SMA Research by Antonio Wong

Introduction

The purpose of the study is to investigate the risk and return of a very simple market timing model,

across different tradable markets around the world. The traditional buy and hold strategy has become

increasing under pressure in the latest financial crisis. Lots of blue chip companies especially banks have

drop in value in excess of 80%. Therefore it is of great interest if a timing model would alert investors in

the early stage and allow him to stay out of the crisis time. During the past decade, a lot of new complex

model or indicators have been developed due to the ever advancing computer power. Thousands of

parameters have been created or added-in trying to predict the direction of the market. But sometimes

simple is best. The only significant variable in any index is the price. Therefore in this study only the

simplest indicator will be use, which is the Simple Moving Average (SMA) of the index price.

Data

Thanks to the increasing popularity of the ETF market, we can now trade nearly every major market in

the form of ETF, which has tight bid-ask spread and huge liquidity. These ETF usually would track the

corresponding MSCI Index. Therefore in this study we would mainly be using MSCI Index. 7 developed

markets, 6 emerging markets, and Goldman Sachs Commodity Index (GSCI) are chosen, which are

believed to truly reflect the real market trend, if there is any, as these are major markets and represents a

significant proportion of the world’s GDP as total.

The markets are as follows:

Developed:

Australia, Germany, Hong Kong, Japan, Singapore, Switzerland, UK, US

Emerging:

Brazil, China, India, Korea, Russia, Taiwan

Commodity:

Goldman Sachs Commodity Index (GSCI)

Most of the Indices were launched at 1988, so we have a full 20 years of data for testing.

Only Price Indices are used in the study, not Total Return. So dividends are not being reinvested. It is

sufficient to use the Price Indices as we are only trying to compare the risk and return of Time Model vs

Buy and Hold.

Weekly Closing data are being used in the study.

System

First of all it is necessary to decide what period of weekly SMA the study is going to use.

Below is the average CAGR, drawdown% and Sharpe Ratio of different time period used for DM

(Developed Market), EM (Emerging Market) and DM+EM.

Exhibit 1. Annualised Return for different regions

Model DM Average DM Rank EM Average EM Rank DM+EM Average Average Rank

4 weeks 5.9% 13 17.8% 3 11.85% 3 8 weeks 7.4% 2 18.1% 2 12.74% 2 12 weeks 7.6% 1 18.3% 1 12.94% 1 16 weeks 7.0% 4 15.1% 4 11.05% 4 20 weeks 6.2% 10 14.7% 7 10.48% 7 24 weeks 6.2% 11 14.8% 6 10.53% 6 28 weeks 6.6% 7 14.9% 5 10.74% 5 32 weeks 6.2% 12 14.1% 8 10.11% 10 36 weeks 6.5% 9 13.8% 9 10.14% 9 40 weeks 6.5% 8 13.8% 10 10.15% 8 44 weeks 6.7% 6 12.6% 11 9.63% 12 48 weeks 6.9% 5 12.0% 13 9.45% 13 52 weeks 7.1% 3 12.2% 12 9.67% 11 Buy & Hold 4.9% 14 4.9% 14 4.93% 14

Exhibit 2. Drawdown% for different regions

Model DM Average DM Rank EM Average EM Rank DM+EM Average Average Rank

4 weeks -31.3% 2 -41.0% 2 -36.14% 1 8 weeks -31.0% 1 -44.6% 5 -37.80% 3 12 weeks -32.9% 6 -39.7% 1 -36.30% 2 16 weeks -32.8% 4 -44.1% 4 -38.42% 4 20 weeks -32.9% 5 -46.4% 7 -39.65% 7 24 weeks -34.1% 10 -50.7% 12 -42.41% 13 28 weeks -32.6% 3 -50.8% 13 -41.68% 11 32 weeks -34.7% 11 -47.8% 8 -41.23% 9 36 weeks -33.1% 7 -45.1% 6 -39.09% 5 40 weeks -35.3% 13 -43.3% 3 -39.27% 6 44 weeks -33.5% 8 -48.9% 9 -41.15% 8 48 weeks -33.5% 9 -49.8% 11 -41.65% 10 52 weeks -35.2% 12 -49.5% 10 -42.35% 12 Buy & Hold -61.0% 14 -82.5% 14 -71.73% 14

