# The Logical-Invest “Universal Investment Strategy”–A Walk Forward Process on SPY and TLT

I’m sure we’ve all heard about diversified stock and bond portfolios. In its simplest, most diluted form, it can be comprised of the SPY and TLT etfs. The concept introduced by Logical Invest, in a Seeking Alpha article written by Frank Grossman (also see link here), essentially uses a walk-forward methodology of maximizing a modified Sharpe ratio, biased heavily in favor of the volatility rather than the returns. That is, it uses a 72-day moving window to maximize total returns between different weighting configurations of a SPY-TLT mix over the standard deviation raised to the power of 5/2. To put it into perspective, at a power of 1, this is the basic Sharpe ratio, and at a power of 0, just a momentum maximization algorithm.

The process for this strategy is simple: rebalance every month on some multiple of 5% between SPY and TLT that previously maximized the following quantity (returns/vol^2.5 on a 72-day window).

Here’s the code for obtaining the data and computing the necessary quantities:

```require(quantmod)
require(PerformanceAnalytics)
getSymbols(c("SPY", "TLT"), from="1990-01-01")
returns <- returns[-1,]
configs <- list()
for(i in 1:21) {
weightSPY <- (i-1)*.05
weightTLT <- 1-weightSPY
config <- Return.portfolio(R = returns, weights=c(weightSPY, weightTLT), rebalance_on = "months")
configs[[i]] <- config
}
configs <- do.call(cbind, configs)
cumRets <- cumprod(1+configs)
period <- 72

roll72CumAnn <- (cumRets/lag(cumRets, period))^(252/period) - 1
roll72SD <- sapply(X = configs, runSD, n=period)*sqrt(252)
```

Next, the code for creating the weights:

```sd_f_factor <- 2.5
modSharpe <- roll72CumAnn/roll72SD^sd_f_factor
monthlyModSharpe <- modSharpe[endpoints(modSharpe, on="months"),]

findMax <- function(data) {
return(data==max(data))
}

weights <- t(apply(monthlyModSharpe, 1, findMax))
weights <- weights*1
weights <- xts(weights, order.by=as.Date(rownames(weights)))
weights[is.na(weights)] <- 0
weights\$zeroes <- 1-rowSums(weights)
configs\$zeroes <- 0
```

That is, simply take the setting that maximizes the monthly modified Sharpe Ratio calculation at each rebalancing date (the end of every month).

Next, here’s the performance:

```stratRets <- Return.portfolio(R = configs, weights = weights)
rbind(table.AnnualizedReturns(stratRets), maxDrawdown(stratRets))
charts.PerformanceSummary(stratRets)
```

Which gives the results:

```> rbind(table.AnnualizedReturns(stratRets), maxDrawdown(stratRets))
portfolio.returns
Annualized Return                 0.1317000
Annualized Std Dev                0.0990000
Annualized Sharpe (Rf=0%)         1.3297000
Worst Drawdown                    0.1683851
```

With the following equity curve:

Not perfect, but how does it compare to the ingredients?

Let’s take a look:

```stratAndComponents <- merge(returns, stratRets, join='inner')
charts.PerformanceSummary(stratAndComponents)
rbind(table.AnnualizedReturns(stratAndComponents), maxDrawdown(stratAndComponents))
apply.yearly(stratAndComponents, Return.cumulative)
```

Here are the usual statistics:

```> rbind(table.AnnualizedReturns(stratAndComponents), maxDrawdown(stratAndComponents))
Annualized Return            0.0907000    0.0783000         0.1317000
Annualized Std Dev           0.1981000    0.1381000         0.0990000
Annualized Sharpe (Rf=0%)    0.4579000    0.5669000         1.3297000
Worst Drawdown               0.5518552    0.2659029         0.1683851
```

In short, it seems the strategy performs far better than either of the ingredients. Let’s see if the equity curve comparison reflects this.

Indeed, it does. While it does indeed have the drawdown in the crisis, both instruments were in drawdown at the time, so it appears that the strategy made the best of a bad situation.

Here are the annual returns:

```> apply.yearly(stratAndComponents, Return.cumulative)
2002-12-31  -0.02054891  0.110907611        0.01131366
2003-12-31   0.28179336  0.015936985        0.12566042
2004-12-31   0.10695067  0.087089794        0.09724221
2005-12-30   0.04830869  0.085918063        0.10525398
2006-12-29   0.15843880  0.007178861        0.05294557
2007-12-31   0.05145526  0.102972399        0.06230742
2008-12-31  -0.36794099  0.339612265        0.19590423
2009-12-31   0.26352114 -0.218105306        0.18826736
2010-12-31   0.15056113  0.090181150        0.16436950
2011-12-30   0.01890375  0.339915713        0.24562838
2012-12-31   0.15994578  0.024083393        0.06051237
2013-12-31   0.32303535 -0.133818884        0.13760060
2014-12-31   0.13463980  0.273123290        0.19637382
2015-02-20   0.02773183  0.006922893        0.02788726
```

2002 was an incomplete year. However, what’s interesting here is that on a whole, while the strategy rarely if ever does as well as the better of the two instruments, it always outperforms the worse of the two instruments–and not only that, but it has delivered a positive performance in every year of the backtest–even when one instrument or the other was taking serious blows to performance, such as SPY in 2008, and TLT in 2009 and 2013.

