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Swiss Market Analysis Stocks, Reits, Government Bonds, Money Market As end of July 2013 Finance Online GmbH and Rmetrics Association Zurich www.rmetrics.org [email protected]

Swiss Multi Asset Portfolio

SIX CHF Swiss Market Index (SMIC) [1|1]SIX CHF SMI MCap TR Index (SMIMC) [1|1]SIX CHF SWIIT TR Reits Fund (SWIIT) [0|0]SIX CHF SBGM 3-7Y TR Bond Idx (SBGM3T) [0|0]BBA CHF 1M Libor Wealth (LIBOR1MW) [2|2]

Parameter Settings:Last Update: Jul 2013BCP Flexible: 24 MonthsTransaction Throttle: OnIndependent Averaging: OffLeverage Factor: 1

Wea

lth

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Wealth and Stabilized Wealth Indices

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BSP Stability

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Component Tendency IndicatorsTr

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Rm

etric

s

3 Trades p.a.

Monthly Performance of Equal Weigths PortfolioJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec EWP #M>0 HIT% G/L MIN MAX

2001 1.5 -3.0 -4.3 0.6 0.3 -2.5 -4.4 -2.5 -9.4 2.0 3.8 0.5 -17.3 6 50 0.3 -9.4 3.8

2002 -1.0 0.5 3.6 -0.7 0.9 -4.7 -6.1 -0.3 -4.9 2.1 2.2 -3.6 -11.8 5 42 0.4 -6.1 3.6

2003 -2.2 -0.9 0.4 5.1 2.7 1.3 1.9 2.7 -0.4 3.7 1.0 1.9 17.3 9 75 5.9 -2.2 5.1

2004 3.9 1.4 -1.3 1.0 0.4 0.0 -2.5 0.1 1.7 -0.1 1.2 2.3 7.9 8 67 3.0 -2.5 3.9

2005 2.3 1.3 0.4 -0.5 2.6 1.4 3.8 -0.6 3.2 -1.8 1.9 2.7 16.9 9 75 6.9 -1.8 3.8

2006 1.8 2.3 1.2 1.6 -3.4 -0.3 1.8 1.8 1.7 1.9 1.3 3.2 14.8 10 83 5.0 -3.4 3.2

2007 3.4 -2.4 2.3 2.8 0.5 -1.3 -1.6 -0.9 -0.4 0.5 -3.1 -0.6 -0.6 5 42 0.9 -3.1 3.4

2008 -5.6 1.2 -2.2 2.7 1.5 -5.5 0.5 1.5 -4.5 -9.5 -0.7 -0.3 -20.9 5 42 0.3 -9.5 2.7

2009 -0.9 -5.1 2.3 6.4 2.2 0.9 3.9 2.7 2.2 -0.7 0.5 2.9 17.4 9 75 3.6 -5.1 6.4

2010 0.6 -0.2 3.6 -0.4 -1.9 -1.4 1.3 -0.3 2.4 0.7 0.0 2.1 6.5 7 58 2.6 -1.9 3.6

2011 -0.2 0.9 -0.8 1.6 0.4 -2.9 -2.8 -2.6 -0.5 2.9 -2.4 2.2 -4.3 5 42 0.7 -2.9 2.9

2012 1.5 2.1 0.9 0.6 -2.2 1.0 3.0 -0.5 0.9 -0.4 2.1 0.9 9.8 9 75 4.2 -2.2 3.0

2013 2.9 0.9 1.8 1.7 0.8 -3.1 1.7 6.6 6 86 3.1 -3.1 2.9

Performance and Risk StatisticsBSP EWP

Mean Monhtly Return % 0.72 0.50

Mean Monthly Standard Dev % 1.89 2.75

Average Annualized Return % 8.99 6.13

Average Ann. Volatility % 6.54 9.52

Sharpe Ratio 0.38 0.18

Maximum Drawdown % -13.35 -30.67

No of Positive Months 154.00 138.00

Pos/Neg No of Month Ratio 2.66 1.86

Monthly Gain/Loss Ratio 2.86 1.60

Semi Deviation 0.01 0.02

Historical VaR (95%) -0.02 -0.05

Historical ES (95%) -0.04 -0.07

Kurtosis Monthly Returns 5.92 2.66

Monthly Performance of Binary Stability PortfolioJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec BSP #M>0 HIT% G/L MIN MAX