Exhibit 3. Sharpe Ratio for different regions

Model DM Average DM Rank EM Average EM Rank DM+EM Average Average Rank

4 weeks 0.453 13 0.675 3 0.564 5 8 weeks 0.580 1 0.720 2 0.650 1 12 weeks 0.554 3 0.722 1 0.638 2 16 weeks 0.541 5 0.635 4 0.588 3 20 weeks 0.531 6 0.618 5 0.575 4 24 weeks 0.556 2 0.545 12 0.551 9 28 weeks 0.530 7 0.558 11 0.544 12 32 weeks 0.520 8 0.588 10 0.554 7 36 weeks 0.491 12 0.607 7 0.549 11 40 weeks 0.494 11 0.608 6 0.551 8 44 weeks 0.501 10 0.600 8 0.551 10 48 weeks 0.519 9 0.592 9 0.555 6 52 weeks 0.549 4 0.537 13 0.543 13 Buy & Hold 0.331 14 0.287 14 0.309 14

Exhibit 4. Annualized Return% on different weekly SMA period.

Let’s look into Exhibit 4 first. For the emerging market, we can see that there is a clear downtrend of

annualized return% in the emerging market, Return% starts high with lower SMA period, and fades

towards higher SMA period. For the developed market, the result is less clear, some markets follow the

trend of the emerging market, but some tends to do better when the SMA period is longer. One

similarity of both DM and EM is that there exists a SMA period, in which the annualized return% will

beat the Buy and Hold Strategy.

In Exhibit 1, it lists out the average annualized return% for all the SAM period tested for DM, EM and

DM+EM, and their relative ranks within their category. We see that, as we noticed in Exhibit 4, low

SMA period and high SMA period Model tend to have better result in DM, while in EM the higher the

SMA period, the lower the performance, and while combing DM+EM, the 12 weeks SMA period Model

have the highest rank, with 12.94% annualized return over 20 years.

In Exhibit 2, there is the drawdown%. While in Exhibit 1, the 2 highest SMA period tested ranks 5 and 3

respectively, they only ranks 9 and 12 in drawdown% ranking for DM. On EM and DM+EM, the trend

is pretty much the same as in annualized return% ranking.

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In Exhibit 3, it shows the Sharpe ratio. In the DM+EM Rank, the 8 and 12 weeks SMA Models stand out

among all the others, with 0.65, and 0.638 respectively, separating apart from the third rank 16 weeks

SMA model, with Sharpe Ratio = 0.588. Notice that the Sharpe ratio for buy & hold strategy rank the

lowest, which is 0.23 points off compare to the second lowest, the 52 weeks Model. Indeed buy & hold

strategy ranks rock bottom in all the metrics.

As Sharpe ratio measures the risk adjusted return of a model, we will choose the 8-week SMA period

Model, which is the highest rank in DM+EM, for our study. It is also important to notice that in both

annualized return% and drawdown% ranking, the 8-week SMA period Model is also rank among the

highest, with 2nd and 3

rd rank respectively.

Result

Exhibit 5. Data of 8-week SMA Model for different markets

We see that in all 14 markets studied; only 3 markets underperform the Timing Model, which are Swiss,

US, and UK. This phenomenon has already been noticed in Exhibit 4, as in these markets period towards

52-weeks seem to do better. We would explore this in details later on. From Exhibit 5, we can see that

the average winning% only comes at 42.17%, which means there are actually more losing trades than

winning trades. But what makes the Timing Model performs better than buy & hold strategy is that the

payoff ratio (average profit% / average loss%) is very high, average profit% (12.61%) is significantly

greater than average loss% (-3.54%) , and the average drawdown% (-37.96%) is significantly lower than

the buy & hold strategy (-70.2%). On annualized return%, DM+EM beats buy & hold by 7.03%, while if

we only concentrates on the EM, it beats buy & hold by 13.17%. A buy and hold strategy will only gives

investor 264% return over 20 years, but the 8-week Timing Model gives 1419% return, excluding

dividend reinvest, as all data used are price return only. Sharpe Ratio is 0.62 vs 0.31.