For the record, here is the weight of SPY in the strategy.

```weightSPY <- apply(monthlyModSharpe, 1, which.max)
weightSPY <- do.call(rbind, weightSPY)
weightSPY <- (weightSPY-1)*.05
align <- cbind(weightSPY, stratRets)
align <- na.locf(align)
chart.TimeSeries(align[,1], date.format="%Y", ylab="Weight SPY", main="Weight of SPY in SPY-TLT pair")
```

Now while this may serve as a standalone strategy for some people, the takeaway in my opinion from this is that dynamically re-weighting two return streams that share a negative correlation can lead to some very strong results compared to the ingredients from which they were formed. Furthermore, rather than simply rely on one number to summarize a relationship between two instruments, the approach that Frank Grossman took to actually model the combined returns was one I find interesting, and undoubtedly has applications as a general walk-forward process.

NOTE: I am a freelance consultant in quantitative analysis on topics related to this blog. If you have contract or full time roles available for proprietary research that could benefit from my skills, please contact me through my LinkedIn here.

# The Quarterly Tactical Strategy (aka QTS)

This post introduces the Quarterly Tactical Strategy, introduced by Cliff Smith on a Seeking Alpha article. It presents a variation on the typical dual-momentum strategy that only trades over once a quarter, yet delivers a seemingly solid risk/return profile. The article leaves off a protracted period of unimpressive performance at the turn of the millennium, however.

First off, due to the imprecision of the English language, I received some help from TrendXplorer in implementing this strategy. Those who are fans of Amibroker are highly encouraged to visit his blog.

In any case, this strategy is fairly simple:

Take a group of securities (in this case, 8 mutual funds), and do the following:

Rank a long momentum (105 days) and a short momentum (20 days), and invest in the security with the highest composite rank, with ties going to the long momentum (that is, .501*longRank + .499*shortRank, for instance). If the security with the highest composite rank is greater than its three month SMA, invest in that security, otherwise, hold cash.

There are two critical points that must be made here:

1) The three-month SMA is *not* a 63-day SMA. It is precisely a three-point SMA up to that point on the monthly endpoints of that security.
2) Unlike in flexible asset allocation or elastic asset allocation, the cash asset is not treated as a formal asset.

Let’s look at the code. Here’s the data–which are adjusted-data mutual fund data (although with a quarterly turnover, the frequent trading constraint of not trading out of the security is satisfied, though I’m not sure how dividends are treated–that is, whether a retail investor would actually realize these returns less a hopefully tiny transaction cost through their brokers–aka hopefully not too much more than \$1 per transaction):

```require(quantmod)
require(PerformanceAnalytics)
require(TTR)

#get our data from yahoo, use adjusted prices
symbols <- c("NAESX", #small cap
"PREMX", #emerging bond
"VEIEX", #emerging markets
"VFIIX", #GNMA mortgage
"VFINX", #S&P 500 index
"VGSIX", #MSCI REIT
"VGTSX", #total intl stock idx
"VUSTX") #long term treasury (cash)

getSymbols(symbols, from="1990-01-01")
prices <- list()
for(i in 1:length(symbols)) {
}
prices <- do.call(cbind, prices)
colnames(prices) <- gsub("\\.[A-z]*", "", colnames(prices))

#define our cash asset and keep track of which column it is
cashAsset <- "VUSTX"
cashCol <- grep(cashAsset, colnames(prices))

#start our data off on the security with the least data (VGSIX in this case)
prices <- prices[!is.na(prices[,7]),]

#cash is not a formal asset in our ranking
cashPrices <- prices[, cashCol]
prices <- prices[, -cashCol]
```

Nothing anybody hasn’t seen before up to this point. Get data, start it off at most recent inception mutual fund, separate the cash prices, moving along.

What follows is a rather rough implementation of QTS, not wrapped up in any sort of function that others can plug and play with (though I hope I made the code readable enough for others to tinker with).

Let’s define parameters and compute momentum.

```#define our parameters
nShort <- 20
nLong <- 105
nMonthSMA <- 3

#compute momentums
rocShort <- prices/lag(prices, nShort) - 1
rocLong <- prices/lag(prices, nLong) - 1
```

Now comes some endpoints functionality (or, more colloquially, magic) that the xts library provides. It’s what allows people to get work done in R much faster than in other programming languages.

```#take the endpoints of quarter start/end
quarterlyEps <- endpoints(prices, on="quarters")
monthlyEps <- endpoints(prices, on = "months")

#take the prices at quarterly endpoints
quarterlyPrices <- prices[quarterlyEps,]

#short momentum at quarterly endpoints (20 day)
rocShortQtrs <- rocShort[quarterlyEps,]

#long momentum at quarterly endpoints (105 day)
rocLongQtrs <- rocLong[quarterlyEps,]
```

In short, get the quarterly endpoints (and monthly, we need those for the monthly SMA which you’ll see shortly) and subset our momentum computations on those quarterly endpoints. Now let’s get the total rank for those subset-on-quarters momentum computations.

```#rank short momentum, best highest rank
rocSrank <- t(apply(rocShortQtrs, 1, rank))

#rank long momentum, best highest rank
rocLrank <- t(apply(rocLongQtrs, 1, rank))

#total rank, long slightly higher than short, sum them
totalRank <- 1.01*rocLrank + rocSrank

#function that takes 100% position in highest ranked security
maxRank <- function(rankRow) {
return(rankRow==max(rankRow))
}

#apply above function to our quarterly ranks every quarter
rankPos <- t(apply(totalRank, 1, maxRank))
```

So as you can see, I rank the momentum computations by row, take a weighted sum (in slight favor of the long momentum), and then simply take the security with the highest rank at every period, giving me one 1 in every row and 0s otherwise.

