5.2 Strategy Implementation
The final step is implementing this strategy to create a signal. Let’s begin by reading in the aggregate indicator and return files to our R studio workspace.
x <- as.matrix(mat.read(indicator.file)) # GET ACTIVE/PASSIVE INDICATOR C:\\EPFR\\monthly\\ActPasCtry-monthly.csv
y <- mat.read(ret.file) # GET TOTAL RETURN INDEX C:\\EPFR\\returns\\PsuedoReturns-Country-ETF-daily.csvBefore the data is ready, we will first need to apply the mat.daily.to.monthly() function to ensure that return data is correctly indexed by month, as mentioned previously (help: ?mat.daily.to.monthly()).
One of our first options is choosing the universe we want to use. EPFR has tested this signal within three different universes of countries: ACWI (All Country World Index), EAFE (Europe, Australasia, and the Far East), and EM (Emerging Markets). For this example, we choose ACWI, which includes 52 countries.
Depending on what universe \(idx\) the user chooses to test, the indicator file \(x\) and return file \(y\) must both be subset to the correct countries. Running the code below, which calls from functions contained inlibrary('EPFR'), helps identify every member that was included the selected universe during the period over which we are backtesting.
x <- x[, is.element(dimnames(x)[[2]], Ctry.msci.members.rng(idx, dimnames(x)[[1]][1], dimnames(x)[[1]][dim(x)[1]]))] # SUBSET TO INDEX COUNTRIESA few other adjustments must also be applied to our monthly Active/Passive signal data to ensure that it aligns with returns. First, the internally-generated fund returns are only available with sufficient coverage from the end of 2015 onwards. Second, fund returns for country ISO codes JO and VE are unavailable.
startdate <- "20150512"
x <- x[rownames(x)>=startdate, ] # SUBSET TIME PERIOD
ctry <- c('JO', 'VE')
x <- x[, !(dimnames(x)[[2]] %in% ctry)]Next, we will need to ensure that the data structure in \(x\) and \(y\) are completely aligned, having the same column names in the same order. Below we will subset the columns of \(y\) to use the same countries, in the same order as \(x\).
* Note: subsetting can also be done when creating the indicator and return files
5.2.1 Moving Sum of Indicator
Next, we set up a variable for our lookback period. This variable will be the window of time across which we smooth the signal for each country. The lookback period we choose for our demonstrations is 12 months.
Now, using the function from the library('EPFR.r'), called compound.flows() we compute the moving sum of our signal over the trailing lookback period for each country.
| AU | BR | CA | CN | ID | IN | JP | KR | MX | MY | PH | RU | SG | TH | TR | TW | ZA | AR | CL | CO | CZ | EG | HU | IL | NZ | NO | PE | PL | SE | CH | GB | AT | BE | DK | FI | FR | DE | GR | IE | IT | NL | PT | ES | HK | US | MA | PK | AE | QA | SA | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 202201 | -5.117164 | 4.678409 | -5.655730 | 2.567462 | 4.723583 | 5.463615 | -5.396886 | 5.092788 | 5.806146 | -8.940355 | 0.2127890 | 11.291808 | 6.580787 | -4.331993 | 4.598560 | 1.717442 | -2.337778 | 37.33551 | -1.852158 | -4.854193 | 4.747390 | 31.76519 | 28.36629 | -2.172202 | -4.960506 | -0.2916124 | 13.09126 | 7.164393 | -1.817267 | -1.976079 | -1.1403057 | 2.2294622 | -5.361904 | 0.1641512 | -4.941868 | -1.144588 | -2.466260 | 21.57215 | 9.252658 | -2.382309 | -1.250053 | 1.183348 | -4.141872 | 1.628550 | 0.5623372 | 2.442255 | 36.00374 | -2.001183 | -4.747304 | -4.489196 |
