRets <- na.omit(syntheticRets)
  
  # vxxRets are syntheticRets
  vxxRets <- syntheticRets
  
  # repeat same process for vxz -- except it's dr/dt * 4th contract + 5th + 6th + 1-dr/dt * 7th contract
  vxzToday <- termStructure[,4] * lag(wtC1) + termStructure[,5] + termStructure[,6] + termStructure[,7] * lag(wtC2)
  vxzYesterday <- lag(termStructure[,4]) * lag(wtC1) + lag(termStructure[, 5]) + lag(termStructure[,6]) + lag(termStructure[,7]) * lag(wtC2)
  syntheticVxz <- (vxzToday/vxzYesterday) - 1
  
  # on zero expiries, next day will be equal (4+5+6)/lag(5+6+7) - 1
  zeroVxz <- (termStructure[,4] + termStructure[,5] + termStructure[,6])/
    lag(termStructure[,5] + termStructure[,6] + termStructure[,7]) - 1
  syntheticVxz[index(syntheticVxz)[zeroes]] <- zeroVxz[index(syntheticVxz)[zeroes]]
  syntheticVxz <- na.omit(syntheticVxz)
  
  vxzRets <- syntheticVxz
  
  # first attempt at a new VMIN/VMAX, with the 2-6 paradigm -- not for use with actual futures, but to guide ETP analysis
  vmaxToday <- termStructure[,2] * lag(wtC1) + termStructure[,3] + termStructure[,4] + 
    termStructure[,5] + termStructure[,6] * lag(wtC2)
  vmaxYesterday <- lag(termStructure[,2]) * lag(wtC1) + lag(termStructure[,3]) + lag(termStructure[,4]) + 
    lag(termStructure[,5]) + lag(termStructure[,6]) * lag(wtC2)
  syntheticVmax <- (vmaxToday/vmaxYesterday) - 1
  
  zeroVmax <- (termStructure[,2] + termStructure[,3] + termStructure[,4] + termStructure[,5])/
    lag(termStructure[,3] + termStructure[,4] + termStructure[,5] + termStructure[,6]) - 1
  syntheticVmax[index(syntheticVmax)[zeroes]] <- zeroVmax[index(syntheticVmax)[zeroes]]
  
  vmaxRets <- syntheticVmax
  
  
  # write out weights for actual execution
  if(last(drDt$dr!=0)) {
    print(paste("Previous front-month weight was", round(last(drDt$dr)/last(drDt$dt), 5)))
    print(paste("Front-month weight at settle today will be", round((last(drDt$dr)-1)/last(drDt$dt), 5)))
    if((last(drDt$dr)-1)/last(drDt$dt)==0){
      print("Front month will be zero at end of day. Second month becomes front month.")
    }
  } else {
    print("Previous front-month weight was zero. Second month became front month.")
    print(paste("New front month weights at settle will be", round(last(expiryStructure[,2]-1)/last(expiryStructure[,2]), 5)))
  }
  
  return(list(vxxRets, vxzRets, vmaxRets))
}

Let's compare instruments now. The vixTermStructure.R file is one that I have shown before in a separate post. Furthermore, one of these files will not be accessible as it was provided to me by a subscriber, so I will leave it up to them as to whether they wish to share the file or not.

require(downloader)
require(quantmod)
require(PerformanceAnalytics)
require(TTR)
require(Quandl)
require(data.table)
source("vixTermStructure.R")
newVmin <- syntheticXIV(termStructure, expiryStructure)[[3]]*-1

# using xivh data from a subscriber, not public
xivh <- read.csv("xivh.csv", stringsAsFactors = FALSE)
xivh <- xts(xivh[,2], order.by=as.Date(xivh[,1], format = '%m/%d/%Y'))


download("https://dl.dropboxusercontent.com/s/950x55x7jtm9x2q/VXXlong.TXT", 
         destfile="longVXX.txt") #requires downloader package

vxx <- xts(read.zoo("longVXX.txt", format="%Y-%m-%d", sep=",", header=TRUE))
vxx2 <- Quandl("EOD/VXX", start_date="2018-01-01", type = 'xts')
vxx2Rets <- Return.calculate(vxx2$Adj_Close)
vxxRets <- Return.calculate(Cl(vxx))
vxxRets['2014-08-05'] <- .071 # not sure why Helmuth Vollmeier's VXX data has a 332% day here
vxxRets <- rbind(vxxRets, vxx2Rets['2018-02-08::'])

shortVxx <- (vxxRets * -1) - .1/252 # short, cover, rebalance re-short daily, 10% annualized cost of borrow
newSvxy <- shortVxx * .5