Now let’s do the other end of what determines position, which is the SMA filter. In this case, we need monthly data points for our three-month SMA, and then subset it to quarters to be on the same timescale as the quarterly ranks.

```#SMA of securities, only use monthly endpoints
#subset to quarters
#then filter
monthlyPrices <- prices[monthlyEps,]
monthlySMAs <- xts(apply(monthlyPrices, 2, SMA, n=nMonthSMA), order.by=index(monthlyPrices))
quarterlySMAs <- monthlySMAs[index(quarterlyPrices),]
smaFilter <- quarterlyPrices > quarterlySMAs
```

Now let’s put it together to get our final positions. Our cash position is simply one if we don’t have a single investment in the time period, zero else.

```finalPos <- rankPos*smaFilter
finalPos <- finalPos[!is.na(rocLongQtrs[,1]),]
cash <- xts(1-rowSums(finalPos), order.by=index(finalPos))
finalPos <- merge(finalPos, cash, join='inner')
```

Now we can finally compute our strategy returns.

```prices <- merge(prices, cashPrices, join='inner')
returns <- Return.calculate(prices)
stratRets <- Return.portfolio(returns, finalPos)
table.AnnualizedReturns(stratRets)
maxDrawdown(stratRets)
charts.PerformanceSummary(stratRets)
plot(log(cumprod(1+stratRets)))
```

So what do things look like?

Like this:

```> table.AnnualizedReturns(stratRets)
portfolio.returns
Annualized Return                    0.1899
Annualized Std Dev                   0.1619
Annualized Sharpe (Rf=0%)            1.1730
> maxDrawdown(stratRets)
[1] 0.1927991
```

And since the first equity curve doesn’t give much of an indication in the early years, I’ll take Tony Cooper’s (of Double Digit Numerics) advice and show the log equity curve as well.

In short, from 1997 through 2002, this strategy seemed to be going nowhere, and then took off. As I was able to get this backtest going back to 1997, it makes me wonder why it was only started in 2003 for the SeekingAlpha article, since even with 1997-2002 thrown in, this strategy’s risk/reward profile still looks fairly solid. CAR about 1 (slightly less, but that’s okay, for something that turns over so infrequently, and in so few securities!), and a Sharpe higher than 1. Certainly better than what the market itself offered over the same period of time for retail investors. Perhaps Cliff Smith himself could chime in regarding his choice of time frame.

In any case, Cliff Smith marketed the strategy as having a higher than 28% CAGR, and his article was published on August 15, 2014, and started from 2003. Let’s see if we can replicate those results.

```stratRets <- stratRets["2002-12-31::2014-08-15"]
table.AnnualizedReturns(stratRets)
maxDrawdown(stratRets)
charts.PerformanceSummary(stratRets)
plot(log(cumprod(1+stratRets)))
```

Which results in this:

```> table.AnnualizedReturns(stratRets)
portfolio.returns
Annualized Return                    0.2862
Annualized Std Dev                   0.1734
Annualized Sharpe (Rf=0%)            1.6499
> maxDrawdown(stratRets)
[1] 0.1911616
```

A far improved risk/return profile without 1997-2002 (or the out-of-sample period after Cliff Smith’s publishing date). Here are the two equity curves in-sample.

In short, the results look better, and the SeekingAlpha article’s results are validated.

Now, let’s look at the out-of-sample periods on their own.

```stratRets <- Return.portfolio(returns, finalPos)
earlyOOS <- stratRets["::2002-12-31"]
table.AnnualizedReturn(earlyOOS)
maxDrawdown(earlyOOS)
charts.PerformanceSummary(earlyOOS)
```

Here are the results:

```> table.AnnualizedReturns(earlyOOS)
portfolio.returns
Annualized Return                    0.0321
Annualized Std Dev                   0.1378
Annualized Sharpe (Rf=0%)            0.2327
> maxDrawdown(earlyOOS)
[1] 0.1927991
```

And with the corresponding equity curve (which does not need a log-scale this time).

In short, it basically did nothing for an entire five years. That’s rough, and I definitely don’t like the fact that it was left off of the SeekingAlpha article, as anytime I can extend a backtest further back than a strategy’s original author and then find skeletons in the closet (as happened for each and every one of Harry Long’s strategies), it sets off red flags on this end, so I’m hoping that there’s some good explanation for leaving off 1997-2002 that I’m simply failing to mention.

Lastly, let’s look at the out-of-sample performance.

```lateOOS <- stratRets["2014-08-15::"]
charts.PerformanceSummary(lateOOS)
table.AnnualizedReturns(lateOOS)
maxDrawdown(lateOOS)
```

With the following results:

```> table.AnnualizedReturns(lateOOS)
portfolio.returns
Annualized Return                    0.0752
Annualized Std Dev                   0.1426
Annualized Sharpe (Rf=0%)            0.5277
> maxDrawdown(lateOOS)
[1] 0.1381713
```

And the following equity curve:

Basically, while it’s ugly, it made new equity highs over only two more transactions (and in such a small sample size, anything can happen), so I’ll put this one down as a small, ugly win, but a win nevertheless.

