**From Guinness to GARCH**, and kindly contributed to R-bloggers)

Adam Duncan Also avilable on R-bloggers.com

Some time ago, I read an interesting article about an interview with David Swensen, the renownd money manager from Yale University’s investment office. He’s quite famous and is considered by many to be the architect of the modern “endowment portfolio.” The point of the article was to suggest a way for ordinary investors to replicate the “endowment portfolio” using widely available, low cost ETFs. This is not the original piece I read, but this article conveys the essentials of the original post. This idea appealed to me and I wrote down the tickers and weights in my notebook for some later date when I could take action on it.

From the article I linked to above…

“Here’s a look at Swensen’s asset allocation recommendations:”

Asset Class | % |
---|---|

Domestic Stocks | 30% |

Foreign Developed Stocks | 15% |

Emerging Market Stocks | 5% |

Real Estate and Natural Resources | 20% |

U.S. Treasury Bonds | 15% |

U.S. Inflation-Protected Securities (TIPS) | 15% |

All of the ETFs suggested in the original article were Vanguard ETFs and that seemed fine with me. I should also note that this simple ETF portfolio differs from a typical endowment portfolio in many non-trivial ways. But, my goals were pretty modest at the start and the allocations seemed pretty sensible.

So, on October 17th, 2012 I deployed an initial investment of 250,000 into the following portfolio of ETFs. This post is going to show you how to monitor such a portfolio in R. For people familiar with quantmod and Performance Analytics, the discussion will be pretty rudimentary. In the next post I will try to raise some questions about VaR excessions, drawdowns, and de-risking. So, let’s get started.

First we need to specify a data source and the tickers for our portfolio. I’ll also fetch data for the DOW and the SP500, as well as the 2yr US swap rate. All for benchmarking purposes.

```
library(quantmod, warn.conflicts = FALSE, quietly = TRUE)
library(PerformanceAnalytics, warn.conflicts = FALSE, quietly = TRUE)
library(knitr, warn.conflicts = FALSE, quietly = TRUE)
# Set up the data source and the tickers for all the ETFs...
data.source = c("yahoo")
tickers.etf = c("VGSIX", "VUSTX", "VGTSX", "VFISX", "VTSMX", "VFITX", "VEIEX", "VIPSX")
tickers.human = c("Real Est", "USTSY Long", "For Eq", "USTSY Short", "All Eq", "USTSY Int.", "EM Eq", "Infl Sec.")
tickers.bench = c("DJIA", "^GSPC")
tsy.2y <- c("DGS2")
# Get the data from yahoo and FRED...
suppressWarnings(getData(tickers.etf, data.source))
```

```
VGSIX 1
VUSTX 2
VGTSX 3
VFISX 4
VTSMX 5
VFITX 6
VEIEX 7
VIPSX 8
```

```
suppressWarnings(getData(tickers.bench, data.source))
```

```
DJIA 1
^GSPC 2
```

```
suppressWarnings(getData(tsy.2y, datasrc = "FRED"))
```

```
DGS2 1
```

I use of a couple of helper functions I wrote to make life a little easier: getData(), makeIndex(), calcWeights(), and getOHLC(). The code for these functions can be found at the end of this post.

Next, put all the variables that were just loaded into the environment into a list and set the inception date of the portfolio:

```
etfs <- list(VGSIX, VUSTX, VGTSX, VFISX, VTSMX, VFITX, VEIEX, VIPSX)
first.date <- c("2012-10-17/") # inception data for portfolio...
# Get all the closing prices into a vector starting from the inception date...
etfs_close <- getOHLC(etfs, "C")
etfs_close <- etfs_close[first.date]
# Specify the initial number of shares that were purchased and the initial investment...
shares <- c(2347.447, 977.96, 867.798, 1167.414, 2086.846, 1080.06, 1409.844, 2615.382)
init.invest <- 250000
```

Now that we have the relevant data and some information about the number of shares purchased and the original investment amount, we can set up a portfolio. First we need to sort out some basic mechanics. For example, we need to have the most recent closing price for each of the tickers we imported. We need this in order to mark-to-market the portfolio today:

```
mtm_last <- sum(last(etfs_close) * shares)
mtm_last
```

```
## [1] 266368
```

```
port_value <- as.xts(apply(etfs_close, 1, FUN = function(x) sum(x * shares)))
plot.xts(port_value, las = 1) # A line chart of the portfolio value in dollars...
```

