Work Outline by Costea, Andrei by Andrei Costea

Work Outline Spring 2007 to Summer 2008 This document is intended to be a brief reference of the work that I have conducted in the field of finance, mainly concerning the Romanian capital market. Last draft: 3/01/2010. Andrei Costea 6/13/2008

Table of Contents 1. Financial Modeling 1.1 Market Analysis 1.1.1 Statistical Properties (01.2002 to 04.2008) 1.1.2 Market Efficiency Analysis (01.2002 to 04.2008) 1.1.3 Historical Beta (01.2002 to 04.2007) 1.1.4 Historical International Correlation (01.2002 to 04.2007) 1.1.5 Monte Carlo Simulation (01.2002 to 06.2008 / 07.2008 to 01.2014) 1.2 Portfolio Selection 1.2.1 Portfolio Selection (01.2002 to 09.2007) 1.2.2 Portfolio Selection (01.2002 to 04.2008) 1.2.3 Classical Portfolio Selection and Estimation Risk (01.2002 to 04.2008) 1.2.4 A Trivial Portfolio Selection Approach and Estimation Risk (01.2002 to 04.2008) 1.3 Capital Asset Pricing Model (01.2002 to 04.2008) 1.3.1 Risk Analysis 1.3.2 Higher Moments CAPM 1.3.3 Lower‐Partial‐Moment CAPM 1.3.4 Excess Loss CAPM 1.3.5 Market Efficiency Analysis

6 9 12 16 18 20 21 22 23

2. Product Structuring and Derivatives (07.2007 to 06.2008) 2.1 Constant Proportion Portfolio Insurance 2.2 Synthetic Put Hedge 2.3 Synthetic Put and Synthetic Call

25 27 30

3. Equity Valuation

1 2 4 4 5

1.1 Market Analysis 1.1.1 Statistical Properties (01.2002 to 04.2008) This section offers a succinct view on the statistical properties of four indices that are most evocative for the Romanian Capital Market. The adjacent table is plotted using continuous returns. The BET indices include securities listed on the main market of the Bucharest Stock Exchange (BSE) and the RASD‐C index is a composite index for the securities of the RASDAQ market. The BET index is a blue chip index, BET‐C is a composite index and BET‐FI reflects the financial sector not included in BET‐C. The so called INDEX is a weighted index of (83%) BET‐C, (12%) BET‐FI and (5%) RASD‐C. The time series used are on a monthly basis and span over the period from January 2002 to April 2008. The monthly returns are the end of period returns for the respective months. The sources of the data for all the following sections are Vanguard, Bloomberg, the Bucharest Stock Exchange and the Romanian Central Bank (BNR).

1.1.2 Market Efficiency Analysis (01.2002 to 04.2008)

This section investigates whether the market is efficient in respect to the 1 month autocorrelations of the indices. As it can be observed in the table from the previous section, the RASD‐C index presents an unusually high autocorrelation in almost all cases.

The regression was conducted by considering the t+1 return to be endogenous. The results are insignificant with the exception, again, of the RASD‐C index.

1.1.3 Historical Beta (01.2002 to 04.2007)

In this section the evolution of the systematic risk is plotted by starting with an initial period of one year (02.2002 to 01.2003) and then progressively rolling over to the next period by keeping the initial period unchanged.

1.1.4 Historical International Correlation (01.2002 to 04.2007)

This section follows the same computation methodology of the previous section in order to plot an evolution of the correlation of the local market to international markets. The international indices used are the MX indices published by Morgan Stanley Capital International.

1.1.5 Monte Carlo Simulation (01.2002 to 06.2008 / 07.2008 to 01.2014)

This section illustrates a Monte Carlo simulation for the BET‐C index. Ten thousand different simulations were used for a time interval of 76 months, from 07.2008 to 10.2014. The figure also plots two randomly selected examples used in the simulation and a linear regression trend line.

1.2 Portfolio Selection 1.2.1 Portfolio Selection (01.2002 to 09.2007)

In this section a classical mean variance optimization was conducted using Excel Solver. The first part shows an ex‐ante optimization for the period of 01.2002 to 09.2007. The second part illustrates a second ex‐ante optimization completed for the period of 01.2002 to 09.2006 and an ex‐post analysis of the evolution of the two minimum‐variance portfolios. Included are all the 57 securities traded on the main market of the BSE as well the first 10 by daily liquidity of the RASDAQ market.

a. The ex ante optimization:

b. The ex‐post analysis:

The following table presents the results of the two optimized MVPs as well as those of the INDEX and the two BET‐C and BET‐FI indices. Additionally, an equally weighted portfolio (same % for all assets) and an equally distributed portfolio (one unit of each asset) are also plotted.