If anyone has any questions or comments about this strategy, I’d love to see them, as this is basically a first-pass replica. To Mr. Cliff Smith’s credit, the results check out, and when the worst thing one can say about a strategy is that it had a period of a flat performance (aka when the market crested at the end of the Clinton administration right before the dot-com burst), well, that’s not the worst thing in the world.

More replications (including one requested by several readers) will be upcoming.

NOTE: I am a freelance consultant in quantitative analysis on topics related to this blog. If you have contract or full time roles available for proprietary research that could benefit from my skills, please contact me through my LinkedIn here.

# A New Harry Long Strategy and A Couple of New PerfA Functions

So, Harry Long (of Houston) came out with a new strategy on SeekingAlpha involving some usual mix of SPXL (3x leveraged SPY), TMF (3x leveraged TLT), and some volatility indices (in this case, ZIV and TVIX). Now, since we’ve tread this path before, expectations are rightfully set. It’s a strategy that’s going to look good in the sample he used, it’s going to give some performance back in the crisis, and it’ll ultimately prove to be a simple-to-implement, simple-to-backtest strategy with its own set of ups and downs that does outperform the usual buy-and-hold indices.

Once again, a huge thanks to Mr. Helmuth Vollmeier for the long history volatility data.

So here’s the code (I’ll skip a lot of the comparing equity curves of my synthetic instruments to the Yahoo-finance variants, as you’ve all seen that before) to get to the initial equity curve comparison.

```require(downloader)
require(PerformanceAnalytics)

destfile="longVXX.txt")
TVIXrets &amp;amp;lt;- Return.calculate(Cl(VXX))*2
getSymbols("TVIX", from="1990-01-01")
TVIX &amp;amp;lt;- TVIX[-which(index(TVIX)=="2014-12-30"),] #trashy Yahoo data, removing obvious bad print
charts.PerformanceSummary(compare)
charts.PerformanceSummary(compare["2012::"])
charts.PerformanceSummary(compare["2013::"])
charts.PerformanceSummary(compare["2014::"])
charts.PerformanceSummary(compare["2015::"]) #okay we're good

destfile="longZIV.txt")
ZIVrets &amp;amp;lt;- Return.calculate(Cl(ZIV))

getSymbols("SPY", from="1990-01-01")

getSymbols("TMF", from="1990-01-01")
getSymbols("TLT", from="1990-01-01")
tmf3TLT &amp;amp;lt;- merge(TMFrets, 3*TLTrets, join='inner')
charts.PerformanceSummary(tmf3TLT)
discrepancy &amp;amp;lt;- as.numeric(Return.annualized(tmf3TLT[,2]-tmf3TLT[,1]))
tmf3TLT[,2] &amp;amp;lt;- tmf3TLT[,2] - ((1+discrepancy)^(1/252)-1)
charts.PerformanceSummary(tmf3TLT)
modifiedTLT &amp;amp;lt;- 3*TLTrets - ((1+discrepancy)^(1/252)-1)
TMFrets &amp;amp;lt;- modifiedTLT

components &amp;amp;lt;- cbind(SPXLrets, ZIVrets, TMFrets, TVIXrets)
components &amp;amp;lt;- components["2004-03-29::"]
stratRets &amp;amp;lt;- Return.portfolio(R = components, weights = c(.4, .2, .35, .05), rebalance_on="years")
charts.PerformanceSummary(stratRets)
compare &amp;amp;lt;- merge(stratRets, SPYrets, join='inner')
charts.PerformanceSummary(compare["2011::"])

With the following equity curve display:

So far, so good. Let’s look at the full backtest performance.
charts.PerformanceSummary(compare)

With the resultant equity curve:

Which, given what we’ve seen before, isn’t outside the realm of expectation.
For those interested in the log equity curves, here you go:
compare[is.na(compare)] &amp;amp;lt;- 0
plot(log(cumprod(1+compare)), legend.loc="topleft")

And for fun, let’s look at the outperformance equity curve.
diff &amp;amp;lt;- compare[,1] - compare[,2]
charts.PerformanceSummary(diff, main="relative performance")

And the result:

Now this is somewhere in the ballpark of what you’d love to see from your strategy against a benchmark — aside from a couple of spikes which do a number on the corresponding drawdowns chart, it looks like a steady outperformance.
However, the new features I’d like to introduce in this blog post are a quicker way of generating the usual statistics table I display, and a more in-depth drawdown analysis.
Here’s how:
rbind(table.AnnualizedReturns(compare), maxDrawdown(compare))

Which gives us the following result:
&amp;amp;gt; rbind(table.AnnualizedReturns(compare), maxDrawdown(compare))
Annualized Return                 0.2181000    0.0799000
Annualized Std Dev                0.2159000    0.1982000
Annualized Sharpe (Rf=0%)         1.0100000    0.4030000
Worst Drawdown                    0.4326138    0.5518552

Since this saves me typing, I’ll be using this format from now on. And as a bonus, it displays annualized standard deviation. While I don’t particularly care for that statistic as I believe that max drawdown captures the notion of “here’s the pain on the other end of your returns” better than “here’s how much your strategy wiggles from day to day”, the fact that it’s thrown in and is a statistic that a lot of other people (particularly portfolio managers, pension fund managers, etc.) are interested in, so much the better.
Now, moving onto a more in-depth analysis of drawdown, PerformanceAnalytics has the following functionality:
dd &amp;amp;lt;- table.Drawdowns(compare[,1], top=100)
dd &amp;amp;lt;- dd[dd\$Depth &amp;amp;lt; -.05,]
dd
sum(dd\$"To Trough")/nrow(compare)

