CitiGroup On TrendFollowing
CitiGroup On TrendFollowing
CitiGroup On TrendFollowing
Trend Models
can simple trend strategies work long term?
Dr Jessica James
Overview
Trend models – general overview
In- and out-of-sample testing
Trend model enhancements
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Trend is popular
85% of CTA returns are explained by simple trend following
The figure rises to almost 100% when carry and option trading are included
They are without doubt the most popular systematic rule-based strategies used
by overlay managers and currency alpha funds
They may be backtested relatively easily
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Trend models
The idea of a trend is intimately connected with that of momentum – if a
currency moves in one direction in one period, it is likely to continue that
direction in the next
However, there will be reversals within larger trends, and the key to successful
trend following is to discover when a trend starts and ends, and not be taken in
by false signals
Moving average models are historically very successful at capturing trends and
they have many different variations
• simple MA
• multiple MA
• exponential
• Garch
• fade in/out
We use the simplest possible – a simple single MA – for research purposes.
• further complexity may be added if a principle is established
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Trending or not?
We sought to establish which currencies ‘trend’ or not by looking at the results
of the simplest possible trend following strategy – that of a single moving
average
By buying when the rate was above a simple arithmetic moving average, and
selling when it was below, we obtained a P/L curve for the trading strategy
since the start of the data set, in 1992
We looked at every length of moving average strategy from 5 to 130 days
We use USD/JPY and USD/CAD as opposite examples
Forwards are not included but tests with full MTM calculations indicate that they
make little difference, even to USD/JPY
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Annual return
10% 6%
0.0 4%
0.4
5% -0.2 2%
0.2 0%
-0.4
0% -2%
0.0 -0.6 -4%
-0.2 -5% -0.8 -6%
0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140
Days in moving average Days in moving average
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More currencies
Annual Returns and IR as a function of moving average Annual Returns and IR as a function of moving average
length for USD/CHF length for USD/AUD
0.2
Annual return
Annual return
0.0 5% 6%
-0.2 0.0 4% there is
0% 2%
-0.4 -0.2 0% extraordinary
-0.6 -5% -2%
-0.8
-0.4
-4% stability of
-1.0 -10% -0.6 -6%
0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140
performance with
Days in moving average Days in moving average respect to the
Information Ratio Annual Return Information Ratio Annual Return moving average
Annual Returns and IR as a function of moving average Annual Returns and IR as a function of moving average
length for EUR/USD length for EUR/JPY
Information Ratio
0.4 8%
Annual return
Annual return
6% 0.4
0.2 4% 6%
0.3
0.0 2% 4%
0% 0.2
-0.2 2%
-2% 0.1
-0.4 -4% 0.0 0%
-0.6 -6% -0.1 -2%
0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140
Days in moving average Days in moving average
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45%
40%
returns in % face
35%
30%
25%
20%
15%
10%
5%
0%
-5%
88
89
90
91
92
93
94
95
96
97
98
99
00
01
02
Date
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There is a best
Variation of Annual Return with days in moving avarage ‘region’ around 70
days but in general
10.00%
results are not
USD/JPY
8.00% sensitive to the
USD/CHF
EUR/USD number of days
6.00% EUR/JPY
EUR/GBP
Annual return
GBP/USD
40
45
50
55
60
65
70
75
80
85
90
95
100
GBP/CHF
-2.00%
Average
-4.00%
Days in moving average
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GBP/JPY
0.20 CHF/JPY
USD/AUD
0.00 USD/CAD
20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 EUR/CHF
-0.20 GBP/USD
GBP/CHF
-0.40 Average
-0.60
Days in moving average
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-40% GBP/CHF
CHF/JPY
-60%
92
93
94
95
96
97
98
99
00
01
02
03
04
05
Date
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USD/AUD
0%
USD/CAD The latest 6weeks or so
-5% EUR/USD however have been much
-10% EUR/JPY better, seeing the returns of
EUR/GBP trends to the markets after the
-15%
EUR/CHF US elections were complete
-20% GBP/USD
-25% GBP/JPY
Nov-04
Jan-04
Jun-04
Jul-04
Jan-05
Feb-04
Mar-04
Apr-04
May-04
Aug-04
Sep-04
Oct-04
Dec-04
Feb-05
Mar-05
GBP/CHF
CHF/JPY
Date
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MA model details
We use the simplest moving average crossover strategy
Each average is equally weighted
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Length
of data EURUSD USDJPY AUDUSD GBPUSD USDCAD EURCHF EURNOK EURSEK
period
1MA 3yr 0.633 0.873 0.558 0.293 0.215 0.260 0.513 0.573
2MA 3yr 0.700 0.873 0.568 0.293 0.215 0.265 0.523 0.610
3MA 3yr 0.713 0.873 0.570 0.293 0.218 0.265 0.520 0.623
4MA 3yr 0.710 0.873 0.570 0.293 0.218 0.265 0.523 0.615
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In-sample results
Even in-sample, there is very little to be gained from moving to more than one
moving average
The results in the 4MA section are barely better than those in the 1MA section
This begs the question, why do users ever have more than one moving
average?