1.2.2 Portfolio Selection (01.2002 to 04.2008)

This section follows the same methodology as the previous section but considers an extended sample from 01.2002 to 04.2008. The ex‐post analysis is conducted for the time interval of 04.2007 to 04.2008.

a. The ex‐ante optimization:

b. The ex‐post analysis:

One of the reasons for this ex‐post period to have been chosen was the fact that it also incorporates the time interval during which the financial and US real estate crisis developed. The long‐short MVP does not exhibit the same fabulous outperformance of the previous ex‐post analysis. Its outperformance is mostly due to the first period and in the following periods it loses some momentum. The long only MVP is outperformed by one of the trivial portfolios and does not even achieve a preservation of the initial capital. 11

1.2.3 Classical Portfolio Selection and Estimation Risk (01.2002 to 04.2008) This section is mainly focused on the consequences of the estimation risk associated with classical portfolio optimization. The results are in line with the general findings of the literature. The first part presents an ex ante optimization for 01.2002 to 04.2008 whereas the second part is concentrated on the ex post evolution of the long‐short MV and Tangency portfolios considering 23 rolling over periods starting with 05.2006 to 04.2008 and ending with 03.2008 to 04.2008. The optimization is conducted via Lagrange.

a. The ex‐ante optimization: 12

The adjacent figure plots the allocation level on the ordinate and the expected volatility for each risk class on the circular abscissa starting clockwise with the minimum variance allocation.

b. The ex‐post analysis:

The following two graphics plot the allocation level on the ordinate and the expected volatility for each rolling‐over period on the circular abscissa starting clockwise with the first period.

1.2.4 A Trivial Portfolio Selection Approach and Estimation Risk (01.2002 to 04.2008)

This section is concerned with illustrating an alternative trivial portfolio optimization method and, similarly to the previous section, providing an overview of the estimation risk.

The objective function is a utility function which includes the turnover return over the whole investment interval and the variance of the monthly returns. The optimization is done in such a way as for the portfolio to deliver the highest possible value over each period. As the figures below show, the risk aversion parameter becomes irrelevant in this optimization scheme. The out‐of‐sample analysis is conducted for 26 rolling‐over periods starting with 05.2005 to 04.2008 and ending with 06.2007 to 0.4.2008.

1.3 Capital Asset Pricing Model (01.2002 to 04.2008) 1.3.1 Risk Analysis BUBOR: RF Rate: MRP1: MRP2: MRP3: mean

0.0807 0.04 0.3473 0.0792 0.055 volatility

variance

co-variance

skewness

kurtosis

coco-kurtosis skewness -3.0255 4.8339 -2.5744 3.6494 -3.7868 7.3772 -1.5543 2.0860 -3.0075 5.0245 -2.0689 2.5804 -3.9576 8.4554 -3.5559 6.7635 -3.8550 7.9040 -3.7201 7.3515 -3.2095 5.5960 -3.7758 7.5526 -2.5185 3.5467 -2.9980 4.9402 -4.4706 10.7322 -3.0922 5.0501 -1.5000 1.4647 -2.6083 3.9659 -3.1058 5.3652 -1.1513 1.1502 -1.4403 1.7560 -0.8881 0.7074 -2.0678 2.6185 -2.7771 4.6063 -1.7515 2.1246 -2.7798 4.8759 -0.5615 0.5352 -3.1204 5.5470 -0.9842 0.9277 -2.7466 4.4754 -0.5834 0.6697 -4.0676 9.6689 -5.9590 18.7712

INDEX SNP TLV BIO IMP SCD PTR SIF1 SIF2 SIF3 SIF4 SIF5 PCL CMP ART ATB SOCP SNO OIL AZO AMO ARM BRM CBC COMI EPT PEI STZ SRT UAM ZIM DAFR ARAX

42.80% 35.75% 56.25% 24.86% 42.27% 28.56% 58.72% 49.71% 54.29% 52.50% 44.23% 53.26% 36.26% 43.33% 65.96% 45.33% 21.11% 37.59% 45.64% 15.81% 20.41% 11.52% 29.80% 40.94% 24.78% 38.37% 5.91% 45.50% 13.13% 40.02% 6.60% 61.32% 91.41%

