Diseño y desarrollo de páginas Web

CAPÍTULO II MARCO TEÓRICO

2.11 Análisis de riesgo

2.12.1 Diseño y desarrollo de páginas Web

Applying risk-based allocation in the equity space is probably where we see the most published research. In this section, we apply our risk-based allocations in six equity universes: US equities, European equities, Asia ex Japan equities, Japan equities, emerging markets equities, and finally global equities.

US equities

We use MSCI USA as our investment universe. For US equities, MaxDiversification and GlobalMinVar significantly outperform the other strategies, with higher Sharpe ratios (see Figure 163) and lower downside risks (see Figure 164). More importantly, all risk-based allocations considerably exceed the capitalization weighted benchmark.

Consistently with what we found recently (see Cahan, et al [2013]), we start to detect increased level of crowding (or less chance of diversification) for EquallyWgted, InvVol, RiskParity, and GlobalMinVar strategies (see Figure 167 and Figure 168). If investors are worried about crowding, MinTailDependence and MaxDiversification strategies are great alternatives to the GlobalMinVar.

Figure 161: Investment universe Figure 162: Wealth curve

0 200 400 600

NO - 99M12 NO - 00M06 NO - 00M12 NO - 01M06 NO - 01M12 NO - 02M06 NO - 02M12 NO - 03M06 NO - 03M12 NO - 04M06 NO - 04M12 NO - 05M06 NO - 05M12 NO - 06M06 NO - 06M12 NO - 07M06 NO - 07M12 NO - 08M06 NO - 08M12 NO - 09M06 NO - 09M12 NO - 10M06 NO - 10M12 NO - 11M06 NO - 11M12 NO - 12M06 NO - 12M12

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

0 1 2 3 4 5

99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

Benchmark Equally w eighted Inverse Vol Risk parity Global min variance Max diversification Min tail dependence

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Page 82 Deutsche Bank Securities Inc.

Figure 163: Sharpe ratio Figure 164: CVaR/expected shortfall

.0 .2 .4 .6 .8

Benchmark Equally w eighted Inverse Vol Risk parity Global min variance Max diversification Min tail dependence

SharpeRatio

-.12 -.11 -.10 -.09 -.08 -.07

Benchmark Equally w eighted Inverse Vol Risk parity Global min variance Max diversification Min tail dependence

modifiedCVaR_ES95

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Figure 165: Diversification ratio Figure 166: Weighted portfolio tail dependence

1.2 1.6 2.0 2.4 2.8 3.2 3.6

DR - 99M12 DR - 00M06 DR - 00M12 DR - 01M06 DR - 01M12 DR - 02M06 DR - 02M12 DR - 03M06 DR - 03M12 DR - 04M06 DR - 04M12 DR - 05M06 DR - 05M12 DR - 06M06 DR - 06M12 DR - 07M06 DR - 07M12 DR - 08M06 DR - 08M12 DR - 09M06 DR - 09M12 DR - 10M06 DR - 10M12 DR - 11M06 DR - 11M12 DR - 12M06 DR - 12M12

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

.0 .1 .2 .3 .4 .5

WTD_EM - 99M12 WTD_EM - 00M06 WTD_EM - 00M12 WTD_EM - 01M06 WTD_EM - 01M12 WTD_EM - 02M06 WTD_EM - 02M12 WTD_EM - 03M06 WTD_EM - 03M12 WTD_EM - 04M06 WTD_EM - 04M12 WTD_EM - 05M06 WTD_EM - 05M12 WTD_EM - 06M06 WTD_EM - 06M12 WTD_EM - 07M06 WTD_EM - 07M12 WTD_EM - 08M06 WTD_EM - 08M12 WTD_EM - 09M06 WTD_EM - 09M12 WTD_EM - 10M06 WTD_EM - 10M12 WTD_EM - 11M06 WTD_EM - 11M12 WTD_EM - 12M06 WTD_EM - 12M12

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Deutsche Bank Securities Inc. Page 83 Figure 167: Clustering the strategies Figure 168: Grouping the strategies.

GlobalMinVar Benchmark EquallyWgted InvVol RiskParity MaxDiversification MinTailDependence

0.00.20.4

Cluster Dendrogram

-0.5 0.0 0.5

-0.50.00.5

Benchmark EquallyWgted InvVol RiskParity

GlobalMinVar

MaxDiversification MinTailDependence

pearson

Eigenvalue Ratio Plot

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

European equities

We use MSCI Europe as our investment universe (i.e., Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Israel, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, and UK). Interestingly, in European equities, it is the simpler strategies that end up winning – EquallyWgted, InvVol, and RiskParity. All risk-based strategies substantially outpace the capitalization weighted benchmark, in terms of higher Sharpe ratios (see Figure 171) and lower downside risks (see Figure 172). We see much less level of crowding for risk-based strategies in European equities. In addition, our MinTailDependence portfolio again forms its own cluster and offers investors a great way to avoid crowded strategies like GlobalMinVar (see Figure 174).