In this case, we have four instruments to test out in my proprietary strategy: short VXX (with a fairly conservative 10% cost of borrow), new VMIN, XIVH, new SVXY.

Again, this is not something that readers can replicate, but these are the results from testing when plugging in these new instruments as a replacement for XIV in my aggressive strategy:

newInstruments

And here are their performance statistics, from the following function:

stratStats <- function(rets) {
  stats <- rbind(table.AnnualizedReturns(rets), maxDrawdown(rets))
  stats[5,] <- stats[1,]/stats[4,]
  stats[6,] <- stats[1,]/UlcerIndex(rets)
  rownames(stats)[4] <- "Worst Drawdown"
  rownames(stats)[5] <- "Calmar Ratio"
  rownames(stats)[6] <- "Ulcer Performance Index"
  return(stats)
}


stratStats(compare['2011::'])
                          Short VXX 10% borrow cost      XIVH  new_VMIN   newSVXY
Annualized Return                          0.874800 0.7175000 0.6062000 0.6103000
Annualized Std Dev                         0.366000 0.3409000 0.2978000 0.2845000
Annualized Sharpe (Rf=0%)                  2.390400 2.1048000 2.0356000 2.1454000
Worst Drawdown                             0.272466 0.2935258 0.2696844 0.2460193
Calmar Ratio                               3.210676 2.4444188 2.2478124 2.4806994
Ulcer Performance Index                   10.907803 8.7305137 8.8142560 9.5887865

In other words, the short VXX (or rather, the new SVXY, leveraged twice back to its original state), using a more conservative cost of borrow for shorting than I've seen at other institutions, still delivers superior results to other instruments. Furthermore, XIVH's volume, as of today, was less than 50,000 shares at a price of $14 (so only around $700,000 in volume). The new VMIN and new SVXY lose a lot of aggregate return, though reduce a little bit of drawdown in the process. While the strategy is certainly still attractive from a risk-reward perspective ("only" 60% return per year), it is nevertheless frustrating to not be able to realize its full potential due to lack of instruments.

I personally hope that we may see a return of -1x inverse VIX products by the end of 2018 or sooner. For my own personal trading, looking at the results of this post, at a cursory first glance, my inclination seems to be that for individuals (namely, myself) interested in taking a near-curve short-vol position under the constraints of neither margin (in which case the best alternative would be to leverage the new 50% SVXY lite twice back up to its original settings) nor shorting (in which case short VXX rebalanced daily gives equivalent exposure), nor options (sell VXX calls/buy VXX puts) that XIVH is the best that can be done from a 10,000 foot view. That said, I certainly hope that XIVH will increase its volume from here on out, as it seems to be the best product to trade in order to express a near-month, short-vol bet in the volatility trading space. However, once again, I will be giving Vance Harwood's work a read-over with regards to XIVH, and I recommend any individual determined to remain in the VIX complex after Feb. 5 to do the same.

That said, XIVH does have its own quirks, as it may take a dynamic long vol position from time to time. However, because of the way my particular strategy is set up, its entries on short volatility are what I'd call careful, so as to maximize the chances of XIVH taking a short volatility position. Nevertheless, this is indeed some adverse news for me (I cannot speak for other individuals who may have different constraints with their brokerages). Nevertheless, while I cannot decide for others, I will continue to trade my strategy, as I see it as less of a good thing being better than nothing at all, and ~60% per year is still vastly better than one can achieve in almost any other market without leverage or other sophisticated execution.

