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# Introduction

Active funds have done poorly over the last ten years, and in most cases, struggled to justify their fees. A growing list of commentators appropriately advocate for index funds, although sometimes go a little beyond what we believe to be fairly representing the facts. The inspiration for this article is this post by Asset Builder blog site American Funds Says, “We Can Beat Index Funds” scrutinizing claims by the fund group. Asset Builder asserts that “Even without this commission, the S&P 500 beat the aggregate returns of these (”American“) funds over the past 1-, 3-, 5-, 10- and 15-year periods”. In the post, there is a supporting chart showing a group of American Funds (“AF”) funds compared to the Vanguard Total Market (“TMI”) index. This analysis struck us in conflict with our own experience as actual holders of a core portfolio of eight AF over the last 20 years, so this post will be about exploring this data.

In this article, we will download the weekly closing prices of the relevant AF and the most comparable Vanguard Funds, re-construct our portfolio and estimate the corresponding weighting of different asset classes for each, replicate a relevant benchmark portfolio of Vanguard index funds, and explore their relative performance histories over the period to try to square the two perspectives. We will also consider the possibility that AF’s declining out-performance versus our customized benchmark over the last 15 years may have to do with growing fee differentials with index alternatives.

As usual, Redwall would like to avoid defending to any particular viewpoint other than to follow the data and see where it leads. If we have made any mistakes in our assumptions or the data used, we welcome polite commentary to set us straight. We have no relationship with the AF, and for the most part are sympathetic to those who say that index funds may be the best choice for most investors. All the code is available on Github for anybody to replicate. Also to be clear, Redwall is not an investment adviser and is making no investment recommendations.

# Set Up of AF Portfolio

During the 2000 bear market, Redwall put substantial research into its investment strategy, and concluded that the AF had a competitive advantage over other mutual fund groups. Capital Group, the operator of the AF, was founded at the beginning of the Great Depression in 1932. Capital had a large group of experienced managers sitting in different locations around the world, with varied perspectives, owning a heavy component of their own funds, with each investing in concentrated portfolio of their own highest conviction ideas. Managers had strong incentive to think long-term instead of for the next quarter. If the style of one manager of the fund was out of sync with the current flavor of the market, others might pick up the pace. The cost of research could be leveraged over a much larger asset base than most mutual funds while still keeping running costs at a manageable level. Being one of the largest managers, analysts and managers would always have access to the best information and advice. Convinced that AF were a solid set-it and forget-it portfolio, investments were were made with monthly dollar-cost averaging without paying loads, and mostly between 2001-2004.

# Description of American Funds Held

The AF don’t fit well into the traditional Morningstar investment categories. By in large, its portfolios are many times larger than other active funds, and mostly stick to the largest of the large capitalization global stocks. Washington Mutual mostly owns US mega caps value stocks and holds no cash, while Amcap often moves down the market capitalization spectrum a bit with growth stocks, and will hold a substantial amount of cash. Capital Income builder has a mix of US and overseas stocks which pay high dividends with room to grow. Income Fund of America is similar to Capital Income builder, but has a more US oriented mix and takes more credit risk. Capital World Growth and Income is like Washington Mutual in its stock selection, but will hold a small amount of credit at times when it makes more sense than the equity. New Perspective owns the largest multinational companies domiciled in the US and around the world, but have acquired the competency to expand across borders.

# New Geography of Investing

It was probably from operating New Perspective, set up to invest in companies having a majority of revenues of coming from outside of their country of domicile, which led AF to discover a new way of looking at its portfolios. In the New Geography of Investing campaign launched in 2016, they do an excellent job of explaining the concept that a portfolio shouldn’t be constrained by company domicile, a central pillar of the Morningstar ratings platform. In addition to the country of domicile, AF now disclose the aggregated geographic mix of revenues of all of its portfolios on their website, and explain clearly that it doesn’t prioritize fitting its portfolios into Morningstar regional boxes at the expense of finding the best investments. Because of this, a single index benchmark may be less applicable to AF funds than some others.

# Doublecheck Asset Builder Values

We believe that Asset Builder were referring to no-load AF in their table, but were not sure. It has been possible to buy American Fund F-1 class shares load-free since 2016 (with a 3 bps higher annual expense ratio), so there is no reason for anyone that doesn’t want to pay the up-front sales changes for advice to pay one. As shown below, we calculate that Asset Builder’s ending value for is 3-4% too high for the Vanguard Fund, but also too low for 4 out of the 5 AF without loads. For the most part, their assertion that AF’s funds lose to the S&P still holds up, even with these adjustments. If taxes were taken into account, it would widen the performance advantage of TMI. Still, this is a strange pattern (tilting the calculation in favor of TMI and against AF), and makes us a little suspicious of Asset Builder. The assertion doesn’t take into account risk. As we will discuss below, the AF funds are all less volatile than the market over the period.