• Possibly multiple strategies are easier to trade in that positions are built up gradually
rather than put on all at once.
• There seems no reason to do with performance which would lead us to use many
rather than one.
The second feature of the table worth discussing is that universally, the IRs are
better for the shorter data periods
This finding is consistent with a lack of stationarity in moving average models
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Out-of-sample testing
Length
of data EURUSD USDJPY AUDUSD GBPUSD USDCAD EURCHF EURNOK EURSEK We expect to see a
period
decrease in IR for
0.960 0.952 0.778 0.312 0.348 0.432 0.568 0.618
2yr
0.148 0.525 0.053 -0.208 -0.298 -0.248 -0.045 0.058 the out-of-sample
0.633 0.873 0.558 0.293 0.215 0.260 0.513 0.573
tests, due to
1MA 3yr
0.128 0.688 0.090 -0.235 -0.263 -0.120 0.043 -0.010 inevitable noise-
0.650 0.827 0.570 0.200 0.207 0.267 0.347 0.400 fitting.
4yr
0.260 0.520 -0.133 -0.253 -0.193 -0.103 -0.060 0.173
What we are
0.980 0.965 0.802 0.312 0.350 0.432 0.600 0.788
2yr
0.157 0.465 0.038 -0.208 -0.295 -0.248 -0.040 0.015 searching for is the
0.700 0.873 0.568 0.293 0.215 0.265 0.523 0.610
number of fitted
2MA 3yr
0.135 0.700 0.143 -0.235 -0.263 -0.130 0.045 -0.065 parameters which
0.657 0.827 0.573 0.200 0.207 0.270 0.347 0.417 minimises the
4yr
0.207 0.520 -0.153 -0.127 -0.240 -0.100 -0.060 0.110 decrease between in
2yr
0.977 0.965 0.813 0.312 0.352 0.432 0.597 0.758 and out-of-sample
0.143 0.458 0.050 -0.252 -0.297 -0.270 -0.043 0.018
tests.
0.713 0.873 0.570 0.293 0.218 0.265 0.520 0.623
3MA 3yr
0.163 0.633 0.085 -0.235 -0.265 -0.130 0.028 -0.050
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Out-of-sample results
Unfortunately, it is not possible to draw any firm conclusions about the ideal
number of parameters in a trend model
It can be said that nothing performs significantly better out-of-sample than the
1MA model
There are only two currency pairs for which the out-of-sample results are
significantly positive
• USD/JPY yields good information ratios both in and out-of-sample
• EUR/USD results are also all positive for out of sample periods, though not quite as
high
The results for the other currency pairs are either negative or little different from
zero for all out-of-sample periods, regardless of the number of MAs used or the
length of the sample under test
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Is trend dead??
We find that to our surprise there is no evidence that more than one moving
average is useful or necessary
Only USD/JPY and EUR/USD show positive out-of-sample results for any trend
strategy variant!