What follows is a series of functions from the PerformanceAnalytics package that will help us look at the performance of the portfolio. The benchmark portfolio will be a 60/40 stock and intermediate bond portfolio. I don’t think using the SP500 is really a sensible benchmark because going all-in on stocks seems, well non-sensical. As it turns out, the 60/40 (just like the 1/n) portfolio is actually tough to beat.

```
bench.60 <- periodReturn(GSPC[first.date][, 4], period = "daily", subset = NULL, type = "log")
bench.40 <- periodReturn(VFITX[first.date][, 4], period = "daily", subset = NULL, type = "log")
bench_ret <- 0.6 * bench.60 + 0.4 * bench.40 # Return stream for the 60/40 benchmark portfolio...
port_ret <- periodReturn(port_value, period = "daily", subset = NULL, type = "log") # Ret. stream for our portfolio...
port_index <- makeIndex(port_ret, inv = FALSE, ret = TRUE) # Our portfolio indexed to 100 at inception...
bench_index <- makeIndex(bench_ret, inv = FALSE, ret = TRUE) # Benchmark portfolio indexed to 100 at our inception date...
# Setting up some variables to mach the PerformanceAnalytics lexicon...
Ra <- port_ret
Rb <- bench_ret
dts <- index(Ra, 0)
Rb <- xts(Rb, dts)
Rf <- as.numeric(last(DGS2)/100/252)
```

The performance of our portfolio relative to the benchmark:

```
chart.RelativePerformance(Ra, as.vector(Rb), main = "Relative Performace vs. Benchmark", xaxis = TRUE)
```

How much our portfolio outperforms the benchmark on an anuualized basis:

```
act.premium <- ActivePremium(Ra, Rb, scale = 252)
act.premium
```

```
## [1] -0.04434
```

The weights of the portfolio at inception, now, and over time:

```
# The initial weights of the portfolio:
weights_init <- (first(etfs_close) * shares)/init.invest
weights_init
```

```
## VGSIX.Close VUSTX.Close VGTSX.Close VFISX.Close VTSMX.Close
## 2012-10-17 0.2039 0.05152 0.05078 0.05034 0.3034
VFITX.Close VEIEX.Close VIPSX.Close
## 2012-10-17 0.05068 0.1515 0.1547
```

```
# The weights of the portfolio now:
weights_last <- (last(etfs_close) * shares)/init.invest
weights_last
```

```
## VGSIX.Close VUSTX.Close VGTSX.Close VFISX.Close VTSMX.Close
## 2013-07-22 0.2264 0.04604 0.05387 0.04997 0.3563
## VFITX.Close VEIEX.Close VIPSX.Close
## 2013-07-22 0.04908 0.142 0.1419
```

```
# Change in weights since inception:
weights_chg <- as.vector(weights_last) - as.vector(weights_init)
weights_chg
```

```
## [1] 0.0225355 -0.0054766 0.0030894 -0.0003736 0.0528389 -0.0015985
## [7] -0.0095305 -0.0128677
```

```
# Display the weights of each asset over time:
port_weights <- calcWeights(etfs_close, shares, init.invest)
par(mfrow = c(2, 2))
for (i in 1:length(tickers.etf)) {
plot.xts(port_weights[, i], las = 1, type = "l", main = paste(tickers.human[i]))
}
```

The evolution of weights over time:

Price evolution over time:

```
par(mfrow = c(2, 2))
for (i in 1:length(tickers.etf)) {
plot.xts(makeIndex(etfs_close[, i], inv = FALSE, ret = FALSE), las = 1,
type = "l", main = paste(tickers.human[i]))
}
```

Let’s generate return streams for all of the ETFs in the portfolio and then perform some operations on them:

```
etfs.ret <- NULL # A data frame that holds all of the etf return streams...
for (i in 1:length(tickers.etf)) {
temp <- as.xts(periodReturn(etfs_close[, i], period = "daily", type = "log"))
etfs.ret <- cbind(etfs.ret, temp)
}
names(etfs.ret) <- tickers.human
head(etfs.ret)
```

```
## Real Est USTSY Long For Eq USTSY Short All Eq
## 2012-10-17 0.0000000 0.000000 0.000000 0 0.000000
## 2012-10-18 0.0105385 -0.005329 -0.003423 0 -0.002203
## 2012-10-19 -0.0073193 0.011385 -0.011728 0 -0.016681
## 2012-10-22 -0.0059867 -0.005297 0.006226 0 0.000000
## 2012-10-23 -0.0092808 0.011317 -0.018796 0 -0.013264
## 2012-10-24 -0.0004663 -0.007530 0.001404 0 -0.002845
## USTSY Int. EM Eq Infl Sec.
## 2012-10-17 0.0000000 0.000000 0.0000000
## 2012-10-18 -0.0008529 -0.001490 0.0006759
## 2012-10-19 0.0025565 -0.014265 0.0033727
## 2012-10-22 -0.0025565 0.010530 -0.0013477
## 2012-10-23 0.0025565 -0.018121 0.0026936
## 2012-10-24 -0.0008514 0.001523 -0.0033681
```

Here is a chart that shows the relative performance vs. the benchmark portfolio for each of the assets in the portfolio. I don’t love the color scheme, but we can fix that later.

```
par(mfrow = c(1, 1))
chart.RelativePerformance(etfs.ret, as.vector(Rb), main = "Relative Performace vs. Benchmark",
colorset = c(1:8), xaxis = TRUE, ylog = FALSE, legend.loc = "bottomleft",
cex.legend = 0.8)
```