In any case, that is the update after the Proshares announcement. It is a tough pill to swallow, and I hope that better options will emerge in the future for those individuals that respect the history of short vol products, think twice before entering into positions, and accept the losses that come with the territory as a result of using such products.

Thanks for reading.

NOTE: I am seeking full-time employment, long-term consulting projects, and networking in relation to my skill set. For those that are interested in my skill set, feel free to reach out and leave a note to me on my LinkedIn profile.

Creating a Table of Monthly Returns With R and a Volatility Trading Interview

This post will cover two aspects: the first will be a function to convert daily returns into a table of monthly returns, complete with drawdowns and annual returns. The second will be an interview I had with David Lincoln (now on youtube) to talk about the events of Feb. 5, 2018, and my philosophy on volatility trading.

So, to start off with, a function that I wrote that’s supposed to mimic PerforamnceAnalytics’s table.CalendarReturns is below. What table.CalendarReturns is supposed to do is to create a month X year table of monthly returns with months across and years down. However, it never seemed to give me the output I was expecting, so I went and wrote another function.

Here’s the code for the function:

require(data.table)
require(PerformanceAnalytics)
require(scales)
require(Quandl)

# helper functions
pastePerc <- function(x) {return(paste0(comma(x),"%"))}
rowGsub <- function(x) {x <- gsub("NA%", "NA", x);x}

calendarReturnTable <- function(rets, digits = 3, percent = FALSE) {
  
  # get maximum drawdown using daily returns
  dds <- apply.yearly(rets, maxDrawdown)
  
  # get monthly returns
  rets <- apply.monthly(rets, Return.cumulative)
  
  # convert to data frame with year, month, and monthly return value
  dfRets <- cbind(year(index(rets)), month(index(rets)), coredata(rets))
  
  # convert to data table and reshape into year x month table
  dfRets <- data.frame(dfRets)
  colnames(dfRets) <- c("Year", "Month", "Value")
  monthNames <- c("Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec")
  for(i in 1:length(monthNames)) {
    dfRets$Month[dfRets$Month==i] <- monthNames[i]
  }
  dfRets <- data.table(dfRets)
  dfRets <- data.table::dcast(dfRets, Year~Month)
  
  # create row names and rearrange table in month order
  dfRets <- data.frame(dfRets)
  yearNames <- dfRets$Year
  rownames(dfRets) <- yearNames; dfRets$Year <- NULL
  dfRets <- dfRets[,monthNames]
  
  # append yearly returns and drawdowns
  yearlyRets <- apply.yearly(rets, Return.cumulative)
  dfRets$Annual <- yearlyRets
  dfRets$DD <- dds
  
  # convert to percentage
  if(percent) {
    dfRets <- dfRets * 100
  }
  
  # round for formatting
  dfRets <- apply(dfRets, 2, round, digits)
   
  # paste the percentage sign
  if(percent) {
    dfRets <- apply(dfRets, 2, pastePerc)
    dfRets <- apply(dfRets, 2, rowGsub)
    dfRets <- data.frame(dfRets)
    rownames(dfRets) <- yearNames
  }
  return(dfRets)
}

Here’s how the output looks like.