Why the Timing Model works, and why not.

If in all markets, the 8-week TM has outperformed B&H, in terms of return%, drawdown% and Sharpe

Ratio, we might have conclude that the TM really can do a good job. But there are 3 markets that are

underperformed, so we are going to investigate on why these markets don’t work, and indeed we are

going to also investigate why the TM works in other markets, as it is crucial to understand the

underlying edge of the system. For a system to outperform the market, there must be an edge on it,

otherwise it might just be pure luck.

We noticed before that the 3 underperforming markets are Swiss, US and UK. These markets have

common characteristics, namely they are all developed markets, and are more mature compare to others,

meaning a greater history, and their economy are more self-depended in a sense. The second thing is

although a short time frame model doesn’t wok in these 3 markets, a longer time frame model does.

We can see clearly in Exhibit 6 that the 52 week Model ranks 1st in all 3 measures, and the 8 week

Model only rank between 11 and 12.

Annualised Return% Drawdown% Sharpe Ratio

Model US,UK,Swiss Rank Model US,UK,Swiss Rank Model US,UK,Swiss Rank

4 weeks 3.8% 13 4 weeks -33.0% 3 4 weeks 0.38 14 8 weeks 3.8% 12 8 weeks -38.7% 11 8 weeks 0.38 12 12 weeks 4.5% 9 12 weeks -33.8% 5 12 weeks 0.44 9 16 weeks 4.5% 10 16 weeks -36.7% 10 16 weeks 0.44 8 20 weeks 3.7% 14 20 weeks -39.8% 13 20 weeks 0.38 12 24 weeks 4.4% 11 24 weeks -39.7% 12 24 weeks 0.43 10 28 weeks 5.5% 8 28 weeks -34.8% 7 28 weeks 0.52 6 32 weeks 5.7% 6 32 weeks -36.0% 9 32 weeks 0.54 5 36 weeks 5.6% 7 36 weeks -34.5% 6 36 weeks 0.52 6 40 weeks 6.1% 5 40 weeks -33.7% 4 40 weeks 0.56 4 44 weeks 6.4% 3 44 weeks -35.1% 8 44 weeks 0.58 3 48 weeks 7.1% 2 48 weeks -28.1% 2 48 weeks 0.64 1 52 weeks 7.2% 1 52 weeks -26.7% 1 52 weeks 0.64 1 Buy & Hold 6.1% 4 Buy & Hold -52.1% 14 Buy & Hold 0.43 11

Exhibit 6. Average AR, DD, and SR for US, UK and Swiss

The reason this phenomenon exists might be that the matured markets have less volatility. The 8 week

TM is based on a short time frame. If the probability of a whipsaw market is higher, then the system is

very likely to have a lot of losing trade in that market status, as the price will only be moving up and

down around the SMA, therefore giving a lot of wrong signal. It can be seen that the Losing% of these

markets are over 60% from Exhibit 6, which is higher than all other markets, except Japan. On the other

hand, if we adjust the short time frame to longer one, say 52 week, the TM would outperform B&H, in

terms of all 3 measures. As it is a long time frame, as long as the market is trending in the long run, the

Model would not give as much false signal as the short time frame Model, as the whipsaw would happen

above/ below the SMA. Exhibit 7 and 8 is the price chart for MSCI US between 2004-2007. Although

on a long term uptrend, there are many whipsaw markets in between. A 8 week TM would made some

“Buy High Sell Low” trades during the whipsaw, while the 52 week Model, as the SMA is well below

when these whipsaw happens, it would made less false trades.