2001 1.5 -3.0 -1.4 -0.5 0.1 0.2 0.5 0.7 0.1 1.6 -0.4 -0.9 -1.5 7 58 0.8 -3.0 1.6

2002 0.3 0.6 0.4 0.3 0.9 0.8 1.1 0.7 1.0 1.0 -0.3 1.1 7.8 11 92 23.9 -0.3 1.1

2003 1.3 1.2 -0.8 -0.4 1.9 0.2 0.7 2.7 -0.7 3.7 1.2 1.7 12.8 9 75 8.0 -0.8 3.7

2004 3.9 1.4 -1.3 1.0 0.3 0.1 -2.8 0.3 1.4 -0.1 1.2 2.3 7.7 9 75 2.8 -2.8 3.9

2005 2.3 1.3 0.1 -0.5 2.6 1.4 3.8 -0.6 3.2 -1.8 1.9 1.9 15.7 9 75 6.5 -1.8 3.8

2006 1.8 2.3 1.4 1.8 -3.4 -0.1 1.6 1.7 1.8 2.0 1.1 2.7 14.5 10 83 5.0 -3.4 2.7

2007 3.6 -2.5 2.3 2.9 0.8 -1.1 -1.7 -1.2 0.4 0.0 0.5 -0.3 3.7 7 58 1.5 -2.5 3.6

2008 1.6 0.1 0.2 -0.6 -0.3 -0.4 1.8 0.6 2.8 -2.1 1.8 1.4 6.8 8 67 2.9 -2.1 2.8

2009 1.5 0.1 0.5 0.6 0.3 0.1 3.9 2.7 2.2 -0.7 0.5 2.9 14.9 11 92 23.8 -0.7 3.9

2010 0.6 -0.2 3.6 -0.4 -1.9 -1.4 1.3 -0.3 2.4 0.7 0.0 2.1 6.5 7 58 2.6 -1.9 3.6

2011 -0.2 0.9 -0.7 1.6 0.0 -2.9 -2.8 0.9 0.7 0.0 -0.1 0.7 -1.8 7 58 0.7 -2.9 1.6

2012 0.3 0.5 0.0 0.5 0.7 -0.1 2.5 -0.6 0.3 0.3 0.9 0.9 6.1 10 83 10.4 -0.6 2.5

2013 2.9 0.9 1.4 1.6 0.8 -2.2 1.2 6.5 6 86 3.9 -2.2 2.9

Benchmark StatisticsBSP to EWP

Alpha 0.00

Beta 0.48

Beta+ 0.63

Beta- 0.33

R-squared 0.48

Annualized Alpha 0.06

Correlation 0.70

Correlation p-value 0.00

Tracking Error 0.07

Active Premium 0.03

Information Ratio 0.45

Treynor Ratio 0.18

How to Read this Factsheet

AbbreviationsEWP: Equal Weigths Portfolio, BSP: Binary Stability Portfolio

Wealth and Stabilized Wealth Indicesfor the BSP portfolio (orange), the EWP portfolio (black), the premium (brown) and the No-Loss-Half-Profitbenchmark (blue).

Drawdowns of Wealth and Stabilized Wealth Indicesfor the BSP portfolio (orange) and the EWP portfolio (black).

Retroactive Garch[1,1] Volatilityshowing the standard deviation bands for the BSP portfolio (orange) and the EWP portfolio (black).

Retroactive Bayesian Change Point Probabilityfor the BSP portfolio returns (orange) and the EWP portfolio returns (black).

EWP Stabilityshowing the posterior probability and related quantities for the EWP portfolio.

Portfolio Betasshowing the beta+ and beta- regression results.

BSP Stabilityshowing the same as for the Equal Weights Portfolio.

Rolling 36 Months Returnsfor the BSP portfolio (orange) and the EWP portfolio (black).