spy <- Quandl("EOD/SPY", type='xts', start_date='1990-01-01')
spyRets <- Return.calculate(spy$Adj_Close)
calendarReturnTable(spyRets, percent = FALSE)
        Jan    Feb    Mar    Apr    May    Jun    Jul    Aug    Sep    Oct    Nov    Dec Annual    DD
1993  0.000  0.011  0.022 -0.026  0.027  0.004 -0.005  0.038 -0.007  0.020 -0.011  0.012  0.087 0.047
1994  0.035 -0.029 -0.042  0.011  0.016 -0.023  0.032  0.038 -0.025  0.028 -0.040  0.007  0.004 0.085
1995  0.034  0.041  0.028  0.030  0.040  0.020  0.032  0.004  0.042 -0.003  0.044  0.016  0.380 0.026
1996  0.036  0.003  0.017  0.011  0.023  0.009 -0.045  0.019  0.056  0.032  0.073 -0.024  0.225 0.076
1997  0.062  0.010 -0.044  0.063  0.063  0.041  0.079 -0.052  0.048 -0.025  0.039  0.019  0.335 0.112
1998  0.013  0.069  0.049  0.013 -0.021  0.043 -0.014 -0.141  0.064  0.081  0.056  0.065  0.287 0.190
1999  0.035 -0.032  0.042  0.038 -0.023  0.055 -0.031 -0.005 -0.022  0.064  0.017  0.057  0.204 0.117
2000 -0.050 -0.015  0.097 -0.035 -0.016  0.020 -0.016  0.065 -0.055 -0.005 -0.075 -0.005 -0.097 0.171
2001  0.044 -0.095 -0.056  0.085 -0.006 -0.024 -0.010 -0.059 -0.082  0.013  0.078  0.006 -0.118 0.288
2002 -0.010 -0.018  0.033 -0.058 -0.006 -0.074 -0.079  0.007 -0.105  0.082  0.062 -0.057 -0.216 0.330
2003 -0.025 -0.013  0.002  0.085  0.055  0.011  0.018  0.021 -0.011  0.054  0.011  0.050  0.282 0.137
2004  0.020  0.014 -0.013 -0.019  0.017  0.018 -0.032  0.002  0.010  0.013  0.045  0.030  0.107 0.075
2005 -0.022  0.021 -0.018 -0.019  0.032  0.002  0.038 -0.009  0.008 -0.024  0.044 -0.002  0.048 0.070
2006  0.024  0.006  0.017  0.013 -0.030  0.003  0.004  0.022  0.027  0.032  0.020  0.013  0.158 0.076
2007  0.015 -0.020  0.012  0.044  0.034 -0.015 -0.031  0.013  0.039  0.014 -0.039 -0.011  0.051 0.099
2008 -0.060 -0.026 -0.009  0.048  0.015 -0.084 -0.009  0.015 -0.094 -0.165 -0.070  0.010 -0.368 0.476
2009 -0.082 -0.107  0.083  0.099  0.058 -0.001  0.075  0.037  0.035 -0.019  0.062  0.019  0.264 0.271
2010 -0.036  0.031  0.061  0.015 -0.079 -0.052  0.068 -0.045  0.090  0.038  0.000  0.067  0.151 0.157
2011  0.023  0.035  0.000  0.029 -0.011 -0.017 -0.020 -0.055 -0.069  0.109 -0.004  0.010  0.019 0.186
2012  0.046  0.043  0.032 -0.007 -0.060  0.041  0.012  0.025  0.025 -0.018  0.006  0.009  0.160 0.097
2013  0.051  0.013  0.038  0.019  0.024 -0.013  0.052 -0.030  0.032  0.046  0.030  0.026  0.323 0.056
2014 -0.035  0.046  0.008  0.007  0.023  0.021 -0.013  0.039 -0.014  0.024  0.027 -0.003  0.135 0.073
2015 -0.030  0.056 -0.016  0.010  0.013 -0.020  0.023 -0.061 -0.025  0.085  0.004 -0.017  0.013 0.119
2016 -0.050 -0.001  0.067  0.004  0.017  0.003  0.036  0.001  0.000 -0.017  0.037  0.020  0.120 0.103
2017  0.018  0.039  0.001  0.010  0.014  0.006  0.021  0.003  0.020  0.024  0.031  0.012  0.217 0.026
2018  0.056 -0.031     NA     NA     NA     NA     NA     NA     NA     NA     NA     NA  0.023 0.101