This does not necessarily mean that trend models are useless for currency
pairs other than these two, but it does suggest that they should not be applied
blindly
An indicator which allowed investors to judge when trend models were likely to
work or not would undoubtedly improve their performance
Our results indicate that investors should think carefully when designing trend-
following strategies, and use these techniques in conjunction with other signals
rather than as simple stand-alone strategies.
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A Model Example
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0.2
USD/SEK
USD/NOK
0.1
The only currency
EUR/CHF
0
EUR/SEK GBP/USD which gives
-0.1 EUR/NOK
USD/AUD
acceptable returns
-0.2 in both is EUR/USD.
-0.3
USD/CAD
-0.4
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00
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Trend followers:
USD/JPY, CHF/JPY,
Information ratios for trend and option selling strategies GBP/JPY, EUR/JPY,
EUR/GBP, USD/CHF,
0.5
USD/JPY EUR/USD and
0.4 CHF/JPY
EUR/JPY USD/NOK
0.3
EUR/USD
GBP/JPY EUR/GBP USD/CHF Option sellers:
Average trend IR
0.2
USD/SEK
0.1
USD/NOK USD/SEK, GBP/USD,
EUR/CHF
EUR/NOK, USD/AUD,
0
EUR/SEK GBP/USD EUR/CHF
-0.1 EUR/NOK
USD/AUD
-0.2
-0.3
USD/CAD
-0.4
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00
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would need to be leveraged to construct a reasonable Option selling currencies for 25 delta strategy
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be achievable, for a
30% variety of reasons
20%
10%
0%
-10%
-20%
92
93
94
95
96
97
98
99
00
01
Date 02
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Stationarity of behaviour
A legitimate concern with this type of strategy is that the alpha-generating
behaviour does not persist, and will not be there to exploit in the future
These concerns may be minimised by using as little optimisation as possible,
which we have done
• there is only one moving average used for the whole time period, and only one option
selling strategy
Also, for those currencies which ‘work’ as either trend followers or option
sellers, they seem to deliver a roughly constant performance over past years
There is nothing to suggest that results for 92 – 97 would be significantly
different from results from 97 – 02.
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Which trend?
Overall, the exact trend strategy has little impact on results.
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As expected, these
results are overall
Returns to 80 day simple moving average strategies
mediocre, with only the
very strong trending
120% currencies like USD/JPY
USD/JPY
100%
USD/CHF Trend following results for 80 day moving average delivering good returns.
80%
USD/AUD Average annual
Currency Information ratio
return
Strategy Returns
60% USD/CAD
EUR/USD USD/JPY 0.618 6.88%
40% USD/CHF 0.384 4.15%
EUR/JPY
20% USD/AUD -0.109 -1.14%
EUR/GBP USD/CAD -0.285 -1.81%
0% EUR/CHF EUR/USD 0.377 3.81%
GBP/USD EUR/JPY 0.510 5.86%
-20% EUR/GBP 0.619 5.08%
GBP/JPY EUR/CHF -0.042 -0.16%
-40%
Average GBP/USD 0.040 0.33%
-60% GBP/JPY 0.499 6.42%
Average 0.627 2.94%
Jun-92
Jun-93
Jun-94
Jun-95
Jun-96
Jun-97
Jun-98
Jun-99
Jun-00
Jun-01
Jun-02
Date
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USD/CAD
20% USD/CHF 0.005 0.04%
EUR/USD they need to have
10% EUR/JPY USD/AUD 0.718 5.42%
EUR/GBP USD/CAD 0.550 2.78% comparable levels of
0%
EUR/CHF EUR/USD 0.314 2.90% returns. The straddle
-10% GBP/USD EUR/JPY -0.195 -2.10%
GBP/JPY EUR/GBP -0.053 -0.41%
writing strategy returns
-20%
Average EUR/CHF 0.470 2.19% are small compared with
-30% GBP/USD 0.167 1.64% the trend following, so
Jun-92
Jun-93
Jun-94
Jun-95
Jun-96
Jun-97
Jun-98
Jun-99
Jun-00
Jun-01
Jun-02
Jun-03
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Return in % of face
formed by the addition of the two 30%
has a much healthier IR of 0.91 20%
0%
intelligently chooses which 80 day trend
-10% Weekly straddle writing x2
strategy is currently likely to do Average of trend and straddle
-20%
best should better this result
Jun-92
Jun-93
Jun-94
Jun-95
Jun-96
Jun-97
Jun-98
Jun-99
Jun-00
Jun-01
Jun-02
again.