Rolling 36 Months Drawdownfor the BSP portfolio (orange) and the EWP portfolio (black).

Component Tendency Indicatorsshowing the smoothed precentual investemnt in each asset component. The blue curves (darkblue: SMIC, blue:SMIMC, lightblue: SWIIT) belong to the risky assets and the green curves to the riskless assets (darkgreen:SBGM3T, green: LIBOR1MW).

Number of Trades per Monthincluding all five investments.

Monthly Performance of Equal Weigths Portfoliotable shows for each month the logarithmic returns together with its annual sum (EWP), the number of positivemonths (#M>0), the hit ratio (HIT%), the gain and loss ratios of the returns (G/L) and the minimum (MIN) andmaximum (MAX) returns.

Monthly Performance of Binary Stability Portfoliotable shows the same as for the Monthly Performance of Equal Weigths Portfolio.

Performance and Risk Statisticstable calculates perfomance and risk measure for each of the two portfolios.

Benchmark Statistics

table benchmarks the BSP portfolio versus the EWP portfolio.

Software and Data Sources

All calculations were done with the R and Rmetrics statistical software environments, for furhter information werefer to www.rmetrics.org. The used data sources include Bloomberg, Barclays Indices, British Bankers Associa-tion, CBOE,Cohen and Steers, EuroMTS, Federal Reserve, Swiss Exchange, Standard & Poors, and STOXX.

Disclaimer

This document is copyrighted and its content is confidential and may not be reproduced or provided to otherswithout the express written permission of the authors. This material has been prepared solely for informationalpurposes only and it is not intended to be and should not be considered as an offer, or a solicitation of an offer,or an invitation or a personal recommendation to buy or sell any stocks and bonds, or any other fund, securityor financial instrument, or to participate in any investment strategy, directly or indirectly. It is intended for usein research only by those recipients to whom it was made directly available by the authors of the document.

Asset Classes

The asset components for the Swiss Multi Asset Portfolio are

� SIX CHF Swiss Market Index (SMIC)

� SIX CHF SMI MCap TR Index (SMIMC)

� SIX CHF SWIIT TR Reits Fund (SWIIT)

� SIX CHF SBGM 3-7Y TR Bond Idx (SBGM3T)

� BBA CHF 1M Libor Wealth (LIBOR1MW)

The market benchmark is the equal weights market portfolio composed from the SMIC, SMIMC,SWIIT, and SBGM3T.

Strategy

The following parameteres were used:

� Last update: Jul 2013

� Data Frequency: End of Month

� Number of Assets: 4 + 1

� Currency: CHF

� Strategy: BCP Flexible

� Window Length: 24 Months

� Transaction Throttle: On

� Independent Averaging: Off

� Leverage Factor: 1

3

Indices and Drawdowns

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lth

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CH Wealth and Stabilized Wealth Indices

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Rm

etric

s

Figure 1: In the upper chart the black curve shows the Equal Weights Portfolio The orangecurve is the index composed from the stabilized market components. In the lower chart thedrawdowns are displayed. The black curve is for the Equal Weights Portfolio and the orangecurve is calculated from the stabilized index components. Note, the Binary Stability Portfolioshows a significant stable and capital protecting increase of wealth with low drawdowns andshort recovery times. The strategy also benefits from positive performance trends, favours abalanced allocation of equal risk contributions, and maintains volatility to low levels.

SMIC | SMIMC | SWIIT | SBGM3T | LIBOR1MWJul 2013 | CHF | BCP Flexible: 24 Month | Throttle: On | Independent Average: Off | Leverage: 1

4

Volatility and Stability

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etric

s

Figure 2: In the upper chart the two standard deviation bands for the Binary Stability Portfolio(orange) and the Equal Weights Portfolio (black) are displayed as calculated from a GARCH(1,1)time series model. The bars reflect the logarithmic returns, note, exceedances mark high riskyperiods. The lower chart shows the posterior bayesian change point probability as calculatedfrom a Markov Chain Monte Carlo simulation. The black curve represents the Equal WeightsPortfolio, the Binary Stability Portfolio is colored in orange. Note, high peaks reflect highinstabilities. Both, the GRACH(1,1) volatilities and the Bayesian change point probability arecalculated retroactively over the samples.