And with percentage formatting:

calendarReturnTable(spyRets, percent = TRUE)
Using 'Value' as value column. Use 'value.var' to override
         Jan      Feb     Mar     Apr     May     Jun     Jul      Aug      Sep      Oct     Nov     Dec   Annual      DD
1993  0.000%   1.067%  2.241% -2.559%  2.697%  0.367% -0.486%   3.833%  -0.726%   1.973% -1.067%  1.224%   8.713%  4.674%
1994  3.488%  -2.916% -4.190%  1.121%  1.594% -2.288%  3.233%   3.812%  -2.521%   2.843% -3.982%  0.724%   0.402%  8.537%
1995  3.361%   4.081%  2.784%  2.962%  3.967%  2.021%  3.217%   0.445%   4.238%  -0.294%  4.448%  1.573%  38.046%  2.595%
1996  3.558%   0.319%  1.722%  1.087%  2.270%  0.878% -4.494%   1.926%   5.585%   3.233%  7.300% -2.381%  22.489%  7.629%
1997  6.179%   0.957% -4.414%  6.260%  6.321%  4.112%  7.926%  -5.180%   4.808%  -2.450%  3.870%  1.910%  33.478% 11.203%
1998  1.288%   6.929%  4.876%  1.279% -2.077%  4.259% -1.351% -14.118%   6.362%   8.108%  5.568%  6.541%  28.688% 19.030%
1999  3.523%  -3.207%  4.151%  3.797% -2.287%  5.538% -3.102%  -0.518%  -2.237%   6.408%  1.665%  5.709%  20.388% 11.699%
2000 -4.979%  -1.523%  9.690% -3.512% -1.572%  1.970% -1.570%   6.534%  -5.481%  -0.468% -7.465% -0.516%  -9.730% 17.120%
2001  4.446%  -9.539% -5.599%  8.544% -0.561% -2.383% -1.020%  -5.933%  -8.159%   1.302%  7.798%  0.562% -11.752% 28.808%
2002 -0.980%  -1.794%  3.324% -5.816% -0.593% -7.376% -7.882%   0.680% -10.485%   8.228%  6.168% -5.663% -21.588% 32.968%
2003 -2.459%  -1.348%  0.206%  8.461%  5.484%  1.066%  1.803%   2.063%  -1.089%   5.353%  1.092%  5.033%  28.176% 13.725%
2004  1.977%   1.357% -1.320% -1.892%  1.712%  1.849% -3.222%   0.244%   1.002%   1.288%  4.451%  3.015%  10.704%  7.526%
2005 -2.242%   2.090% -1.828% -1.874%  3.222%  0.150%  3.826%  -0.937%   0.800%  -2.365%  4.395% -0.190%   4.827%  6.956%
2006  2.401%   0.573%  1.650%  1.263% -3.012%  0.264%  0.448%   2.182%   2.699%   3.152%  1.989%  1.337%  15.847%  7.593%
2007  1.504%  -1.962%  1.160%  4.430%  3.392% -1.464% -3.131%   1.283%   3.870%   1.357% -3.873% -1.133%   5.136%  9.925%
2008 -6.046%  -2.584% -0.903%  4.766%  1.512% -8.350% -0.899%   1.545%  -9.437% -16.519% -6.961%  0.983% -36.807% 47.592%
2009 -8.211% -10.745%  8.348%  9.935%  5.845% -0.068%  7.461%   3.694%   3.545%  -1.923%  6.161%  1.907%  26.364% 27.132%
2010 -3.634%   3.119%  6.090%  1.547% -7.945% -5.175%  6.830%  -4.498%   8.955%   3.820%  0.000%  6.685%  15.057% 15.700%
2011  2.330%   3.474%  0.010%  2.896% -1.121% -1.688% -2.000%  -5.498%  -6.945%  10.915% -0.406%  1.044%   1.888% 18.609%
2012  4.637%   4.341%  3.216% -0.668% -6.006%  4.053%  1.183%   2.505%   2.535%  -1.820%  0.566%  0.900%  15.991%  9.687%
2013  5.119%   1.276%  3.798%  1.921%  2.361% -1.336%  5.168%  -2.999%   3.168%   4.631%  2.964%  2.589%  32.307%  5.552%
2014 -3.525%   4.552%  0.831%  0.695%  2.321%  2.064% -1.344%   3.946%  -1.379%   2.355%  2.747% -0.256%  13.462%  7.273%
2015 -2.963%   5.620% -1.574%  0.983%  1.286% -2.029%  2.259%  -6.095%  -2.543%   8.506%  0.366% -1.718%   1.252% 11.910%
2016 -4.979%  -0.083%  6.724%  0.394%  1.701%  0.350%  3.647%   0.120%   0.008%  -1.734%  3.684%  2.028%  12.001% 10.306%
2017  1.789%   3.929%  0.126%  0.993%  1.411%  0.637%  2.055%   0.292%   2.014%   2.356%  3.057%  1.209%  21.700%  2.609%
2018  5.636%  -3.118%      NA      NA      NA      NA      NA       NA       NA       NA      NA      NA   2.342% 10.102%