34.60% 43.11% 33.59% 74.06% 53.40% 45.29% 56.13% 50.87% 50.63% 49.13% 49.29% 49.36% 44.69% 46.59% 61.81% 39.13% 47.83% 52.42% 50.97% 49.70% 63.51% 43.88% 50.38% 68.40% 58.94% 88.11% 47.37% 54.11% 46.21% 59.61% 49.55% 76.06% 66.81%

11.97% 18.59% 11.29% 54.85% 28.51% 20.52% 31.51% 25.88% 25.64% 24.14% 24.30% 24.37% 19.97% 21.71% 38.20% 15.31% 22.88% 27.48% 25.98% 24.70% 40.34% 19.25% 25.38% 46.79% 34.74% 77.64% 22.44% 29.28% 21.35% 35.53% 24.55% 57.85% 44.63%

0.1197 0.1219 0.0918 -0.0131 0.1332 0.0973 0.0875 0.1610 0.1617 0.1553 0.1576 0.1578 0.0881 0.0898 0.0986 0.0812 0.0679 0.0834 0.0744 0.0459 0.0451 0.0580 0.0688 0.0733 0.0630 0.1226 0.0552 0.0853 0.0442 0.0797 0.0602 0.0627 0.0522

6.61 34.54 30.61 -119.27 32.22 15.09 20.33 50.09 21.80 43.26 27.63 30.98 26.88 8.20 52.96 43.94 19.95 38.87 84.64 28.44 30.29 27.20 -9.51 62.48 49.04 213.32 44.57 -8.70 45.34 53.33 -5.76 6.44 31.90

477.35 574.37 393.64 2,800.90 740.96 282.84 304.93 926.21 346.17 853.33 504.96 368.94 350.18 31.48 498.56 363.21 220.90 391.09 989.34 188.83 237.04 685.32 291.22 976.05 341.78 5,331.80 547.62 228.98 293.04 330.08 350.44 101.40 303.73

APC TBM OLT ASA DUCL ARS TUFE CMF BRD PPL

39.58% 24.33% 42.45% 5.22% 40.49% 29.78% 38.08% 22.18% 37.01% 60.52%

43.02% 34.73% 67.61% 48.15% 51.06% 53.01% 51.56% 98.88% 40.92% 47.51%

18.51% 12.06% 45.71% 23.18% 26.07% 28.10% 26.58% 97.77% 16.74% 22.57%

0.0640 0.0431 0.1016 0.0413 0.0383 0.0292 0.0328 0.0270 0.0785 0.0477

39.95 5.68 65.85 30.61 49.93 -21.23 52.78 -253.13 -62.24 10.26

255.44 188.93 795.04 227.38 559.97 955.66 705.80 6,945.54 841.85 21.41

-2.6766 -1.6602 -2.9653 -0.4645 -2.6789 -1.9768 -2.5298 -1.4558 -2.5555 -3.9920

MECF RRC BCC COTE BRK FLA VNC TEL IPRU EXC CEON ALR COS AUCS MPN EFO ELJ RMAR ALBZ TRAI ENP COFI ALT ALU

-15.10% 2.18% 0.70% 40.34% 9.86% -13.18% -2.26% 7.18% 62.43% 55.13% 84.20% 43.66% 43.37% 98.05% 27.59% 33.82% 13.90% 67.93% 161.14% 89.93% 10.77% 159.92% -53.46% 11.32%

165.78% 43.48% 42.94% 59.78% 69.64% 21.52% 45.69% 43.01% 60.64% 53.43% 110.88% 49.66% 75.15% 102.48% 80.19% 48.69% 51.08% 128.94% 114.25% 87.33% 103.31% 202.74% 49.78% 66.77%

274.82% 18.91% 18.44% 35.74% 48.50% 4.63% 20.87% 18.50% 36.77% 28.54% 122.94% 24.66% 56.48% 105.03% 64.30% 23.70% 26.09% 166.25% 130.54% 76.27% 106.72% 411.03% 24.78% 44.58%

0.0766 0.1017 0.1108 0.0645 0.0798 0.0430 0.0903 0.0932 0.0667 0.0361 0.0133 0.0725 0.0245 0.0807 0.0676 0.0729 0.1326 0.0574 0.2826 0.1052 0.3161 0.0917 0.0399 0.1610

-218.34 7.17 -9.64 45.86 18.12 -32.47 17.33 0.78 2.43 82.93 11.24 33.69 149.91 22.16 54.41 24.79 47.68 122.86 161.61 88.28 -93.27 -3.02 -8.47 88.16