5

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Rm

etric

s

Figure 3: The chart plots the returns of the Equal Weights Portfolio against the returns of theBinary Stability Portfolio. A point that lies above the red line indicates that the return of theBSP has been improved compared to the return of the EWP and vice versa. The points abovethe red line are colored green, the points below are colored orange if they are still positive andred if negative. The blue line on the left side has the slope of beta-. The smaller this slope getsas 1, the better the strategy improves the negative returns. The blue line on the right side hasthe slope of beta+. The higher this slope gets as 1 the better the strategy improves the positivereturns. Note that for our strategy the maximum of beta+ without leverage is 1.


6

Rolling Alpha, Beta, R-Squared

Time

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Rm

etric

s

Figure 4: From top to bottom the 36 months rolling Alpha, Beta, and R-Squared between theEqual Weights Portfolio and Binary Stability Portfolio are displayed. Alpha is the degree towhich the returns of the BSP are not due to the returns that could be captured from the EWP.Beta describes the portions of the returns of the BSP that could be directly attributed to thereturns of a passive investment in the EWP. R-Squared shows the degree of fit of the BSP tothe EWP.


7

Monthly Calendar Returns and Correlations

Performance of the Equal Weigths Portfolio

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec EWP #M>0 HIT% G/L MIN MAX

2001 1.5 -3.0 -4.3 0.6 0.3 -2.5 -4.4 -2.5 -9.4 2.0 3.8 0.5 -17.3 6 50 0.3 -9.4 3.8

2002 -1.0 0.5 3.6 -0.7 0.9 -4.7 -6.1 -0.3 -4.9 2.1 2.2 -3.6 -11.8 5 42 0.4 -6.1 3.6

2003 -2.2 -0.9 0.4 5.1 2.7 1.3 1.9 2.7 -0.4 3.7 1.0 1.9 17.3 9 75 5.9 -2.2 5.1

2004 3.9 1.4 -1.3 1.0 0.4 0.0 -2.5 0.1 1.7 -0.1 1.2 2.3 7.9 8 67 3.0 -2.5 3.9

2005 2.3 1.3 0.4 -0.5 2.6 1.4 3.8 -0.6 3.2 -1.8 1.9 2.7 16.9 9 75 6.9 -1.8 3.8

2006 1.8 2.3 1.2 1.6 -3.4 -0.3 1.8 1.8 1.7 1.9 1.3 3.2 14.8 10 83 5.0 -3.4 3.2

2007 3.4 -2.4 2.3 2.8 0.5 -1.3 -1.6 -0.9 -0.4 0.5 -3.1 -0.6 -0.6 5 42 0.9 -3.1 3.4

2008 -5.6 1.2 -2.2 2.7 1.5 -5.5 0.5 1.5 -4.5 -9.5 -0.7 -0.3 -20.9 5 42 0.3 -9.5 2.7

2009 -0.9 -5.1 2.3 6.4 2.2 0.9 3.9 2.7 2.2 -0.7 0.5 2.9 17.4 9 75 3.6 -5.1 6.4

2010 0.6 -0.2 3.6 -0.4 -1.9 -1.4 1.3 -0.3 2.4 0.7 0.0 2.1 6.5 7 58 2.6 -1.9 3.6

2011 -0.2 0.9 -0.8 1.6 0.4 -2.9 -2.8 -2.6 -0.5 2.9 -2.4 2.2 -4.3 5 42 0.7 -2.9 2.9

2012 1.5 2.1 0.9 0.6 -2.2 1.0 3.0 -0.5 0.9 -0.4 2.1 0.9 9.8 9 75 4.2 -2.2 3.0

2013 2.9 0.9 1.8 1.7 0.8 -3.1 1.7 6.6 6 86 3.1 -3.1 2.9

Performance of the Binary Stability Portfolio

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec BSP #M>0 HIT% G/L MIN MAX