Figure 169: Investment universe Figure 170: Wealth curve

0 200 400 600 800

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

0 1 2 3 4

99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

Benchmark Equally w eighted Inverse Vol Risk parity Global min variance Max diversification Min tail dependence

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Page 84 Deutsche Bank Securities Inc.

Figure 171: Sharpe ratio Figure 172: CVaR/expected shortfall

.15 .20 .25 .30 .35

Benchmark Equally w eighted Inverse Vol Risk parity Global min variance Max diversification Min tail dependence

SharpeRatio

-.20 -.18 -.16 -.14 -.12

Benchmark Equally w eighted Inverse Vol Risk parity Global min variance Max diversification Min tail dependence

modifiedCVaR_ES95

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Figure 173: Diversification ratio Figure 174: Weighted portfolio tail dependence

1 2 3 4 5

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

.0 .2 .4 .6

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Deutsche Bank Securities Inc. Page 85 Figure 175: Clustering the strategies Figure 176: Grouping the strategies.

MinTailDependence Benchmark EquallyWgted InvVol RiskParity GlobalMinVar MaxDiversification

0.00.20.4

Cluster Dendrogram

-0.5 0.0 0.5

-0.50.00.5

Benchmark EquallyWgtedGlobalMinVarRiskParityInvVol MaxDiversification MinTailDependence

pearson

Eigenvalue Ratio Plot

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Asian equities

We use the MSCI Pacific ex Japan as our investment universe (i.e., Hong Kong, Singapore, China, India, Indonesia, Korea, Malaysia, Philippines, Taiwan, and Thailand).

In this universe, MinTailDependence shows the highest Sharpe ratio (see Figure 179) and lowest downside risk (see Figure 180), followed by GlobalMinVar. Again, all risk-based allocations significantly beat the capitalization weighted benchmark. Similar to what we find in European equities, risk-based allocations still offer great diversification benefit in the Asia ex Japan universe. MinTailDependence again shows its uniqueness (see Figure 183) and is likely to avoid crowded trades (see Figure 182).

Figure 177: Investment universe Figure 178: Wealth curve

0 200 400 600

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

0 2 4 6 8

99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

Benchmark Equally w eighted Inverse Vol Risk parity Global min variance Max diversification Min tail dependence

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Page 86 Deutsche Bank Securities Inc.

Figure 179: Sharpe ratio Figure 180: CVaR/expected shortfall

.2 .4 .6 .8

Benchmark Equally w eighted Inverse Vol Risk parity Global min variance Max diversification Min tail dependence

SharpeRatio

-.17 -.16 -.15 -.14 -.13

Benchmark Equally w eighted Inverse Vol Risk parity Global min variance Max diversification Min tail dependence

modifiedCVaR_ES95

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Figure 181: Diversification ratio Figure 182: Weighted portfolio tail dependence

1 2 3 4 5

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

.0 .1 .2 .3 .4

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Deutsche Bank Securities Inc. Page 87 Figure 183: Clustering the strategies Figure 184: Grouping the strategies.

MinTailDependence Benchmark RiskParity EquallyWgted InvVol GlobalMinVar MaxDiversification

0.00.20.4

Cluster Dendrogram

-0.5 0.0 0.5

-0.50.00.5

Benchmark EquallyWgtedRiskParityInvVol

GlobalMinVar MaxDiversification MinTailDependence

pearson

Eigenvalue Ratio Plot

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Japanese equities

We use the MSCI Japan as our investment universe. GlobalMinVar has the highest Sharpe ratio (see Figure 187), while MinTailDependence has the lowest downside risk (see Figure 188). MinTailDependence again seems to be quite unique (see Figure 191), with significantly lower chance of crowding (see Figure 190), while the traditional risk-based strategies appear to be getting crowded in recent years.

Figure 185: Investment universe Figure 186: Wealth curve

0 100 200 300 400

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

0.4 0.8 1.2 1.6 2.0 2.4

99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Page 88 Deutsche Bank Securities Inc.

