# Which index should you be tracking?

How do you calculate the average performance of a stock market?

This is a harder question to answer than it may at first seem. For example, the FTSE 100 Index is a measure of the aggregate market capitalisation of the 100 companies in the index. The problem is that the index is greatly influenced by the larger companies in it (the five largest companies in the index account for 27% of the total market capitalisation, while the 21 smallest companies in the index account for only 5% of total capitalisation).

So, how representative is the FTSE 100 Index of the average performance of the 100 component companies?

In the following chart the bars shows the proportion of FTSE 100 companies that out-performed the index in each year for the period 2005-2015, and for reference the line plots the index value. For example, in 2005 55% of the FTSE 100 companies out-performed the index.

As can be seen there is quite a range of annual behaviour here: in 2007 46% of companies out-performed the index, while in 2012, 77% of companies out-performed. In other words, tracking the FTSE 100 Index in 2012 resulted in under-performing 77% of the individual stock performance. In only year, 2007, less than 50% of stock out-performed the index.

For comparison the following is a similar chart to that above, but this time for the FTSE 250 Index.

As can be seen, for the mid-cap index the variability of the proportion of out-performers is far less than for the large-cap index, and the years of individual companies out and under-performance are evenly matched.

A reason for this is that size disparity is greater within the FTSE 100 than the FTSE 250: in the former the largest company has a market capitalisation 47  times greater than the smallest company in the index, the equivalent figure for the FTSE 250 is 10 times.

## Equally-weighted indices

In 2015 the indexing company FTSE Russell introduced a new index to address this. The index is called the FTSE 100 Semi Annual Equally Weighted Index, and each of the 100 companies in the index is given a weight of 1% (that is re-balanced every six months).

NB. Deutsche Bank launched an ETF tracking this index, ticker: XFEW).

Such an index is sometimes called a price-weighted index. Before the age of computers it was common to calculate stock indices this way. For example, the FT 30, Dow Jones Industrial Average, and Nikkei 225 were (or are still) price-weighted indices.

If an investor believes that larger stocks will underperform smaller stocks for a period, then switching out of a traditional market-cap weighted tracker (such as a FTSE 100 ETF) into an equally-weighted tracker  may make sense.

Here’s the system:

At the end of every month,

• if the index is above its 10-month simple moving average: the portfolio is 100% in the market
• if the index is below its 10-month simple moving average: the portfolio is 100% in cash

And that’s it.

So, if we take the FTSE 100 Index as an example, if at the end of a month the FTSE 100 is above its 10-month simple moving average then either,

• the portfolio moves into the market by buying, say FTSE 100 ETFs, (these will be the easiest instrument for most investors, but equally futures, CFDs or spread bets could be used), or
• nothing needs to be done if the portfolio is ready in the market.

Conversely, if at the end of a month the FTSE 100 is below its 10-month simple moving average then the portfolio sells the ETFs and moves 100% to cash; if it is already in cash then nothing is done.

[NB. OK, it's possible that this isn't absolutely the simplest trading system imaginable, but apart from buy and hold it is unlikely there are many systems much simpler than this one!]

The following chart illustrates such a portfolio for the FTSE 100 Index since 1995. The diamond markers indicate the decisions made at the end of each month whether to be in the market (green diamond) or in cash (red diamond).

Roughly, one can see that the system kept the portfolio in the market in uptrends and out of the market (in cash) when the market fell.

This trading system is well-known in the US, what we will look at here is:

1. If the trading system can be profitably applied to the FTSE 100 Index.
2. Whether 10 months is the optimum parameter for the moving average (or would a 5-month, or 15-month, moving average produce superior results)?

Terminology: we will use SMATS(10) to refer to the 10-month simple moving average trading system. And SMATS(5) for the trading system using the 5-month simple moving average etc. Below we will analyse the trading system for 14 different parameters of the simple moving average, i.e. from SMATS(4) to SMATS(16).

## Performance analysis

First, let’s look at the overall profitability of SMATS.

### Profitability

The following chart plots the values of the SMATS portfolios for the 14 different simple moving averages (i.e. 4-month to 16-month). As a benchmark the FTSE 100 is added (i.e. this is the value of a buy and hold FTSE 100 portfolio). All values were re-based to start at 100.

Some observations:

1. By the end of the 20-year period all the SMATS portfolios had out-performed the FTSE 100 – except SMATS(5).
2. By the end of the period, SMATS(10) had the highest value; although it can be seen that it wasn’t consistently the most profitable throughout the whole period.
3. For the first six years (up to August 2001) all SMATS under-performed the FTSE 100. This was caused by the market volatility in 1998 and 2001, which caused the portfolios to be whipsawed in and out of the market.

The following chart summarises the final portfolio values in 2016 after running the trading system from 1995.

By 2016 the STATS(10) portfolio had the highest value of all portfolios at 269; the FTSE 100 buy and hold portfolio a value of 199.

### Risk

We’ve looked at profitability, let’s now consider the risk incurred by each portfolio. We’ll use volatility as a (fairly standard) proxy for risk.

The following chart shows the volatility of the portfolios over the 20-year period.

Not surprisingly the FTSE 100 had the highest volatility. The volatility of the SMATS portfolios was less due to the fact they were in cash for part of the time; broadly their volatility increased as the moving average month parameter increased.

The Sharpe Ratio combines returns with volatility to provide a comparative measure of profitability per unit of risk incurred. The ratio’s purpose is to answer questions of the form: is the profitability of a strategy justified by the risk incurred, compared to another strategy?