This brings up the following table (it seems that with multiple return streams, it’ll just default to the first one), and a derived statistic.
&amp;amp;gt; dd
From     Trough         To   Depth Length To Trough Recovery
1  2008-12-19 2009-03-09 2010-03-16 -0.4326    310        53      257
2  2007-10-30 2008-10-15 2008-12-04 -0.3275    278       243       35
3  2013-05-22 2013-06-24 2013-09-18 -0.1617     83        23       60
4  2004-04-02 2004-05-10 2004-09-17 -0.1450    116        26       90
5  2010-04-26 2010-07-02 2010-09-21 -0.1230    104        49       55
6  2006-03-20 2006-06-19 2006-09-20 -0.1229    129        64       65
7  2007-05-08 2007-08-15 2007-10-01 -0.1229    102        70       32
8  2005-07-29 2005-10-27 2005-12-14 -0.1112     97        64       33
9  2011-06-01 2011-08-11 2011-09-06 -0.1056     68        51       17
10 2005-02-09 2005-03-22 2005-05-31 -0.1051     77        29       48
11 2010-11-05 2010-11-17 2011-02-07 -0.1022     64         9       55
12 2011-09-23 2011-10-27 2011-12-19 -0.0836     61        25       36
13 2013-09-19 2013-10-09 2013-10-17 -0.0815     21        15        6
14 2012-05-02 2012-05-18 2012-06-29 -0.0803     42        13       29
15 2012-10-18 2012-11-15 2012-11-29 -0.0721     28        19        9
16 2014-09-02 2014-10-13 2014-11-05 -0.0679     47        30       17
17 2008-12-05 2008-12-08 2008-12-16 -0.0589      8         2        6
18 2011-02-18 2011-03-16 2011-04-01 -0.0580     30        18       12
19 2014-07-23 2014-08-06 2014-08-15 -0.0536     18        11        7
20 2012-04-03 2012-04-10 2012-04-26 -0.0517     17         5       12

What I did was I simply wanted to query the table for all drawdowns that were more than 5%, or the 100 biggest drawdowns (though considering that we have about 20 drawdowns over about a decade, it seems the rule is 2 drawdowns over 5% per year, give or take, and this is a pretty volatile strategy). Lastly, I wanted to know the proportion of the time that someone watching the strategy will be feeling the pain of watching the strategy go to those depths, so I took the sum of the “To Trough” column and divided it by the amount of days of the backtest. This is the result:
&amp;amp;gt; sum(dd\$"To Trough")/nrow(compare)
[1] 0.3005505

I’m fairly certain some individuals more seasoned than I am would do something different given this information and functionality, and if so, feel free to leave a comment, but this is just a licked-finger-in-the-air calculation I did. So, 30% of the time, whoever is investing real money into this will want to go and grab a few more drinks than usual.
Let’s do the same analysis for the relative performance.
tmp &amp;amp;lt;- rbind(table.AnnualizedReturns(diff), maxDrawdown(diff))
rownames(tmp)[4] &amp;amp;lt;- "Worst Drawdown"
tmp

When running only one set of returns, apparently the last row will just simply be called “4”, so I had to manually rename that row. Here’s the result:
&amp;amp;gt; tmp
portfolio.returns
Annualized Return                 0.1033000
Annualized Std Dev                0.2278000
Annualized Sharpe (Rf=0%)         0.4535000
Worst Drawdown                    0.3874082

Far from spectacular, but there it is for what it’s worth.
Now the drawdowns.
dd &amp;amp;lt;- table.Drawdowns(diff, top=100)
dd &amp;amp;lt;- dd[dd\$Depth &amp;amp;lt; -.05,]
dd
sum(dd\$"To Trough")/nrow(diff)

With the following result:
&amp;amp;gt; dd
From     Trough         To   Depth Length To Trough Recovery
1  2008-11-21 2009-06-22 2013-04-04 -0.3874   1097       145      952
2  2008-10-28 2008-11-04 2008-11-19 -0.2328     17         6       11
3  2007-11-27 2008-06-12 2008-10-07 -0.1569    218       137       81
4  2013-05-03 2013-06-25 2013-12-26 -0.1386    165        37      128
5  2008-10-13 2008-10-13 2008-10-24 -0.1327     10         1        9
6  2005-06-08 2006-06-28 2006-11-08 -0.1139    360       267       93
7  2004-03-29 2004-05-10 2004-09-20 -0.1102    121        30       91
8  2007-03-08 2007-06-12 2007-11-26 -0.0876    183        67      116
9  2005-02-10 2005-03-28 2005-05-31 -0.0827     76        31       45
10 2014-09-02 2014-09-17 2014-10-14 -0.0613     31        12       19

In short, the spikes in outperformance gave us some pretty…interesting…drawdown statistics, which just essentially meant that the strategy wasn’t roaring at the same exact time that the SPY had its bounce from the bottom. And for interest, my finger in the air pain statistic:
&amp;amp;gt; sum(dd\$"To Trough")/nrow(diff)
[1] 0.2689908

So approximately 27% of the time, the strategy underperforms its benchmark–meaning that 73% of the time, you’re fairly happy–assuming you’ve chosen the correct benchmark.
In short, overall, more freebies from Harry Long with a title to attract readers. The strategy is what it is–something that boasts strong absolute returns and definitely outperforms SPY, though like anything else, has its moments that it’ll burn you (no pain, no gain, as they say). However, the quicker statistics table functionality combined with the more in-depth drawdown analysis is something that I am definitely happy to have stumbled upon.
NOTE: I am a freelance consultant in quantitative analysis on topics related to this blog. If you have contract or full time roles available for proprietary research that could benefit from my skills, please contact me through my LinkedIn here.
```