Figure 187: Sharpe ratio Figure 188: CVaR/expected shortfall

-.1 .0 .1 .2 .3 .4

Benchmark Equally w eighted Inverse Vol Risk parity Global min variance Max diversification Min tail dependence

SharpeRatio

-.108 -.104 -.100 -.096 -.092 -.088

Benchmark Equally w eighted Inverse Vol Risk parity Global min variance Max diversification Min tail dependence

modifiedCVaR_ES95

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Figure 189: Diversification ratio Figure 190: Weighted portfolio tail dependence

1.2 1.6 2.0 2.4 2.8 3.2 3.6

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

.0 .1 .2 .3 .4 .5

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Deutsche Bank Securities Inc. Page 89 Figure 191: Clustering the strategies Figure 192: Grouping the strategies.

MinTailDependence Benchmark EquallyWgted InvVol RiskParity GlobalMinVar MaxDiversification

0.00.20.4

Cluster Dendrogram

-0.5 0.0 0.5

-0.50.00.5

Benchmark EquallyWgtedRiskParityInvVol GlobalMinVar MaxDiversification

MinTailDependence

pearson

Eigenvalue Ratio Plot

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Emerging markets equities

We use the MSCI EM as our investment universe. Similar to Asia ex Japan, our MinTailDependence portfolio is the clear winner, with substantially higher Sharpe ratio (see Figure 195) and lower downside risk (see Figure 196). It also appears to be highly unique (see Figure 199 and Figure 200), with much lower ex post tail dependence among its holdings (see Figure 198).

Figure 193: Investment universe Figure 194: Wealth curve

0 200 400 600 800 1,000

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

0 2 4 6 8 10

99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Page 90 Deutsche Bank Securities Inc.

Figure 195: Sharpe ratio Figure 196: CVaR/expected shortfall

0.2 0.4 0.6 0.8 1.0 1.2

Benchmark Equally w eighted Inverse Vol Risk parity Global min variance Max diversification Min tail dependence

SharpeRatio

-.17 -.16 -.15 -.14 -.13 -.12

Benchmark Equally w eighted Inverse Vol Risk parity Global min variance Max diversification Min tail dependence

modifiedCVaR_ES95

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Figure 197: Diversification ratio Figure 198: Weighted portfolio tail dependence

1 2 3 4 5 6

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

.0 .1 .2 .3 .4

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Deutsche Bank Securities Inc. Page 91 Figure 199: Clustering the strategies Figure 200: Grouping the strategies.

MinTailDependence Benchmark RiskParity EquallyWgted InvVol GlobalMinVar MaxDiversification

0.00.20.4

Cluster Dendrogram

-0.5 0.0 0.5

-0.50.00.5

Benchmark EquallyWgtedRiskParityInvVol

GlobalMinVar MaxDiversification

MinTailDependence

pearson

Eigenvalue Ratio Plot

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Global equity

Our investment universe is the MSCI World Index, i.e., the developed countries. In the global equity space, MaxDiversification, GlobalMinVar, and MinTailDependence strategies appear to be very robust, with attractive Sharpe ratios (see Figure 203) and reasonable downside risks (see Figure 204). They also form a unique cluster (see Figure 207). MinTailDependence once again proves to be the least crowded strategy (see Figure 206).

Figure 201: Investment universe Figure 202: Wealth curve

0 500 1,000 1,500 2,000

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

0 1 2 3 4 5

99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

Benchmark Equally w eighted Inverse Vol Risk parity Global min variance Max diversification Min tail dependence

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Page 92 Deutsche Bank Securities Inc.

Figure 203: Sharpe ratio Figure 204: CVaR/expected shortfall

.0 .2 .4 .6 .8

Benchmark Equally w eighted Inverse Vol Risk parity Global min variance Max diversification Min tail dependence

SharpeRatio

-.14 -.13 -.12 -.11 -.10 -.09

Benchmark Equally w eighted Inverse Vol Risk parity Global min variance Max diversification Min tail dependence

modifiedCVaR_ES95

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Figure 205: Diversification ratio Figure 206: Weighted portfolio tail dependence

1 2 3 4 5 6

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

.0 .1 .2 .3 .4

Benchmark Equally w eighted

Inverse Vol Risk parity

Global min variance Max diversification Min tail dependence

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Deutsche Bank Securities Inc. Page 93 Figure 207: Clustering the strategies Figure 208: Grouping the strategies.

Benchmark EquallyWgted InvVol RiskParity MaxDiversification GlobalMinVar MinTailDependence

0.000.100.200.30

Cluster Dendrogram

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

-0.6-0.4-0.20.00.20.40.6

Benchmark EquallyWgtedRiskParityInvVol GlobalMinVar

MaxDiversification MinTailDependence

pearson

Eigenvalue Ratio Plot

Source: Axioma, Bloomberg Finance LLP, Compustat, MSCI, Russell, Thomson Reuters, Deutsche Bank Quantitative Strategy

Page 94 Deutsche Bank Securities Inc.

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