2001 1.5 -3.0 -1.4 -0.5 0.1 0.2 0.5 0.7 0.1 1.6 -0.4 -0.9 -1.5 7 58 0.8 -3.0 1.6

2002 0.3 0.6 0.4 0.3 0.9 0.8 1.1 0.7 1.0 1.0 -0.3 1.1 7.8 11 92 23.9 -0.3 1.1

2003 1.3 1.2 -0.8 -0.4 1.9 0.2 0.7 2.7 -0.7 3.7 1.2 1.7 12.8 9 75 8.0 -0.8 3.7

2004 3.9 1.4 -1.3 1.0 0.3 0.1 -2.8 0.3 1.4 -0.1 1.2 2.3 7.7 9 75 2.8 -2.8 3.9

2005 2.3 1.3 0.1 -0.5 2.6 1.4 3.8 -0.6 3.2 -1.8 1.9 1.9 15.7 9 75 6.5 -1.8 3.8

2006 1.8 2.3 1.4 1.8 -3.4 -0.1 1.6 1.7 1.8 2.0 1.1 2.7 14.5 10 83 5.0 -3.4 2.7

2007 3.6 -2.5 2.3 2.9 0.8 -1.1 -1.7 -1.2 0.4 0.0 0.5 -0.3 3.7 7 58 1.5 -2.5 3.6

2008 1.6 0.1 0.2 -0.6 -0.3 -0.4 1.8 0.6 2.8 -2.1 1.8 1.4 6.8 8 67 2.9 -2.1 2.8

2009 1.5 0.1 0.5 0.6 0.3 0.1 3.9 2.7 2.2 -0.7 0.5 2.9 14.9 11 92 23.8 -0.7 3.9

2010 0.6 -0.2 3.6 -0.4 -1.9 -1.4 1.3 -0.3 2.4 0.7 0.0 2.1 6.5 7 58 2.6 -1.9 3.6

2011 -0.2 0.9 -0.7 1.6 0.0 -2.9 -2.8 0.9 0.7 0.0 -0.1 0.7 -1.8 7 58 0.7 -2.9 1.6

2012 0.3 0.5 0.0 0.5 0.7 -0.1 2.5 -0.6 0.3 0.3 0.9 0.9 6.1 10 83 10.4 -0.6 2.5

2013 2.9 0.9 1.4 1.6 0.8 -2.2 1.2 6.5 6 86 3.9 -2.2 2.9

Figure 5: The upper table shows the monthly calendar returns for the Equal Weights Portfolioand the lower table the returns for the Binary Stability Portfolio. The first twelve columns arethe monthly returns, and the last six columns denote the sum of the monthly reurns (EWP),the number of positive month returns (#M>0), the hit rate(HIT%), the gain and loss ratio of thereturns (G/L) and the minimum (MIN) and maximum (MAX) return values over the year.

Correlation between Portfolio Assets

SMIC SMIMC SWIIT SMIC SMIMC SWIIT

SMIMC 0.763 SMIMC 0.642

SWIIT 0.255 0.257 SWIIT 0.219 0.123

SBGM3T -0.221 -0.282 0.248 SBGM3T 0.034 -0.108 0.340

Figure 6: The left table shows the correlation between the assets of the Equal Weights Pportfolioand the right table the correlations between the stabilized assets of the Binary Stability Portfolio.