# Get data from quantmod
tickers <-c("AGTHX","AMCPX","AWSHX","AIVSX","AMRMX", "VTSAX")
asset_builder_data <- lapply(tickers, function(fund) {
getSymbols(
fund,
src = "yahoo",
env = NULL,
from = as.Date("2004-11-30"),
to = as.Date("2019-11-30")
)
})

# Calculate holding period return of $100 invested monthly get_data <- function(xts_obj, load = 0) { # Build data.table dt <- data.table( date = index(xts_obj), price = (Ad(xts_obj[, 6])) ) # Filter monthly dt[, month:=zoo::as.yearmon(date)] dt <- dt[, .SD[1], month] # Adjust load if needed if (!str_detect(names(dt)[3], "price.A.*")) { dt[, shares := 100 / .SD, .SDcols=3] } else { dt[, shares := (100 * (1 - load)) / .SD, .SDcols=3] } # Calculate final value final_price <- as.numeric(dt[nrow(dt), 3]) dt[, final_value := shares * final_price] return <- sum(dt$final_value)

# Return final value
return
}

# Values from Asset Builder table
asset_builder <-
c(42402, 41827, 39981, 37125, 39814, 45112)

# Build comparison table
dt <-data.table(
fund = tickers,
asset_builder,
)
dt
1: AGTHX         42402           43125        40646
2: AMCPX         41827           42539        40093
3: AWSHX         39981           41186        38818
4: AIVSX         37125           37883        35705
5: AMRMX         39814           38989        36747
6: VTSAX         45112           43505        43505

# Customized Vanguard Benchmark Index Portfolio

There is nothing wrong with Asset Builder’s choice of Vanguard Total Market Index (TMI) as a comp for the US funds, but our portfolio also includes several non-US and balanced funds. As shown below, we will be comparing our portfolio to 54.5% of the S&P index. The S&P has an average market capitalization almost twice as large as the Total Market Index, and we believe is more comparable to typical holdings of the AF. We are also including 24.5% of our benchmark in non-US stocks based on our estimated weightings shown in the matrix below. AF also run with a higher amount of cash than index funds, as can be seen with our estimated 7.35% weighting in VFISX below. Cash reserves are a drag on performance during bull markets, so has likely been weighing on AF in recent years. During the 2000 tech crash, extra cash gave AF room to maneuver, and as we show below, helped them achieve ~30% out-performance through the bear market. Our benchmark is more granular, and we believe a more fair comparison than the TMI for our portfolio, but in the end is still only an estimate. Weightings over time have not been static as we have assumed, and we have chosen one set of weightings for the entire 20-year period. A future analysis may look at ways of flexing our weightings matrix over time.

# Funds to query
am_funds <-
c("AMCPX","AWSHX","CAIBX","AMECX","SMCWX","AEPGX", "ANWPX", "CWGIX")
van_funds <-
c("VFINX", "VGTSX", "VBTIX", "VSCIX", "VFISX", "VBINX")
funds <- c(am_funds, van_funds)

# Assumed Vanguard weighting of fund
m <- matrix(
# vfinx, vgtsx, vbtix, vscix,  vfisx, vbinx
c(0.85,  0.05,  0,     0,      0.1,    0,  #amcpx
0.95,  0.02,  0,     0,      0.03,   0,  #awshx
0.35,  0.30,  0.25,  0,      0.1,    0,  #caibx
0.5,   0.15,  0.30,  0,      0.05,   0,  #amecx
0,     0,     0,     0.9,    0.1,    0,  #smcwx
0.05,  0.8,   0,     0.05,   0.1,    0,  #aepgx
0.45,  0.4,  0.05,   0,      0.1,    0,  #cwigx
0.5,   0.45,  0,     0,      0.05,   0), #anwpx
ncol = 6,
byrow=TRUE)

# Weighting of AF portfolio
portfolio <-
c(0.15, 0.20, 0.15, 0.15, 0.05, 0.1, 0.1, 0.1)

# Implied benchmark portfolio
benchmark <- as.vector(colSums(m * portfolio))
benchmark
[1] 0.5450 0.2440 0.0875 0.0500 0.0735 0.0000

In the course of writing this blog, Redwall has frequently expressed amazement that so many analyses, not possible previously, are now enabled so quickly with a few lines of code. Using the quantmod package, here we extract over 20 years of mutual fund data, 80,738 prices for our 14 funds in a matter of seconds, all for free. In addition to stock, mutual fund and index prices, we could just as easily query economic series from FRED with quantmod.