That covers it for the function. Now, onto volatility trading. Dodging the February short volatility meltdown has, in my opinion, been one of the best out-of-sample validators for my volatility trading research. My subscriber numbers confirm it, as I’ve received 12 new subscribers this month, as individuals interested in the volatility trading space have gained a newfound respect for the risk management that my system uses. After all, it’s the down months that vindicate system traders like myself that do not employ leverage in the up times. Those interested in following my trades can subscribe here. Furthermore, recently, I was able to get a chance to speak with David Lincoln about my background, and philosophy on trading in general, and trading volatility in particular. Those interested can view the interview here.

Thanks for reading.

NOTE: I am currently interested in networking, full-time positions related to my skill set, and long-term consulting projects. Those interested in discussing professional opportunities can find me on LinkedIn after writing a note expressing their interest.

How to Make Like A Chrono Trigger Character and Survive the Apocalypse

This impromptu post will be talking about the events of Feb 5, 2018 in the volatility markets.

Allow me to indulge in a little bit of millennial nostalgia. For those that played Chrono Trigger, odds are, one of their most memorable experiences is first experiencing the Kingdom of Zeal–it was a floating kingdom above the clouds of a never-ending ice age, complete with warm scenery, and calming music.

Long story short, it was powered by harvesting magic from…essentially the monster that was the game’s final enemy. What was my favorite setting in the game eventually had this happen to it.

byeZeal

Essentially, the lesson taken from that scenario is: exercise caution first and foremost, and don’t mess around with things one does not understand. After the 2017 that XIV had, when it was seemingly impossible to do any wrong, many system traders looked foolish. Well, it seems that all good things must come to an end, though it isn’t often that they do so this violently.

For the record, my aggressive subscription strategy was flat starting on January 31st, while my conservative strategy was flat for far longer. In short, discretion is sometimes the better part of valor, though those that are interested in what actually constitutes as valor and want to hear it from a quant, you can head over to Alpha Architect. Wes Gray and Jack Vogel will tell you far more about being a badass than I ever could.

However, to put some firm numbers on my trading philosophy:

1*(1+1) = 2.
1*(1-1) = 0.

Make 100% on a trade? You’re a hero for some finite amount of time.
Lose 100%? You’re not just an idiot. You’re done. Kaput. Finished. Career over.

The way I see it is this: in trading, there’s no free lunch, and there are a lot of smart people in the industry.

The way I see it is this:

Risk in the financial markets (especially the volatility trading markets) isn’t like this: shortTail

But like this: longtail

The tails are very long. And in the financial markets, they aren’t so fluffy.

For the record, my subscription strategy, beyond taking a look at my VXX signal, is unaffected by XIV’s termination, as SVXY will slot right in to replace it.

Thanks for reading.

NOTE: I am currently seeking full time employment, consulting opportunities, and networking opportunities in relation to the skills I’ve demonstrated. Contact me on LinkedIn here.

Which Implied Volatility Ratio Is Best?

This post will be about comparing a volatility signal using three different variations of implied volatility indices to predict when to enter a short volatility position.

In volatility trading, there are three separate implied volatility indices that have a somewhat long history for trading–the VIX (everyone knows this one), the VXV (more recently changed to be called the VIX3M), which is like the VIX, except for a three-month period), and the VXMT, which is the implied six-month volatility period.

This relationship gives investigation into three separate implied volatility ratios: VIX/VIX3M (aka VXV), VIX/VXMT, and VIX3M/VXMT, as predictors for entering a short (or long) volatility position.