| 202202 | -5.072419 | 4.637230 | -5.621818 | 2.574939 | 5.331131 | 5.494082 | -5.388036 | 5.121049 | 5.941346 | -8.932020 | 0.4178712 | 10.642956 | 6.848616 | -4.216254 | 4.004105 | 1.822039 | -2.401967 | 39.95124 | -1.770836 | -4.858818 | 4.345430 | 30.62884 | 27.65854 | -2.324806 | -4.962109 | -0.5969357 | 13.16735 | 7.116680 | -1.931579 | -1.983764 | -1.0847287 | 1.6754867 | -5.465089 | 0.2845010 | -4.910503 | -1.164140 | -2.437013 | 21.85479 | 9.576143 | -2.471491 | -1.279265 | 1.084992 | -4.192530 | 1.717976 | 0.5468860 | 2.468647 | 36.43622 | -2.196695 | -4.636670 | -4.465992 |
| 202203 | -5.015681 | 4.643543 | -5.574692 | 2.597466 | 6.155813 | 5.484428 | -5.358121 | 5.147998 | 6.013065 | -8.930333 | 0.5304089 | 11.705001 | 7.138094 | -4.124273 | 3.461151 | 1.894532 | -2.465178 | 41.44260 | -1.847794 | -4.892082 | 3.413912 | 29.36388 | 26.38921 | -2.492902 | -4.796030 | -0.8192064 | 13.35556 | 6.587172 | -1.989177 | -1.978598 | -1.0278146 | 1.3565412 | -5.542525 | 0.2927595 | -4.913480 | -1.203407 | -2.435036 | 21.01725 | 10.011778 | -2.557305 | -1.358146 | 1.102749 | -4.263043 | 1.870577 | 0.5366788 | 2.639549 | 35.90684 | -2.383396 | -4.548398 | -4.496952 |
| 202204 | -4.947918 | 4.535185 | -5.495884 | 2.520172 | 6.801915 | 5.411781 | -5.328401 | 5.101505 | 6.032498 | -8.918860 | 0.4628795 | 10.434452 | 7.345398 | -4.049834 | 2.570905 | 1.894301 | -2.578488 | 43.34312 | -2.056172 | -4.943089 | 2.905736 | 27.74858 | 26.86343 | -2.622450 | -4.680218 | -1.0788292 | 12.86845 | 6.647043 | -1.984618 | -1.980360 | -0.9948773 | 1.1127796 | -5.603665 | 0.3202932 | -4.919820 | -1.221229 | -2.429764 | 19.64961 | 10.381683 | -2.613288 | -1.398923 | 1.051464 | -4.309179 | 1.910272 | 0.6001556 | 2.517206 | 34.76934 | -2.499323 | -4.464717 | -4.523993 |
| 202205 | -4.820733 | 4.507865 | -5.434879 | 2.465613 | 7.397669 | 5.387254 | -5.277615 | 5.057851 | 6.143054 | -8.821450 | 0.3577807 | 9.211567 | 7.630802 | -3.913319 | 1.788540 | 1.904205 | -2.730111 | 43.94098 | -2.188964 | -4.991435 | 2.297136 | 26.12656 | 27.10910 | -2.688053 | -4.603027 | -1.2426424 | 12.76230 | 6.535463 | -1.951538 | -1.976833 | -0.9690803 | 0.8319998 | -5.711483 | 0.3444544 | -4.914463 | -1.230629 | -2.437072 | 18.39921 | 10.585603 | -2.657278 | -1.443286 | 1.065102 | -4.333185 | 2.030077 | 0.6219051 | 2.330161 | 33.43916 | -2.482779 | -4.381071 | -4.558491 |
| 202206 | -4.671999 | 4.474621 | -5.356142 | 2.505159 | 7.969634 | 5.359422 | -5.231112 | 4.989937 | 6.264760 | -8.704054 | 0.1956019 | 8.055630 | 7.883029 | -3.736385 | 1.005881 | 1.885444 | -2.846336 | 45.64295 | -2.337513 | -4.882090 | 1.794952 | 24.42459 | 26.72583 | -2.756549 | -4.485215 | -1.3480140 | 12.58793 | 6.386792 | -1.964803 | -1.980810 | -0.9705799 | 0.5179211 | -5.774074 | 0.3909402 | -4.924925 | -1.248182 | -2.444340 | 17.20674 | 10.804709 | -2.718384 | -1.487150 | 1.255855 | -4.375402 | 2.150373 | 0.6290547 | 2.121053 | 31.55198 | -2.326925 | -4.316165 | -4.519375 |
5.2.2 Total Return Index
We will now convert our percentage returns data \(y\) to total index returns indexed so that time moves forward. To do this, we will use the function ret.to.idx() from library('EPFR.r'). We will also use the functions map.rname() to ensure the row names of the matrices line up with our flow file and ret.idx.gaps.fix() to replace any NA values. Please refer to the library documentation for the complete list of parameters for these functions (tip: ?ret.to.idx(),?ret.idx.gaps.fix() ).