Exhibit 7. 8 week TM Model for MSCI US 2004-2007

Exhibit 8. 52 week TM Model for MSCI US 2004-2007

To test the hypotheses that the 3 matured markets really are less volatile than the other markets, a

measure for volatility is necessary, and the common practice is to use the standard deviation (stdev).

In Exhibit 9, we can see a graph of the average stdev of all 14 markets, it can be seen that Swiss, UK and

US has indeed the lowest stdev. Another observation is that EM has much higher stdev than DM,

averaging only 0.195, while DM’s average is 0.374, over the 20 years, using weekly close. From Exhibit

5 we see that EM’s annualized return% averaged to be 18.11%, while DM’s return is 7.36%, so it seems

like using a short-term Model, annualized return% is positively correlated with Indices with high stdev.

Exhibit 9. Average Standard Deviation of MSCI DM+EM 1988-2008

Exhibit 10. Standard Deviation of different markets, calculated annually

Stdev of MSCI DM+EM

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Average of Stdev

Market Date

Country

The conclusion so far is that for Indices with low stdev, a longer term model is better, while the reverse

is true when the Indices are with high stdev. A shorter term SMA Model is likely to benefit from high

volatility markets, as these markets tend to have better short term trend, either up or down. This concept

might be easier to understand with some graphical examples. From Exhibit 11 we can see the MSCI

Brazil Index, the volatility is high, and there are many short term up/down trends, which last for 3

months, or 12 weeks. For example from Oct 98 to Jun 99, the 8-week TM captures 2 profitable trades in

the up/down trend market.

Exhibit 11. MSCI Brazil 1997-2001

The above example is not a good enough explanation of why the short term TM works well under high

stdev market. To have a better understanding, we need to dig deeper, and try to understand the price

cycle of markets. Let us first look at Exhibit 12 and 13, both are hypothetical examples with stdev equals

0.7. The red line represents 8-week SMA, the small horizontal line represents weekly close, and blue dot

is a buy signal, while red is a sell. The difference between Exhibit 12 and 13 is that in Exhibit 12, the

price cycle is going up 10% for 2 weeks, and down 10% for the next two, while in Exhibit 13, the price

cycle is going up 10% for 10 weeks and 10% down for the next 10 weeks. We can see although the

stdev is the same for both markets, the performance are very different. As the price cycle for Exhibit 12

is only around 5 weeks (the duration it needs to complete the pattern of a reverse V shape), or it can be

described as whipsaw, each of trades are “Buy High Sell Low”, as the price fluctuates around the SMA.

The price cycle basically mismatches with the SMA cycle. On the other hand in Exhibit 13, the price

cycle is around 17 weeks. The TM is making profit every trade as the price cycle has enough trend to

allow the 8-week SMA to give the right signal. Exhibit 14 is another hypothetical example, this time the

price action is the same as Exhibit 13, but the SMA is 20 week, instead of 8 week. Here we can see the

result is very different to the 8-week TM, as all trades turn out to be losing when switching from 8 to 20.

A rough rule of thumb is the time frame of SMA used has to be less than the duration of price cycle, this

would ensure the SMA can properly catch the trend of the price cycle.

. Exhibit 12. Hypothetical Price cycle with 8-week SMA

Exhibit 13. Hypothetical Price cycle with 8-week SMA

Exhibit 14. Hypothetical Price cycle with 20-week SMA

One of the reasons is because of the effect of compounding. When a portfolio’s value drops by 50%, one

need a 100% return to get back to par. One of the most important advantage of any Timing Model is that

the Drawdown% is much lower than B&H, from Exhibit 5 we can see that for every Indices the

Drawdown% is significantly lower than B&H. and this is a critical reason why TM can outperform

B&H.

NOT YET FINISH

In stock market, High Volatility often associates with a trending market, either up or down.