8

Performance Measures

Performance and Risk Statistics

BSP EWP

Mean Monhtly Return % 0.72 0.50

Mean Monthly Standard Dev % 1.89 2.75

Average Annualized Return % 8.99 6.13

Average Ann. Volatility % 6.54 9.52

Sharpe Ratio 0.38 0.18

Maximum Drawdown % -13.35 -30.67

No of Positive Months 154.00 138.00

Pos/Neg No of Month Ratio 2.66 1.86

Monthly Gain/Loss Ratio 2.86 1.60

Kurtosis Monthly Returns 5.92 2.66

Sum of Positive Returns 2.34 2.80

Sum of Negative Returns -0.82 -1.75

No of Negative Months 58.00 74.00

Mean Monthly Drawdown % -2.17 -8.00

Median Monthly Drawdown % -0.59 -4.91

5% Quantile Drawdown -0.09 -0.25

Pearson Skewness of Returns 0.10 -0.32

Semi Deviation 0.01 0.02

Loss Deviation 0.02 0.02

Downside Deviation (MAR=10%) 0.01 0.02

Downside Deviation (Rf=0%) 0.01 0.02

Historical VaR (95%) -0.02 -0.05

Historical ES (95%) -0.04 -0.07

Modified VaR (95%) -0.03 -0.05

Modified ES (95%) -0.06 -0.08

Benchmark Statistics

BSP to EWP

Alpha 0.00

Beta 0.48

Beta+ 0.63

Beta- 0.33

R-squared 0.48

Annualized Alpha 0.06

Correlation 0.70

Correlation p-value 0.00

Tracking Error 0.07

Active Premium 0.03

Information Ratio 0.45

Treynor Ratio 0.18

Figure 7: The upper table lists some selected performance and risk statistics for both investmentstrategies, the Equal Weights Portfolio, and the Binary Stability Portfolio. The lower table liststhe market outperformance of the BSP versus the EWP.


9

Rolling Returns and Drawdowns

Time

% M

onth

ly R

etur

ns

−0.5

0.0

0.5

1.0

1.5


CH Rolling 36 Months Returns

% D

raw

dow

n

−0.5

−0.4

−0.3

−0.2

−0.1

0.0


CH Rolling 36 Months Max Drawdown

Rm

etric

s

Figure 8: The upper graph shows the monthly rolling returns over periods of 36 months. Theblack line belongs to the Equal Weights Portfolio, the orange line represents the Binary StabilityPortfolio and the brown line displays the out- or underperformance, repectively. The lower graphshows the 36 months rolling drawdowns.


10

Return Distribution

−0.10 −0.05 0.00 0.05 0.10

05

1015

2025

Mea

n: 0

.004

96

CH EWP Return Histogram

Returns

Pro

babi

lity

●

●●●

●●●●●●●●

●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●

●●●●●

●

−6 −4 −2 0 2 4 6

−6

−4

−2

02

46

Normal QuantilesE

WP

Ord

ered

Dat

a

Con

fiden

ce In

terv

als:

95%

CH Norm QQ Return Plot

−0.10 −0.05 0.00 0.05 0.10

05

1015

2025

Mea

n: 0

.007

17

CH BSP Return Histogram

Returns

Pro

babi

lity

●

●

●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

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●

−6 −4 −2 0 2 4 6

−6

−4

−2

02

46

Normal Quantiles

BS

P O

rder

ed D

ata

Con

fiden

ce In

terv

als:

95%

CH Norm QQ Return Plot

Figure 9: The graphs show the return histograms (left) and the quantile - quantile plots (right)for the Equal Weigths Portfolio (top) and the Binary Stability Portfolio (bottom). The graphsare typical indicators for the strength of the tails in the ditribution of the returns. Note, thereturns in the quantile - quantile plot are scaled to zero mean and variance one.


11

Market Components

CH Market Components

Time

SM

IC

100200300400500600


Time

SM

IMC

200

400

600

800

1000


Time

SW

IIT

100

150

200

250


Time

SB

GM

3T

100

120

140

160


LIB

OR

1MW

100105110115120


Figure 10: The charts show the market indices from which we composed the Equal Weights andthe Binary Stability Portfolios. The upper charts visualize the risky assets, SMIC (darkblue),SMIMC (blue) and SWIIT (lightblue) and the lower charts the less risky asset, SBGM3T (dark-green) as well as the no risk asset, LIBOR1MW (green). The bold curves belong to the originalindices and the thin curves to the stabilized indices. Note that the stabilized indices are shownincluding additional parameters like the leverage or the transaction throttle.