Here is a chart that shows the returns for each asset class in bar chart form with the 20 day Std Dev and the most recent 1 day VaR (95%) observation indicated by a solid line:

```
par(mfrow = c(1, 1))
charts.BarVaR(etfs.ret[, 1:8], width = 20, gap = 0, methods = "StdDev", p = 0.95,
clean = "none", all = TRUE, show.clean = FALSE, show.horizontal = TRUE,
show.symmetric = FALSE, show.endvalue = TRUE, show.greenredbars = TRUE,
ylim = NA, colorset = 1:12, lty = 1, ypad = 0, legend.cex = 0.8)
```

Here is a nice table of CAPM parameters:

```
table.CAPM(Ra, Rb, scale = 252, Rf = Rf, digits = 4)
```

```
Alpha -0.0002
Beta 1.1291
Beta+ 1.0792
Beta- 1.2131
R-squared 0.8743
Annualized Alpha -0.0512
Correlation 0.9351
Correlation p-value 0.0000
Tracking Error 0.0000
Active Premium -0.0443
Information Ratio -Inf
Treynor Ratio 0.0503
```

And a look at some historical and parametric VaR estimates:

```
chart.VaRSensitivity(Ra, methods = c("HistoricalVaR", "ModifiedVaR", "GaussianVaR"))
```

In the next post, I’ll continue the analysis with a look at the drawdowns, in particular, the most recent drawdown which we still haven’t fully recovered from. Here is a look at the largest drawdowns since the inception date in October of 2012:

```
table.Drawdowns(Ra, top = 5, digits = 4)
```

```
## From Trough To Depth Length To Trough Recovery
## 1 2013-05-22 2013-06-24 <NA> -0.1007 43 23 NA
## 2 2012-10-19 2012-11-15 2012-12-10 -0.0364 34 18 16
## 3 2013-04-12 2013-04-18 2013-04-25 -0.0197 10 5 5
## 4 2012-12-19 2012-12-28 2013-01-02 -0.0171 9 7 2
## 5 2013-02-20 2013-02-25 2013-03-05 -0.0163 10 4 6
```

Keep in mind that with a 1% 1-day VaR (95%), the most recent drawdown was a 10x excession! That ranks up there with some of the largest 1 day experiences from 2008-2009! (See my earlier pieces on using VaR to examine historical crises) That’s a bit alarming and something I’ll discuss more next time.

Thanks for reading!

Disclaimer: This blog post is not intended as investment advice and was written for information purposes only. Please take care when running your own portfolio. Nobody cares as much about your money as you do.

Code Snippets for Helper Functions:

```
getData<-function(tickers,datasrc){
for (i in 1:length(tickers)){
cat(tickers[i],i,"\n")
getSymbols(tickers[i],src=datasrc,
auto.assign=getOption("getSymbols.auto.assign",TRUE),
env=parent.frame())
}
}
makeIndex<-function(x,inv,ret){
# Takes an xts object x and returns an index starting at 100 and evolving as the log returns of x.
# The inv flag tells whether or not to invert the series before calculating returns.
# The ret flag tells whether or not we have been passed a series of returns already.
init.val<-100
dts<-index(x,0)
if (inv==TRUE) data<-1/x else data<-x
if (ret==TRUE){ # we have a series of returns...
ret.series<-x
} else {
ret.series<-periodReturn(data,period="daily",subset=NULL,type="log")
dts<-index(ret.series,0)
}
n<-length(ret.series)
new.series<-ret.series
new.series[1]<-init.val
for (i in 2:n){
new.series[i]<-(1+ret.series[i-1])*new.series[i-1]
}
names(new.series)<-c("index")
return(new.series)
} # My custom index funtion for converting indices to 100 based at inception.
calcWeights<-function(prices,numshares,initial){
ret<-NULL
for (i in 1:length(numshares)){
sh<-numshares[i]
ret<-cbind(ret,sh*prices[,i]/initial)
}
return(ret)
}
getOHLC<-function(assets,OHLC){
# Takes a list of assets and returns either the Open, High, Low, or Close depending
# on the passed value of HLOC. Return value is of type xts/zoo.
ret<-NULL
for (i in 1:length(assets)){
if (OHLC=="O" || OHLC=="Open"){
ret<-cbind(ret,assets[[i]][,1])
} else {
if (OHLC=="H" || OHLC=="High"){
ret<-cbind(ret,assets[[i]][,2])
} else {
if (OHLC=="L" || OHLC=="Low"){
ret<-cbind(ret,assets[[i]][,3])
} else {
if (OHLC=="C" || OHLC=="Close"){
ret<-cbind(ret,assets[[i]][,4])
}
}
}
}
}
return(ret)
}
```

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**From Guinness to GARCH**.

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