5,489.37 -83.82 178.43 284.80 422.77 107.87 32.38 -14.48 202.68 755.55 1,033.27 224.16 2,766.96 131.38 476.52 504.30 418.00 2,302.54 3,139.45 918.77 2,466.30 1,344.42 102.71 874.93

0.6850 0.0218 0.0070 0.4034 0.0986 -0.1318 -0.0226 0.0718 0.6243 0.5513 0.8420 0.4366 0.4337 0.9805 0.2759 0.3382 0.1390 0.6793 1.6114 0.8993 0.1077 1.5992 -0.5346 0.1132

R^2

LPM(2)

SLPM(2)

Co-LPM(2)

LPM(1)

MEL

P(SF)

ELvar

ELvol

ELcovar

UPM(2)

SUPM(2)

Co-UPM(2)

UPM(1)

MEG

P(LO)

EGvar

EGvol

3.53% 5.06% 1.84% 34.86% 8.79% 7.07% 8.52% 6.38% 6.75% 5.78% 7.08% 5.83% 5.77% 6.44% 6.86% 2.74% 7.94% 7.49% 3.80% 8.31% 13.94% 7.60% 10.19% 11.99% 9.83% 10.33% 8.36% 10.56% 6.40% 7.29% 11.41% 19.84% 8.09%

18.80% 22.50% 13.55% 59.04% 29.65% 26.59% 29.20% 25.25% 25.97% 24.04% 26.60% 24.14% 24.03% 25.38% 26.18% 16.55% 28.17% 27.37% 19.50% 28.83% 37.34% 27.57% 31.93% 34.63% 31.35% 32.15% 28.91% 32.50% 25.30% 27.01% 33.78% 44.55% 28.45%

0.04 0.03 0.01 -0.04 0.03 0.03 0.02 0.04 0.04 0.04 0.05 0.04 0.02 0.03 0.02 0.02 0.00 0.03 0.02 0.00 -0.01 0.01 0.01 0.00 0.00 0.03 0.00 0.02 0.01 0.02 0.01 0.02 0.01

24.84% 34.86% 18.30% 62.00% 43.38% 39.65% 44.69% 36.51% 39.58% 34.52% 40.66% 37.85% 38.51% 41.99% 43.98% 25.64% 49.83% 44.21% 34.16% 55.83% 69.49% 48.45% 47.76% 58.09% 60.36% 57.75% 53.35% 47.64% 53.76% 55.85% 59.59% 71.83% 36.21%

91.91% 88.96% 67.70% 176.45% 118.90% 127.56% 122.49% 108.08% 122.02% 106.45% 125.38% 121.79% 114.00% 119.51% 130.17% 70.28% 115.23% 112.82% 84.25% 114.77% 151.24% 108.65% 110.45% 153.53% 148.88% 133.54% 112.81% 130.57% 107.53% 111.71% 122.49% 279.76% 167.49%

27.03% 39.19% 27.03% 35.14% 36.49% 31.08% 36.49% 33.78% 32.43% 32.43% 32.43% 31.08% 33.78% 35.14% 33.78% 36.49% 43.24% 39.19% 40.54% 48.65% 45.95% 44.59% 43.24% 37.84% 40.54% 43.24% 47.30% 36.49% 50.00% 50.00% 48.65% 25.68% 21.62%

6.08% 6.33% 3.02% 71.52% 12.29% 9.36% 10.92% 9.16% 8.55% 8.42% 8.89% 6.64% 6.43% 6.63% 6.48% 3.41% 7.40% 8.57% 3.54% 6.24% 11.51% 7.28% 13.31% 12.31% 6.18% 9.21% 7.16% 14.72% 3.34% 4.35% 11.00% 14.72% 14.60%

24.66% 25.16% 17.37% 84.57% 35.06% 30.60% 33.04% 30.27% 29.24% 29.01% 29.82% 25.78% 25.36% 25.76% 25.45% 18.47% 27.20% 29.28% 18.83% 24.97% 33.92% 26.99% 36.48% 35.08% 24.86% 30.35% 26.76% 38.36% 18.28% 20.86% 33.16% 38.37% 38.21%

0.06 0.11 0.06 -0.19 0.09 0.07 0.08 0.09 0.08 0.10 0.09 0.07 0.05 0.02 0.07 0.03 0.03 0.08 0.09 0.06 0.03 0.04 0.01 0.00 0.05 0.11 0.05 0.10 0.05 0.07 0.03 0.05 0.16