# Get data with quantmod
data <- lapply(funds, function(fund) {
getSymbols(
fund,
src = "yahoo",
env = NULL,
from = as.Date("1997-07-12"),
to = as.Date("2020-06-12")
)
})
names(data) <- funds

# Print a few rows of AWSHX
data$AWSHX['1997-07'] AWSHX.Open AWSHX.High AWSHX.Low AWSHX.Close AWSHX.Volume 1997-07-14 29.66 29.66 29.66 29.66 0 1997-07-15 29.73 29.73 29.73 29.73 0 1997-07-16 29.91 29.91 29.91 29.91 0 1997-07-17 29.73 29.73 29.73 29.73 0 1997-07-18 29.30 29.30 29.30 29.30 0 1997-07-21 29.37 29.37 29.37 29.37 0 1997-07-22 29.97 29.97 29.97 29.97 0 1997-07-23 30.00 30.00 30.00 30.00 0 1997-07-24 30.07 30.07 30.07 30.07 0 1997-07-25 30.03 30.03 30.03 30.03 0 1997-07-28 30.05 30.05 30.05 30.05 0 1997-07-29 30.31 30.31 30.31 30.31 0 1997-07-30 30.61 30.61 30.61 30.61 0 1997-07-31 30.66 30.66 30.66 30.66 0 AWSHX.Adjusted 1997-07-14 8.243302 1997-07-15 8.262762 1997-07-16 8.312786 1997-07-17 8.262762 1997-07-18 8.143247 1997-07-21 8.162707 1997-07-22 8.329458 1997-07-23 8.337800 1997-07-24 8.357253 1997-07-25 8.346141 1997-07-28 8.351695 1997-07-29 8.423957 1997-07-30 8.507337 1997-07-31 8.521233 # Preprocess Data into Weekly Log Returns for Analysis Our data list contains 14 xts (time series) objects with dates and prices of each fund over the period. quantmod also has a suite of tools for processing quantitative market data for stocks, mutual funds and portfolios. In the first line below, we magically select only the adjusted prices and convert them all to weekly log returns. In the second, we merge the time series of all 14 mutual funds on the respective dates into a data.frame. In the third line, we simulate the money growth on$1 of owning the funds in proportion to our portfolio and benchmark vectors and re-balancing every quarter when the target weightings move out of line.

# Convert weekly pries to log returns
fund_returns_list <-
lapply(data, function(fund)

# Build data frame of American and Vanguard funds with weekly log returns by date
fund_returns_df <-
Reduce(function(d1, d2)
merge.xts(d1, d2,
join = 'left',
check.names = TRUE),
fund_returns_list)
names(fund_returns_df) <- funds

# Calculate return on AF re-balanced quarterly with PerformanceAnalytics Return.Portfolio function
portfolio_return <-
Return.portfolio(fund_returns_df[, am_funds],
rebalance_on = 'quarters',
weights = portfolio)

# Calculate return on Vanguard benchmark re-balanced quarterly
benchmark_return <-
Return.portfolio(fund_returns_df[, van_funds],
rebalance_on = 'quarters',
weights = benchmark)

# Show a few lines of portfolio returns
portfolio_return[1:5]
portfolio.returns
1997-07-18      -0.001873959
1997-07-25       0.014072498
1997-08-01       0.007248029
1997-08-08      -0.004673325
1997-08-15      -0.018078169

# AF Steadily Outperforming our Customized Benchmark

The chart below gives a much better “apples-to-apples” benchmark for comparison to our portfolio than the Vanguard Total Market Index would have. It is true that the mainly US-oriented AF that we may not have outperformed as much as the non-US heavy portfolios. But our portfolio is global, and as can be seen here in aggregate, outperforming steadily except for a few relatively short periods. We can see three periods of either under-performance or treading of water relative to the benchmarks at the tail end of the previous two bulls, but then the subsequent out-performance.

chart.RelativePerformance(portfolio_return, benchmark_return)

# Money Difference of AF vs Index Benchmarks

The annual active premium of the AF portfolio over the whole period has been about 1.8% per annum, but as we will discuss below, the fund group’s premium may be compressing. If we choose the starting point to be the beginning of 2003, it falls to 1.02%. Over the full period as shown below in blue, a dollar invested in 1997 would be worth $4.47 while the benchmark would yield$3.03 for the benchmark in orange (a considerable reward for hiring AF even ignoring likely greater tax inefficiency). If we move to 2002 (around when we built our portfolio), the difference falls to $3.16 and$2.66.

chart.CumReturns(
merge.xts(portfolio_return["2002-01-01/"]$portfolio.returns, benchmark_return["2002-01-01/"]$portfolio.returns, join = "left"),
colorset = 1,
begin = "first",
wealth.index = TRUE,
plot.engine = "plotly"
)

# Domestic Equity Funds Leaning Conservatively Throughout the Period

We can see here that both of our mainly US funds managed to reduce their betas and R2 in the run-up and short period after the beginning of the 2000 bear market. Washington Mutual in particular made drastic reductions to exposure, while Amcap did to a lesser extent in 2007-2008. Sharpe ratios are very volatile, and standard deviations briefly reached 60% during 2009 and again this year. Both funds consistently had betas well below one over the entire period, but alpha hardly registers on the graph (This may be down to a scaling issue for us because we are new to this package). AF took a lot of heat for not owning many tech stocks in the run up to the 2000 bust, but the low volatility through that period show it navigating in that period with greater calm than the two subsequent bear markets.

matrix(c(1,2), ncol=2)
[,1] [,2]
[1,]    1    2
charts.RollingRegression(
fund_returns_df[, 1:2],
width = 52,
fund_returns_df[, "VFINX", drop = FALSE],