# The ZOMMA Warthog Index

Harry Long posted another article on SeekingAlpha. As usual, it’s another strategy to be taken with a grain of salt, but very much worth discussing. So here’s the strategy:

Rebalance annually:

50% XLP, 15% GLD, 35% TLT — aka a variation of the stocks/bonds portfolio, just with some gold added in. The twist is the idea that XLP is less risky than SPY. The original article, written by Harry Long, can be found here.

This strategy is about as simple as they come, and is tested just as easily in R.

Here’s the original replication:

```require(PerformanceAnalytics)
require(quantmod)
getSymbols("XLP", from="1990-01-01")
getSymbols("GLD", from="1990-01-01")
getSymbols("TLT", from="1990-01-01")
prices <- prices[!is.na(prices[, 2]),]
rets <- Return.calculate(prices)
warthogRets <- Return.portfolio(rets, weights=c(.5, .15, .35), rebalance_on = "years")
getSymbols("SPY", from="1990-01-01")
comparison <- merge(warthogRets, SPYrets, join='inner')
charts.PerformanceSummary(comparison)
```

And the resulting replicated (approximately) equity curve:

So far, so good.

Now, let’s put the claim of outperforming over an entire cycle to the test.

```years <- apply.yearly(comparison, Return.cumulative)
years <- years[-1,] #remove 2004
years
sum(years[,1] > years[,2])/nrow(years)
sapply(years, mean)
```

And here’s the output:

```> years
2005-12-30        0.07117683   0.04834811
2006-12-29        0.10846819   0.15843582
2007-12-31        0.14529234   0.05142241
2008-12-31        0.05105269  -0.36791039
2009-12-31        0.03126667   0.26344690
2010-12-31        0.14424559   0.15053339
2011-12-30        0.20384853   0.01897321
2012-12-31        0.07186807   0.15991238
2013-12-31        0.04234810   0.32309145
2014-12-10        0.16070863   0.11534450
> sum(years[,1] > years[,2])/nrow(years)
[1] 0.5
> sapply(years, mean)
0.10302756        0.09215978
```

So, even with SPY’s 2008 in mind, this strategy seems to break even on a year-to-year basis, and the returns are slightly better, which I suppose should be par for the course for a backtest against SPY through the recession.

Now, let’s just remove that one year and see how things stack up:

```years <- years[-4,] #remove 2008
sapply(years, mean)
```

And we obtain the following results:

```> sapply(years, mean)
0.1088025         0.1432787
```

In short, the so-called outperformance is largely sample-dependent on the S&P having a terrible year. Beyond that, things don’t look so stellar for the strategy.

Lastly, anytime anyone makes a claim about a strategy outperforming a benchmark, one very, very easy test to do is to simply look at the equity curve of a “market neutral” strategy that shorts the benchmark against the strategy, and see if that looks like an equity curve one would be comfortable holding. Here are the results:

```diff <- comparison[,1] - comparison[,2]
charts.PerformanceSummary(diff, main="short SPY against portfolio")
```

And the resulting equity curve of the outperformance:

Basically, ever since the crisis passed, the strategy has been flat to underperforming against SPY, which is fair enough considering that the market has been on a roar since then.

To hammer the point, let’s look at the equity curves from 2009 onwards.

```#strategy against SPY post-crisis
charts.PerformanceSummary(comparison["2009::"])
```

With the result:

To its credit, the strategy’s equity curve is certainly a smoother ride. At the same time, the underperformance is clear as well. I suppose this makes sense as a portfolio invested 35% in bonds should expect to underperform a portfolio fully invested in equities on an absolute returns basis.

Now, as I did before, in It’s Amazing How Well Dumb Things Get Marketed, I’m going to backtest this strategy as far as I can using proxies from Quandl for gold and bonds, by going directly to the futures. Refer to that post to see that the proxies are relatively decent for the ETFs. In this case, I switched from adjusted to close prices, but the concept should still hold.

```require(IKTrading)
goldFutures <- quandClean(stemCode = "CHRIS/CME_GC", verbose = TRUE)
thirtyBond <- quandClean(stemCode="CHRIS/CME_US", verbose = TRUE)
longPrices <- cbind(Cl(XLP), Cl(goldFutures), Cl(thirtyBond))
longRets <- Return.calculate(longPrices)
longRets <- longRets[!is.na(longRets[,1]),]
names(longRets) <- c("XLP", "Gold", "Bonds")
longWarthog <- Return.portfolio(longRets, weights=c(.5, .15, .35), rebalance_on = "years")
longComparison <- merge(longWarthog, SPYrets, join='inner')
charts.PerformanceSummary(longComparison)
```

And here’s the resultant equity curve comparison:

So, the idea that the strategy outperforms SPY on an absolute returns basis? It seems to be due to SPY’s horrendous performance in 2008, which is a once-in-several-decades event. As you can see, if you started from XLP’s inception to approximately 2005, the strategy was actually in drawdown for all those years, at least if you started in 1998.