The following chart plots the Sharpe Ratio for the 14 portfolios. (The benchmark for the Sharpe Ratio calculation was the FTSE 100 Index.)

SMATS(10) had the highest (i.e. the best) Sharpe Ratio, although close behind were SMATS(14) and SMATS(15).

### Max Drawdown

Maximum Drawdown decribes the maximum loss a portfolio suffered from a previous high value. For example, in this test SMATS(10) had a max drawdown value of 22.8%. This means that over the 20-year test period the portfolio was at most 22.8% under water (from a previous high).

Frankly, max drawdown has more significance for strategies that employ leveraged products (e.g. futures), as drawdowns incur realised losses as margins have to be paid. By contrast in the case of unleveraged equities or ETFs, drawdowns incur unrealised losses. Having said that, unrealised losses can still be uncomfortable and can have a major adverse psychological impact on the investor or trader.

The following chart shows the max drawdown values for the 14 SMATS portfolios and the FTSE 100 Index.

Here the SMATS(10) portfolio only had a middling relative score. The best portfolios (i.e. those with the lowest max drawdowns) were: SMATS(7), SMATS(14), SMATS(15), and SMATS(16).

The following chart shows the average number of trades for the year for each portfolio. For example, over the 20-year test period SMATS(10) portfolio traded 36 times, which is an average of 1.7 times a year.

As would be expected the number of trades decreases as the length of the moving average month parameter increases. In other words, systems get whipsawed less with longer moving averages.

The profitability figures above did not include transaction costs, but with the systems averaging under 2 trades per year the transaction costs would not be significant.

## Summary of analysis

The following table summarises the above analysis. The values are colour-coded with green being the best value through to red being the worst for each respective analysis.

## Conclusion

1. This simple moving average trading system did work for the FTSE 100 (i.e. it out-performed the FTSE 100 Index) over the 20-year period.
2. The best performing portfolio was indeed SMATS(10), i.e. the trading using the 10-month simple moving average. It had the highest absolute profitability and also the highest Sharpe Ratio. After SMATS(10), the best portfolio was the SMATS(14), followed by SMATS(15).

# Diversification with ETFs (update)

This updates the data on a previous analysis of ETF correlation with the FTSE 100 Index.

The following chart shows the 40 ETFs with the highest trading volumes on the LSE and their correlations with the FTSE 100 Index. The ETFs are ranked by the correlation value; the ETFs at the top of the chart have the closest correlation with the FTSE 100 Index.

Notes:

As might be expected the FTSE 100 tracker ETFs are at the top of the above ranking – led by the Vanguard ETF [VUKE].

Rather surprisingly second in the ranking is iShares MSCI World Acc [SWDA], which invests in a broad range of developed companies, but the UK weighting in the ETF is only 7.5%. This ETF has a higher correlation with the FTSE 100 Index than the iShares FTSE 100 [ISF].

Also near the top of the ranking are iShares MSCI Europe Ex-UK [IEUX] and iShares S&P 500 [IDUS].

Most surprising perhaps is the higher ranking of iShares MSCI Emerging Markets [IDEM and IEEM].

In summary, don’t expect much diversification (away from the FTSE 100) by investing in any of the above.

The gold ETFs (Source Physical Markets Gold P-ETC [SGLD], Lyxor Gold Bullion Securities Ltd [GBS] and ETFS Physical Gold [PHAU]) are ranked near the bottom – their correlations are low, albeit not negative.

For maximum diversification away from the FTSE 100, an investor needs to look at the bottom of the list – namely the gilt and T-Bond ETFs (iShares FTSE UK All Stocks Gilt [IGLT] and iShares USD Treasury Bond 7-10 [IDTM]).

Extract taken from The UK Stock Market Almanac.

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# Most traded ETFs – first two months of 2014

The following table shows the LSE-listed ETFs with the greatest average daily trading volume for the last two months (the rank, for comparison, for the last six months is given in the second column).

 Rank(2m) Rank(6m) ETF TIDM 1 1 iShares FTSE 100 ISF 2 2 iShares Markit iBoxx Euro High Yield Bond IHYG 3 3 ETFS Physical Gold PHAU 4 10 Source Physical Markets Gold P-ETC SGLD 5 7 iShares Markit iBoxx \$ High Yield Bond IHYU 6 12 iShares MSCI Emerging Markets IEEM 7 11 iShares V PLC – iShares MSCI Japan Monthly EUR Hedged IJPE 8 13 iShares MSCI Emerging Markets IDEM 9 9 iShares FTSE 250 MIDD 10 4 iShares S&P 500 IUSA 11 14 iShares MSCI World IDWR 12 6 iShares JPMorgan USD Emg Mkts Bond IEMB 13 18 Vanguard S&P 500 ETF VUSD 14 8 iShares S&P 500 IDUS 15 16 iShares MSCI World IWRD 16 20 Vanguard FTSE 100 ETF VUKE 17 19 iShares MSCI Europe Ex-UK IEUX 18 5 Lyxor Gold Bullion Securities Ltd GBS 19 15 iShare \$ Investop Corp Bond Fund LQDE 20 23 iShares MSCI Japan Monthly GBP Hedged IJPH

Trading volumes have increased for emerging market and Japan ETFs in the first two months of the year relative to the previous six months; while volumes have fallen for S&P 500 ETFs.