So, let’s get the data.

require(downloader)
require(quantmod)
require(PerformanceAnalytics)
require(TTR)
require(data.table)

download("http://www.cboe.com/publish/scheduledtask/mktdata/datahouse/vix3mdailyprices.csv", 
         destfile="vxvData.csv")
download("http://www.cboe.com/publish/ScheduledTask/MktData/datahouse/vxmtdailyprices.csv", 
         destfile="vxmtData.csv")

VIX <- fread("http://www.cboe.com/publish/scheduledtask/mktdata/datahouse/vixcurrent.csv", skip = 1)
VIXdates <- VIX$Date
VIX$Date <- NULL; VIX <- xts(VIX, order.by=as.Date(VIXdates, format = '%m/%d/%Y'))


vxv <- xts(read.zoo("vxvData.csv", header=TRUE, sep=",", format="%m/%d/%Y", skip=2))
vxmt <- xts(read.zoo("vxmtData.csv", header=TRUE, sep=",", format="%m/%d/%Y", skip=2))

download("https://dl.dropboxusercontent.com/s/jk6der1s5lxtcfy/XIVlong.TXT",
         destfile="longXIV.txt")

xiv <- xts(read.zoo("longXIV.txt", format="%Y-%m-%d", sep=",", header=TRUE))

xivRets <- Return.calculate(Cl(xiv))

One quick strategy to investigate is simple–the idea that the ratio should be below 1 (I.E. contango in implied volatility term structure) and decreasing (below a moving average). So when the ratio will be below 1 (that is, with longer-term implied volatility greater than shorter-term), and the ratio will be below its 60-day moving average, the strategy will take a position in XIV.

Here’s the code to do that.

vixVix3m <- Cl(VIX)/Cl(vxv)
vixVxmt <- Cl(VIX)/Cl(vxmt)
vix3mVxmt <- Cl(vxv)/Cl(vxmt)

stratStats <- function(rets) {
  stats <- rbind(table.AnnualizedReturns(rets), maxDrawdown(rets))
  stats[5,] <- stats[1,]/stats[4,]
  stats[6,] <- stats[1,]/UlcerIndex(rets)
  rownames(stats)[4] <- "Worst Drawdown"
  rownames(stats)[5] <- "Calmar Ratio"
  rownames(stats)[6] <- "Ulcer Performance Index"
  return(stats)
}

maShort <- SMA(vixVix3m, 60)
maMed <- SMA(vixVxmt, 60)
maLong <- SMA(vix3mVxmt, 60)

sigShort <- vixVix3m < 1 & vixVix3m < maShort
sigMed <- vixVxmt < 1 & vixVxmt < maMed 
sigLong <- vix3mVxmt < 1 & vix3mVxmt < maLong 

retsShort <- lag(sigShort, 2) * xivRets 
retsMed <- lag(sigMed, 2) * xivRets 
retsLong <- lag(sigLong, 2) * xivRets

compare <- na.omit(cbind(retsShort, retsMed, retsLong))
colnames(compare) <- c("Short", "Medium", "Long")
charts.PerformanceSummary(compare)
stratStats(compare)

With the following performance:

3ratios.PNG

> stratStats(compare)
                              Short    Medium     Long
Annualized Return         0.5485000 0.6315000 0.638600
Annualized Std Dev        0.3874000 0.3799000 0.378900
Annualized Sharpe (Rf=0%) 1.4157000 1.6626000 1.685600
Worst Drawdown            0.5246983 0.5318472 0.335756
Calmar Ratio              1.0453627 1.1873711 1.901976
Ulcer Performance Index   3.7893478 4.6181788 5.244137

In other words, the VIX3M/VXMT sports the lowest drawdowns (by a large margin) with higher returns.

So, when people talk about which implied volatility ratio to use, I think this offers some strong evidence for the longer-out horizon as a predictor for which implied vol term structure to use. It’s also why it forms the basis of my subscription strategy.

Thanks for reading.

NOTE: I am currently seeking a full-time position (remote or in the northeast U.S.) related to my skill set demonstrated on this blog. Please message me on LinkedIn if you know of any opportunities which may benefit from my skill set.