5.2.3 Ranking Countries
Next, we sort each of the countries in our universe into five equal bins based on the last 12-month active/passive indicator values for the selected holding period. To do this, we will use the function from library('EPFR.r'), called bbk(). This function will output a standardized backtest result.
The bbk() function requires our 12-month active/passive indicator, the total return index data, and our selected universe. Please refer to the library documentation for the complete list of parameters of this function (tip: ?bbk()).
The first parameter we add is the number of bins we want to use. For our case, we want to use 5 because our strategy is to go long the top fifth and short the bottom fifth.
Since EPFR data is published with a T+23 day lag and is released around 5:00 pm EST, we account for a T+1 month delay in our model.
The day of the week the rebalancing occurs is at the user’s discretion, but for this example we will set the day of the week to trade as N/A.This allows the bbk() function to default to monthly-indexed returns, and avoids trading on a specific weekday on each rebalancing date.
Additionally, we also evaluate the returns for different holding periods. The user can input the return horizons that they are interested in here. For this example, we define a return horizon for monthly, quarterly, semi-annual, and annual rebalancing, but is it important to note that this model can be re-balanced as desired.
Now that we have defined all of our inputs, to rank the countries into quintiles by their 12-month active/passive indicator, we call the function bbk() for a one-month holding period. By adding the selected backtesting universe as an input to the function, we can ensure that the model tracks additions and removals of countries over time, and is therefore able to identify all members on a point-in-time basis.
5.2.4 Model
12-month cumulative indicator ranked into quintiles (computed only where forward returns are available)
| AU | BR | CA | CN | ID | IN | JP | KR | MX | MY | PH | RU | SG | TH | TR | TW | ZA | AR | CL | CO | CZ | EG | HU | IL | NZ | NO | PE | PL | SE | CH | GB | AT | BE | DK | FI | FR | DE | GR | IE | IT | NL | PT | ES | HK | US | MA | PK | AE | QA | SA | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 202210 | NA | 2 | 5 | 2 | 1 | 2 | 5 | 2 | 1 | 5 | 3 | NA | NA | 4 | 3 | 2 | 4 | NA | 4 | 5 | NA | 1 | 1 | 4 | NA | 3 | 1 | 1 | 3 | 4 | 3 | 3 | 5 | 2 | 5 | 3 | 4 | 1 | 1 | 4 | 3 | 2 | 5 | NA | 2 | NA | NA | 3 | 4 | 5 |