9.98% 14.61% 12.12% 20.51% 21.23% 14.14% 25.90% 21.59% 21.38% 20.69% 18.87% 20.93% 15.31% 16.85% 35.02% 14.31% 15.32% 21.19% 23.94% 16.60% 26.75% 11.77% 15.94% 36.21% 25.43% 68.55% 14.11% 20.47% 15.09% 29.59% 13.17% 41.18% 43.60%

31.60% 38.22% 34.82% 45.29% 46.08% 37.60% 50.89% 46.46% 46.24% 45.48% 43.44% 45.75% 39.13% 41.05% 59.18% 37.83% 39.14% 46.03% 48.93% 40.75% 51.72% 34.30% 39.92% 60.18% 50.43% 82.79% 37.56% 45.24% 38.85% 54.40% 36.30% 64.18% 66.03%

0.10 0.10 0.10 0.04 0.12 0.08 0.09 0.13 0.14 0.13 0.13 0.14 0.08 0.08 0.10 0.08 0.08 0.07 0.07 0.05 0.06 0.05 0.07 0.09 0.07 0.10 0.06 0.08 0.04 0.08 0.05 0.07 0.07

68.22% 71.10% 75.31% 87.20% 86.22% 68.59% 104.21% 86.89% 94.60% 87.73% 85.49% 91.83% 75.26% 85.90% 110.82% 71.59% 71.23% 82.31% 80.42% 71.85% 90.17% 60.12% 77.96% 99.58% 85.47% 96.63% 59.35% 93.76% 67.07% 96.41% 66.27% 133.98% 128.86%

95.25% 131.53% 118.57% 153.63% 138.70% 118.04% 175.26% 139.79% 152.18% 141.14% 143.77% 141.58% 129.52% 141.26% 190.72% 129.21% 146.41% 156.17% 152.58% 151.92% 171.10% 130.86% 151.82% 175.45% 175.69% 178.77% 125.48% 165.19% 150.41% 222.96% 153.26% 215.53% 244.51%

71.62% 54.05% 63.51% 56.76% 62.16% 58.11% 59.46% 62.16% 62.16% 62.16% 59.46% 64.86% 58.11% 60.81% 58.11% 55.41% 48.65% 52.70% 52.70% 47.30% 52.70% 45.95% 51.35% 56.76% 48.65% 54.05% 47.30% 56.76% 44.59% 43.24% 43.24% 62.16% 52.70%

6.40% 12.65% 7.46% 16.55% 18.08% 12.69% 18.12% 18.40% 15.19% 16.68% 14.58% 15.59% 12.40% 11.20% 29.96% 11.97% 13.74% 19.89% 25.85% 15.96% 26.30% 11.42% 12.02% 37.86% 26.54% 98.38% 16.61% 13.54% 15.11% 27.43% 11.15% 27.78% 33.32%

25.30% 35.56% 27.31% 40.68% 42.52% 35.63% 42.57% 42.90% 38.97% 40.84% 38.18% 39.48% 35.22% 33.47% 54.73% 34.59% 37.07% 44.60% 50.84% 39.95% 51.29% 33.80% 34.67% 61.53% 51.51% 99.19% 40.76% 36.80% 38.87% 52.38% 33.40% 52.71% 57.73%

0.06 0.12 0.08 0.00 0.13 0.06 0.05 0.13 0.11 0.12 0.12 0.11 0.08 0.04 0.07 0.05 0.09 0.04 0.01 0.04 0.04 0.07 0.03 0.05 0.09 0.14 0.04 0.04 0.00 0.00 0.02 0.02 -0.03