Let’s look at the risk/reward metrics for this timeframe:

```stats <- rbind(Return.annualized(longComparison),
maxDrawdown(longComparison),
SharpeRatio.annualized(longComparison),
Return.annualized(longComparison)/maxDrawdown(longComparison)
)
rownames(stats)[4] <- "Return Over MaxDD"
stats
```

And the results:

```> stats
Annualized Return                       0.0409267   0.05344120
Worst Drawdown                          0.2439091   0.55186722
Annualized Sharpe Ratio (Rf=0%)         0.4846184   0.26295594
Return Over MaxDD                       0.1677949   0.09683706
```

To its credit, the strategy has a significantly better return to risk profile than SPY does, which I hope would be the case for any backtest going up against SPY with 2008 in mind. Overall, the strategy has a bit of merit as a defensive play, and for a simple static allocation based strategy that plays on the defensive side, it delivers what you might expect from a risk-averse strategy, which is reflected in a much better return to drawdown profile than the market. Nevertheless, one should be careful not to misinterpret a strategy whose focus is to control risk for a strategy that aims to swing for the fences. Furthermore, this is a strategy that Harry Long has been so kind as to give away, so take it for what it’s worth–a simple-to-implement defensive strategy which delivers on its defensive promises.

NOTE: I am a freelance consultant in quantitative analysis on topics related to this blog. If you have contract or full time roles available for proprietary research that could benefit from my skills, please contact me through my LinkedIn here.

# 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:

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)

getSymbols("SPXL", from="1990-01-01")
getSymbols("SPY", from="1990-01-01")
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")
getSymbols("TLT", from="1990-01-01")
tmf3TLT <- merge(TMFrets, 3*TLTrets, join='inner')
charts.PerformanceSummary(tmf3TLT)
```

The result:

```> Return.annualized(tmf3TLT[,2]-tmf3TLT[,1])
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
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")
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::"])
```

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)
Annualized Return         0.2305339   0.07937642
> maxDrawdown(stratAndSPY)
Worst Drawdown         0.4901882    0.5518672
> SharpeRatio.annualized(stratAndSPY)
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)
Annualized Return         0.1181923    0.1356003
> maxDrawdown(diffAndModTLT)
Worst Drawdown         0.3930016    0.6348332
> SharpeRatio.annualized(diffAndModTLT)
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")
vxxTvix <- merge(2*VXXrets, TVIXrets, join='inner')
```

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 <- 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
```

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.

# It’s Amazing How Well Dumb Things Work?

Recently, Harry Long posted not one but four new articles on Seeking Alpha called It’s Amazing How Well Dumb Things Work II. The last time I replicated a strategy by Mr. Long, it came up short on the expectations it initially built. For the record, here are the links to the four part series.

While the strategy itself wasn’t the holy grail (nothing is, really, and it did outperform the S&P), it did pay off with some long-history ETF data for which I am extremely grateful (a project I’m currently working on involves those exact indices, I’ll see if I can blog about it), and it did give me the chance to show some R functionality that I hadn’t shown before that point, which in my opinion, made the endeavor more than worth it.

For this particular strategy, I’m not so sure that’s the case.

In short, the S&P 500, gold, and long-term bonds, rebalance to an equal-weight portfolio annually. Dirt simple. So simple, in fact, that I can backtest this strategy back to 1978!

The data I used was the actual GSPC index from Yahoo Finance, and some quandl data that I cleaned up with the quandClean function in my IKTrading package. While some of the futures I originally worked with have huge chunks of missing data, the long term bonds and gold futures are relatively intact. Gold had about 44 missing days in the 21st century when GLD had returns, so there may be some data integrity issues there, though the average return for GLD on those days is about -3 bps, so the general concept demonstration is intact. With the bonds, there were 36 missing days that TLT had returns for, but the average returns for those days were a -18 bps, so I instead imputed those missing days to zero.

In any case, here’s the script to set up the data:

```require(IKTrading)
require(PerformanceAnalytics)
require(quantmod)

getSymbols("^GSPC", from="1800-01-01")
SPrets &lt;- Return.calculate(Cl(GSPC))

goldFutures &lt;- quandClean(stemCode = "CHRIS/CME_GC", verbose = TRUE)
getSymbols("GLD", from="1990-01-01") #quandl's data had a few gaps--let's use GLD to fill them in.
goldGLD &lt;- merge(Cl(goldFutures), Cl(GLD), join='outer')
goldRets &lt;- Return.calculate(goldGLD)
sum(is.na(goldRets[,1]))
mean(goldRets[is.na(goldRets[,1]),2], na.rm=TRUE)
goldRets[is.na(goldRets[,1]),1] &lt;- goldRets[is.na(goldRets[,1]),2] #impute missing returns data with GLD returns data for that day
goldRets &lt;- goldRets[,1]

thirtyBond &lt;- quandClean(stemCode="CHRIS/CME_US", verbose = TRUE)
getSymbols("TLT", from="1990-01-01")
bondTLT &lt;- merge(Cl(thirtyBond), Cl(TLT), join='outer')
bondRets &lt;- Return.calculate(bondTLT)
sum(is.na(bondRets[,1]))
mean(bondRets[is.na(bondRets[,1]),2], na.rm=TRUE) #18 basis points? Just going to impute as zero.
bondRets[is.na(bondRets[,1]),1] &lt;- 0 #there are 259 other such instances prior to this imputing
bondRets &lt;- bondRets[,1]