| 202209 | NA | 2 | 5 | 2 | 1 | 2 | 5 | 2 | 1 | 5 | 3 | NA | NA | 4 | 3 | 2 | 4 | NA | 4 | 5 | 2 | 1 | 1 | 4 | NA | 3 | 1 | 1 | 3 | 4 | 3 | 3 | 5 | 2 | 5 | 3 | 4 | 1 | 1 | 4 | 3 | 2 | 5 | NA | 2 | NA | NA | 4 | 4 | 5 |
| 202208 | NA | 2 | 5 | 2 | 1 | 2 | 5 | 2 | 1 | 5 | 3 | NA | NA | 4 | 3 | 2 | 4 | NA | 4 | 5 | 2 | 1 | 1 | 4 | NA | 3 | 1 | 1 | 3 | 4 | 3 | 3 | 5 | 2 | 5 | 3 | 4 | 1 | 1 | 4 | 3 | 2 | 5 | NA | 2 | NA | NA | 4 | 4 | 5 |
| 202207 | NA | 2 | 5 | 2 | 1 | 2 | 5 | 2 | 1 | 5 | 3 | NA | NA | 4 | 2 | 2 | 4 | NA | 4 | 5 | 2 | 1 | 1 | 4 | NA | 3 | 1 | 1 | 3 | 4 | 3 | 3 | 5 | 3 | 5 | 3 | 4 | 1 | 1 | 4 | 3 | 2 | 5 | NA | 2 | NA | NA | 4 | 4 | 5 |
| 202206 | NA | 2 | 5 | 2 | 1 | 2 | 5 | 2 | 1 | 5 | 3 | NA | NA | 4 | 2 | 2 | 4 | NA | 4 | 5 | 2 | 1 | 1 | 4 | NA | 3 | 1 | 1 | 3 | 4 | 3 | 2 | 5 | 3 | 5 | 3 | 4 | 1 | 1 | 4 | 3 | 2 | 4 | NA | 3 | NA | NA | 4 | 5 | 5 |
| 202205 | NA | 2 | 5 | 2 | 1 | 2 | 5 | 2 | 1 | 5 | 3 | NA | NA | 4 | 2 | 2 | 4 | NA | 4 | 5 | 2 | 1 | 1 | 4 | NA | 3 | 1 | 1 | 4 | 3 | 3 | 2 | 5 | 3 | 5 | 3 | 4 | 1 | 1 | 4 | 3 | 2 | 4 | NA | 3 | NA | NA | 4 | 5 | 5 |
Quintile returns over the equal-weight universe
| Q1 | Q2 | Q3 | Q4 | Q5 | TxB | uRet | |
|---|---|---|---|---|---|---|---|
| 202210 | 0.1123069 | 0.5675860 | -0.2833644 | 0.0805593 | -0.4416673 | 0.5539742 | 1.2956635 |
| 202209 | -0.0535121 | 0.1320834 | -0.0766896 | 0.0116607 | -0.0315104 | -0.0220016 | 0.1737691 |
| 202208 | -0.2578973 | 0.0816368 | 0.2255144 | 0.1625414 | -0.2423176 | -0.0155797 | 0.3692333 |
| 202207 | 0.1518092 | 0.4501508 | -0.0677247 | -0.2478474 | -0.3116759 | 0.4634851 | -0.6708180 |
| 202206 | 0.2348840 | -0.2209259 | 0.6335878 | 0.0079502 | -0.6288742 | 0.8637582 | 0.8609815 |
| 202205 | 0.0731573 | -0.1315785 | -0.0236833 | -0.0810249 | 0.1897048 | -0.1165475 | -1.4172222 |
Def: TxB represents summary statistics for the long/short portfolio (top - bottom = Q1 - Q5 = overall portfolio returns)
5.2.5 Performance
Go long the top basket and short the bottom basket.
Performance over all holding periods
fcn <- function(retW) {as.matrix(bbk(x, y, 1, retW, nBin, doW, T, 0, delay, idx)$summ)} # DEFINE SUMMARY FUNCTION
sapply(split(hz, hz), fcn, simplify = "array") # WRITE SUMMARIES| Q1 | Q2 | Q3 | Q4 | Q5 | TxB | uRet | |
|---|---|---|---|---|---|---|---|
| Monthly | |||||||
| AnnMn | 0.0 | 0.1 | 0.6 | -0.6 | -0.4 | 0.4 | -1.1 |
| AnnSd | 2.0 | 1.3 | 1.0 | 1.2 | 0.9 | 2.6 | 2.3 |
| Sharpe | 1.9 | 8.7 | 64.6 | -48.4 | -41.0 | 15.4 | -49.1 |
| HitRate | 9.0 | 2.6 | 6.4 | -5.1 | -7.7 | 12.8 | -10.8 |