12

Component Drawdowns

CH Component Drawdowns

Time

SM

IC

−0.5−0.4−0.3−0.2−0.1

0.0


Time

SM

IMC

−0.7−0.6−0.5−0.4−0.3−0.2−0.1

0.0


Time

SW

IIT

−0.15

−0.10

−0.05

0.00


Time

SB

GM

3T

−0.04

−0.03

−0.02

−0.01

0.00


LIB

OR

1MW

−1.0

−0.5

0.0

0.5

1.0


Figure 11: The charts show the drawdowns of the market indices from which we composed theEqual Weights and the Binary Stability Portfolios. The upper charts visualize the risky assets,SMIC (darkblue), SMIMC (blue) and SWIIT (lightblue) and the lower charts the less risky asset,SBGM3T (darkgreen) as well as the no risk asset, LIBOR1MW (green). The bold curves belongto the original indices and the thin curves to the stabilized indices. Note that the stabilizedindices are shown including additional parameters like the leverage or the transaction throttle.


13

Stabilized Asset Positions

CH Stabilized Asset Positions

Time

SM

IC


01

Time

SM

IMC


01

Time

SW

IIT


01

Time

SB

GM

3T

0

1

2

3

4


LIB

OR

1MW

0

1

2

3

4


Rm

etric

s

Figure 12: The graph shows the market positions as realized in the Binary Stability Portfolio.The positions can range between zero and four units (the total capital). The risky assets ( SMIC,SMIMC, and SWIIT) are limited to one unit (25%), the less and no risk assets (SBGM3T,LIBOR1MW) are allowed to fill the whole range between zero and four units (100%).


14

Ratio Tendency Indicator

Time

SM

IC −

SM

IMC

− S

WIIT

0

5

10

15

20

25

30

Jan 98 Jan 00 Jan 02 Jan 04 Jan 06 Jan 08 Jan 10 Jan 12 Jan 14

CH Component Tendency Indicator − Risky Assets

SB

GM

3T −

LIB

OR

1MW

0

20

40

60

80

100

Jan 98 Jan 00 Jan 02 Jan 04 Jan 06 Jan 08 Jan 10 Jan 12 Jan 14

CH Less and Non Risky Assets

Rm

etric

s

Figure 13: The two graphs show the ’smoothed’ position tendency taken by each asset overtime. The risky assets, SMIC (darkblue), SMIMC (blue) and SWIIT (lightblue) are in the uppergraph, the less risky asset, SBGM3T (darkgreen) together with the riskfree asset, LIBOR1MW(green) are shown in the lower graph. The orange line shows the long term average investmentpercentage.


15

Rebalancing Frequencies and Durations

Time

Ave

rage

Fre

quen

cy p

er Y

ear

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


CH Rebalancing Frequencies per Year

Time

Ave

rage

Dur

atio

n in

Mon

ths

0

50

100

150


CH Rebalancing Duration Lengths in Months

Time

Trad

es

0

1

2

3

4


CH Number of Trades per Month

Rm

etric

s

3 Trades p.a.

Figure 14: The graphs show the average rebalancing frequencies per year, upper graph, andthe average rebalancing duration lengths in months, middle graph. The rebalancing frequencyreflects the number on how often the total investment is rebalanced in one year, and the rebal-ancing duration lengths give the average time in months of how long it takes ro rebalance thetotal investment. The lower graph displays the number of monthly trades, at maximum 4. The”red” dotted line gives the average number per month.


16

Turning Points Indicator

log

Inde

x E

WP

●●

●

●

●

●

● ●

0.0

0.2

0.4

0.6

0.8

1.0

1.2


CH Equal Weights Portfolio

log

Inde

x B

SP

● ●●●● ●

●●

● ●

Rm

etric

s0.0

0.5

1.0

1.5


CH Binary Stability Portfolio

Rm

etric

s

Figure 15: The two graphs show the logarithmic end of month values of the wealth index (blackcurve) together with its spline smoothed retrospectively filtered values (red curve). The red dotsmark the turn points and the blue horizontal bars mark the down periods. The orange curveshows the structure of the returns. Note, the scale of the returns is not included in the plot.The upper chart belongs to the Equal Weights Portfolio, the lower chart to the Binary StabilityPortfolio.