SPbondGold &lt;- cbind(SPrets, goldRets, bondRets)
SPbondGold &lt;- SPbondGold["1977-12-30::"] #start off at beginning of 1978, since that's when gold futures were first in inception
colnames(SPbondGold) &lt;- c("SandP", "Bonds", "Gold")

DTW_II_returns &lt;- Return.rebalancing(R = SPbondGold, weights = c(1/3, 1/3, 1/3), geometric = FALSE, rebalance_on = "years")
stratSP &lt;- merge(DTW_II_returns, SPrets, join='inner')
colnames(stratSP) &lt;- c("Harry Long Strategy", "S&amp;P 500")

First, let’s recreate the original equity curve, to prove that I’m comparing apples to apples.
#Recreate the original equity curve
charts.PerformanceSummary(stratSP["2004-12-01::"])

So, as you can see, everything seems to match, article confirmed, and that’s good.
But I wrote the backtest to go back to 1978, just so we can see as much of the performance as we possibly can. So, let’s take a look. Now, keep in mind that the article stated the following two assertions:
“As we previously observed, the approach has higher returns and lower drawdowns across an entire bull and bear market cycle than the S&P 500…” and that “…a portfolio manager who employed this decidedly humble, simple approach, would actually have been doing well for clients as a fiduciary.”
Let’s see if the full-period equity curve supports these assertions.
charts.PerformanceSummary(stratSP)

Here are some numerical values to put this into perspective:
&gt; Return.cumulative(stratSP)
Harry Long Article  S&amp;P 500
Cumulative Return           6.762379 20.25606
&gt; Return.annualized(stratSP)
Harry Long Article    S&amp;P 500
Annualized Return         0.05713769 0.08640992
&gt; SharpeRatio.annualized(stratSP)
Harry Long Article   S&amp;P 500
Annualized Sharpe Ratio (Rf=0%)           0.583325 0.4913877
&gt; maxDrawdown(stratSP)
Harry Long Article   S&amp;P 500
Worst Drawdown           0.334808 0.5677539

In short, a 5.7% to an 8.6% annualized return in favor of the S&P 500 since 1978, with both sets of returns sporting substantial drawdowns compared to their annualized rates of return. So while this strategy gives a better risk-adjusted return, you get the return you pay for with the risks taken–smaller max drawdown for a similar Sharpe? Smaller return. Furthermore, the early 80s seem to have hurt this “all-weather” strategy more than the S&P 500.
For fun, let’s leverage the strategy 2x over and see what happens.
stratSP\$leveragedStrat &lt;- stratSP[,1]*2
charts.PerformanceSummary(stratSP)

And this is the resulting equity curve:

Hey, now we’re talking, right?! Well, the late 70s and early 80s say not exactly. But what if I wanted to make myself look better than the strategy justifies? Well, I can simply truncate those drawdowns, by just leaving off everything before 1985! (And put some marketing spin on it to justify it.)
charts.PerformanceSummary(stratSP["1985::"])

Here are some statistics:
&gt; maxDrawdown(stratSP["1985::"])
Harry.Long.Article   S.P.500 leveragedStrat
Worst Drawdown          0.2228608 0.5677539      0.4065492
&gt; Return.annualized(stratSP["1985::"])
Harry.Long.Article    S.P.500 leveragedStrat
Annualized Return         0.05782724 0.08700208      0.1106892
&gt; SharpeRatio.annualized(stratSP["1985::"])
Harry.Long.Article   S.P.500 leveragedStrat
Annualized Sharpe Ratio (Rf=0%)          0.6719875 0.4753468      0.6431376

Now look, higher returns, lower max drawdown, higher Sharpe, we can all go home happy?
Of course not. So what’s the point of this post?
Simply, to not believe everything you see at first glance. There’s often a phrase that’s thrown around that states “you’ll never see a bad backtest”–simply implying that if the backtest is bad, it’s thrown out, and all that’s left are the results with cherry-picked time frames, brute-force curve-fit parameter sets, and who knows what other sort of methodologies baked in to make a strategy look as good as possible.
On my blog, I try my best to be on the opposite side of the spectrum. In instances in which ideas were published years ago, some low-hanging fruit is an out-of sample test. On the opposite side of the spectrum, such as with Mr. Harry Long of SeekingAlpha here, when there are backtests with a very small time frame owing to newly released instruments, I’ll try and provide a much larger context. I provide the code, the data, and explanations in plain English, all to the best of my ability here on this blog. If you don’t wish to take my word for it, you can always run the scripts yourself. Worst to worst, leave a comment, and I’ll answer to the best of my ability.
I’ll have another Harry Long backtest replication up soon.