| Beta | NA | NA | NA | NA | NA | NA | 1.0 |
| Alpha | NA | NA | NA | NA | NA | NA | 0.0 |
| DrawDn | -5.0 | -2.8 | -1.6 | -6.4 | -2.9 | -6.4 | -12.6 |
| DDnBeg | 202201 | 201908 | 202104 | 201708 | 201606 | 202201 | 201908 |
| DDnN | 4 | 20 | 8 | 49 | 54 | 5 | 34 |
| AnnTo | 100 | 122 | 128 | 125 | 88 | 188 | 0 |
| Quarterly | |||||||
| AnnMn | 0.1 | 0.1 | 0.8 | -0.6 | -0.4 | 0.5 | -1.3 |
| AnnSd | 2.1 | 1.3 | 1.0 | 1.2 | 0.8 | 2.6 | 2.1 |
| Sharpe | 4.4 | 10.2 | 76.1 | -51.7 | -52.5 | 20.0 | -62.0 |
| HitRate | 7.8 | 3.8 | 17.1 | -9.2 | -11.9 | 23.6 | -8.5 |
| Beta | NA | NA | NA | NA | NA | NA | 1.0 |
| Alpha | NA | NA | NA | NA | NA | NA | 0.0 |
| DrawDn | -4.7 | -2.6 | -1.1 | -5.9 | -2.9 | -5.8 | -12.1 |
| DDnBeg | 202141 | 201941 | 202037 | 201709 | 201607 | 202141 | 201909 |
| DDnN | 2 | 6 | 3 | 16 | 17 | 2 | 12 |
| AnnTo | 53 | 67 | 66 | 67 | 44 | 97 | 0 |
| Semi-Annual | |||||||
| AnnMn | 0.2 | 0.2 | 0.8 | -0.7 | -0.5 | 0.7 | -1.4 |
| AnnSd | 2.0 | 1.2 | 1.1 | 1.2 | 0.9 | 2.5 | 2.4 |
| Sharpe | 9.0 | 18.2 | 72.5 | -55.0 | -57.8 | 28.1 | -59.1 |
| HitRate | 14.3 | 2.0 | 25.4 | -9.0 | -17.0 | 19.9 | -5.4 |
| Beta | NA | NA | NA | NA | NA | NA | 1.0 |
| Alpha | NA | NA | NA | NA | NA | NA | 0.0 |
| DrawDn | -3.7 | -2.2 | -0.8 | -5.6 | -3.5 | -4.6 | -11.4 |
| DDnBeg | 202125 | 201924 | 201971 | 201710 | 201608 | 202124 | 201908 |
| DDnN | 1 | 4 | 1 | 8 | 10 | 1 | 6 |
| AnnTo | 44 | 53 | 53 | 53 | 37 | 81 | 0 |
| Annually | |||||||
| AnnMn | 0.2 | 0.2 | 0.9 | -0.7 | -0.6 | 0.8 | -1.5 |
| AnnSd | 1.8 | 1.0 | 0.9 | 1.2 | 0.7 | 2.3 | 2.8 |
| Sharpe | 10.5 | 25.1 | 133.6 | -60.9 | -89.6 | 36.4 | -53.1 |
| HitRate | 9.2 | 10.6 | 35.0 | -22.5 | -26.4 | 21.4 | -16.7 |
| Beta | NA | NA | NA | NA | NA | NA | 1.0 |
| Alpha | NA | NA | NA | NA | NA | NA | 0.0 |
| DrawDn | -2.8 | -1.5 | -0.3 | -4.8 | -3.7 | -2.9 | -10.3 |
| DDnBeg | 202073 | 201923 | 202032 | 201706 | 201648 | 202082 | 201906 |
| DDnN | 1 | 2 | 1 | 4 | 4 | 1 | 3 |
| AnnTo | 36 | 42 | 42 | 43 | 34 | 69 | 0 |
Annualized mean one-week returns
| Q1 | Q2 | Q3 | Q4 | Q5 | TxB | uRet | nPrds | |
|---|---|---|---|---|---|---|---|---|
| 2016 | 2.1 | -2.5 | 0.5 | 1.6 | -1.7 | 3.8 | 2.8 | 6 |
| 2017 | -0.2 | -0.5 | 1.0 | 0.0 | -0.4 | 0.1 | -0.2 | 12 |
| 2018 | -1.3 | 1.1 | 1.7 | -1.6 | 0.1 | -1.4 | 0.5 | 12 |
| 2019 | 0.9 | 1.1 | -0.8 | 0.2 | -1.4 | 2.3 | 1.1 | 12 |
| 2020 | 2.3 | -1.0 | 2.7 | -3.6 | -0.4 | 2.6 | -4.6 | 12 |
| 2021 | 2.1 | -1.2 | -1.2 | -0.7 | 0.8 | 1.3 | -5.6 | 12 |
| 2022 | -4.5 | 2.5 | 0.6 | 1.3 | -0.3 | -4.2 | -0.3 | 12 |