17

Structural Change and Break Points Indicator

Pos

terio

r P

roba

bilit

y E

WP

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Pos

terio

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roba

bilit

y B

SP

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met

rics

0.0

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Rm

etric

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Figure 16: The two charts display the results from the retroactive Bayesian change point ana-lytics. The grey bars with a black dot on top mark the stability probabilities for each month ofthe financial return series. These probabilities are smoothed on a whole bundle of curves withdifferent degrees of smoothness dyed by rainbows colours. From their ranges, peaks and diver-gences we can identify more stable, less stable or even unstable regions. The black curve twistingaround 1/2 is a measure for the divergence or spread of the stability. The end of the curves canbe extrapolated and can serve for forecasting market stability. The upper chart belongs to theEqual Weights Portfolio, the lower chart to the Binary Stability Portfolio.


18

Volatility

Vol

atili

ty E

WP

−0.2

−0.1

0.0

0.1

0.2



Vol

atili

ty B

SP

Rm

etric

s−0.2

−0.1

0.0

0.1

0.2



Rm

etric

s

Figure 17: The two graphs show the monthly returns, surrounded by a two sigma band (browncurves) and a fixed 6% band (black lines) of the volatility estimated from a GARCH(1,1) timeseries model. The reduction from stabilization is evident. The upper chart belongs to the EqualWeights Portfolio, the lower chart to the Binary Stability Portfolio.


19

Further Readings

Bacon C.R. [2006], Practical Portfolio Performance Measurement and Attribution, John Wileyand Sons Ltd., Chichester, England.

Barry D., and Hartigan J. A. [1993], A Bayesian Analysis for Change Point Problems, Journalof the American Statistical Association 35, 309-319.

Boudt K., Peterson B, Croux C., [2008], Estimation and decomposition of downside risk forportfolios with non-normal returns, Journal of Risk 11, pp. 79-103.

Erdman Ch., and Emerson J. W. [2008], A fast Bayesian change point analysis for the segmen-tation of microarray data, Bioinformatics vol. 24, pp. 2143-2148.

Filzmoser P. [2004], A Multivariate Outlier Detection Method, Working Paper, Univ. Vienna.

Filzmoser P., Maronna R., and Werner M. [2008], Outlier Identification in High Dimensions,Computational Statistics and Data Analysis 52, 1694–1711.

Maillard S., Roncalli T., Teiletche J., [2010], The Properties of Equally Weighted Risk Contri-bution Portfolios, Journal of Portfolio Management.

Pearson N.D., [2002], Risk Budgeting: Portfolio Problem Solving with Value-at-Risk, WileyFinance, John Wiley and Sons.

Rmetrics, Financial Computing Environment and Software packages, www.rmetrics.org.

Sharpe W. F. [1994], The Sharpe Ratio, Journal of Portfolio Management, Vol. 21, pp. 49-58.

Torrence Ch., and Compo G.P. [1998], A Practical Guide to Wavelet Analysis, Bulletin of theAmerican Meteorological Society 79, 61-78.

Wurtz D., Chalabi Y., Ellis A. Chen W., and Theussl S. [2010], Postmodern Approaches to Port-folio Design: Portfolio Optimization with R/Rmetrics, Proceedings of the Singapore R/RmetricsWorkshop 2010, Rmetrics and Finance Online Publishing, Zurich, pp. 205-213.

Wurtz D. [2011a], Tools for Portfolio Optimzation from R/Rmetrics, Proceedings of the MeielisalpSummerschool and Workshop 2011, Rmetrics Association and Finance Online Publishing, Zurich,pp. 220-229.

Wurtz D., Setz T., and Chalabi Y. , [2011b], Stability Analytics of Vulnerabilities in FinancialTime Series, Econophysics ETH Zurich, Working Paper, December 2011.

Wurtz D., Beiler H., Chalabi, Y., Grimson F., and Setz T. [2011c], Long Term StatisticalAnalysis of U.S. Asset Classes, Rmetrics and Finance Online Publishing, Zurich, April 2011.

Wurtz D., Senner R. [2012], The time evolution of Government bond prices in the Eurozone: ANew Stability Analytics Approach, Econophysics ETH Zurich, Working Paper, Dec. 2011.

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