Date
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Strategy implementation
Option positions are allowed to expire naturally even when they are no longer
appropriate – this is because the high costs of unwinding an oddly dated and
probably out of the money option position are not worthwhile.
When the 1m implied volatility falls below its trailing average, there is a good
chance that a trend will be starting or in place. But because volatility is low, the
trend will in all likelihood not start aggressively.
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Results
Information ratios for individual and combined strategies In nearly every currency the IR
80 day trend Daily straddle Combined has improved dramatically
Currency
following writing portfolio
USD/JPY 0.618 0.385 0.960 The IR of the average portfolio
USD/CHF 0.384 0.005 0.958 has leaped to 1.49
USD/AUD -0.109 0.718 1.128
USD/CAD -0.285 0.550 0.546
We can see above that the
EUR/USD 0.377 0.314 1.009 switching rule has enabled the
EUR/JPY 0.510 -0.195 0.293 combination of two strategies,
EUR/GBP 0.619 -0.053 0.847
EUR/CHF -0.042 0.470 0.919
which yielded 2.94% and 1.19%
GBP/USD 0.040 0.167 0.664 annual returns, to reach a
GBP/JPY 0.499 -0.347 0.370 substantial 6.76% per annum
Average 0.627 0.229 1.492
Given that the identical strategy
Average annual returns for individual and combined strategies
is applied to each currency
without change, there can be
80 day trend Daily straddle writing Combined
Currency
following (2x leverage) portfolio little doubt that this is a real and
USD/JPY 6.88% 4.04% 10.68% useful effect.
USD/CHF 4.15% 0.04% 10.70%
USD/AUD -1.14% 5.42% 8.63%
USD/CAD -1.81% 2.78% 2.99%
EUR/USD 3.81% 2.90% 10.16%
EUR/JPY 5.86% -2.10% 3.30%
EUR/GBP 5.08% -0.41% 6.60%
EUR/CHF -0.16% 2.19% 3.94%
GBP/USD 0.33% 1.64% 6.59%
GBP/JPY 6.42% -4.61% 4.06%
Average 2.94% 1.19% 6.76%
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Results
140%
120% USD/JPY
USD/CHF
100%
USD/AUD
80%
Strategy Returns
USD/CAD
60% EUR/USD
EUR/JPY
40% EUR/GBP
20% EUR/CHF
GBP/USD
0%
GBP/JPY
-20% Average
-40%
Jun-92
Jun-93
Jun-94
Jun-95
Jun-96
Jun-97
Jun-98
Jun-99
Jun-00
Jun-01
Jun-02
Jun-03
Date
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Results
80%
80 day trend
70%
weekly straddle writing x2
60%
Return in % of face
Jun-93
Jun-94
Jun-95
Jun-96
Jun-97
Jun-98
Jun-99
Jun-00
Jun-01
Jun-02
Date
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80%
for the different strategies
60%
40% Note that as this is monthly data,
not quite every ‘switching’ period is
20%
represented, as these can vary on
0% a sub-monthly level.
-20%
Jun-92
Jun-93
Jun-94
Jun-95
Jun-96
Jun-97
Jun-98
Jun-99
Jun-00
Jun-01
Jun-02
Date
switch trend straddle write combination
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This document does not represent an accounting opinion. The Company should consult with their
auditing firm for further accounting opinion on the proposed transactions.
Issued by Citibank N.A., London Branch is regulated by the UK Financial Services Authority
33 Canada Square
Canary Wharf
London E14 5LB
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