3.9299 1.6311 5.2025 0.5526 4.1800 2.5569 3.8560 2.7061 3.6474 8.4475

0.1850 0.1284 0.1886 0.0614 0.0470 0.0253 0.0338 0.0062 0.3073 0.0843

4.12% 4.16% 9.99% 8.55% 6.45% 12.23% 6.71% 78.74% 7.85% 5.31%

20.29% 20.40% 31.61% 29.24% 25.40% 34.97% 25.91% 88.73% 28.02% 23.04%

0.01 0.01 0.02 0.00 0.01 0.01 0.01 -0.02 0.02 0.00

35.58% 33.27% 57.55% 58.19% 43.45% 45.87% 39.01% 58.48% 33.03% 34.82%

101.25% 91.19% 129.05% 123.02% 128.60% 130.55% 125.51% 188.15% 94.00% 122.70%

35.14% 36.49% 44.59% 47.30% 33.78% 35.14% 31.08% 31.08% 35.14% 28.38%

3.37% 4.56% 8.68% 5.66% 5.64% 20.36% 8.66% 215.74% 14.70% 6.45%

18.36% 21.36% 29.47% 23.80% 23.74% 45.12% 29.43% 146.88% 38.34% 25.39%

0.02 0.04 0.09 0.04 0.06 0.05 0.10 0.02 0.09 0.07

15.72% 8.40% 37.24% 14.66% 21.01% 16.62% 21.10% 19.45% 10.05% 20.36%

39.64% 28.98% 61.03% 38.28% 45.83% 40.77% 45.93% 44.10% 31.70% 45.12%

0.07 0.04 0.10 0.04 0.04 0.03 0.04 0.06 0.07 0.07

75.69% 57.93% 100.57% 63.48% 84.48% 76.05% 77.61% 80.96% 70.54% 96.16%

127.29% 99.69% 201.14% 142.34% 148.85% 137.26% 151.13% 142.64% 127.31% 169.43%

59.46% 58.11% 50.00% 44.59% 56.76% 55.41% 51.35% 56.76% 55.41% 56.76%

12.94% 6.22% 40.59% 16.01% 18.55% 14.33% 21.97% 17.30% 4.84% 12.22%

35.97% 24.94% 63.71% 40.01% 43.06% 37.86% 46.87% 41.60% 22.01% 34.96%

0.04 0.01 0.04 0.01 0.00 0.02 0.02 0.05 0.05 0.03

8.3384 0.0218 0.0070 0.4034 0.0986 -0.1318 -0.0226 0.0718 0.6243 0.5513 0.8420 0.4366 0.4337 0.9805 0.2759 0.3382 0.1390 0.6793 1.6114 0.8993 0.1077 1.5992 -0.5346 0.1132

0.0174 0.4489 0.5310 0.0908 0.1157 0.4236 0.4150 0.4657 0.0957 0.0361 0.0012 0.1652 0.0073 0.0409 0.0632 0.1160 0.3383 0.0116 0.3848 0.0668 0.2560 0.0072 0.0441 0.4122

228.02% 8.57% 9.91% 7.92% 21.89% 3.49% 9.47% 8.25% 12.01% 3.11% 44.08% 6.05% 6.76% 26.89% 17.86% 7.01% 8.53% 29.01% 7.46% 9.11% 66.48% 143.39% 20.10% 10.10%

151.00% 29.28% 31.48% 28.15% 46.79% 18.67% 30.78% 28.73% 34.66% 17.62% 66.40% 24.59% 26.01% 51.86% 42.26% 26.47% 29.21% 53.86% 27.32% 30.19% 81.54% 119.74% 44.83% 31.78%

0.02 0.05 0.05 0.01 0.04 0.03 0.04 0.06 0.02 0.01 -0.04 0.02 0.00 0.01 -0.01 0.01 0.02 -0.02 0.02 -0.02 0.04 0.08 0.02 0.08

130.58% 60.60% 54.66% 50.69% 83.81% 36.94% 63.97% 56.19% 50.66% 28.44% 60.05% 46.56% 51.43% 83.62% 76.12% 41.98% 55.66% 78.47% 35.32% 45.50% 87.96% 95.16% 98.66% 70.75%

376.06% 118.67% 136.65% 99.07% 193.80% 65.67% 127.94% 133.44% 199.83% 66.69% 382.17% 107.10% 128.57% 250.87% 147.49% 99.71% 124.68% 211.86% 141.29% 182.00% 205.24% 364.79% 158.72% 121.29%

34.72% 51.06% 40.00% 51.16% 43.24% 56.25% 50.00% 42.11% 25.35% 42.65% 15.71% 43.48% 40.00% 33.33% 51.61% 42.11% 44.64% 37.04% 25.00% 25.00% 42.86% 26.09% 62.16% 58.33%

522.64% 5.32% 9.55% 7.34% 20.02% 2.66% 5.80% 5.88% 15.12% 3.58% 155.73% 4.52% 3.53% 29.33% 16.52% 8.35% 6.42% 40.75% 13.45% 10.19% 116.16% 413.54% 11.74% 5.96%

228.61% 23.06% 30.90% 27.10% 44.75% 16.30% 24.07% 24.26% 38.88% 18.92% 124.79% 21.26% 18.79% 54.15% 40.64% 28.90% 25.34% 63.83% 36.68% 31.93% 107.78% 203.36% 34.26% 24.41%

0.20 0.10 0.09 0.09 0.02 0.05 0.03 0.08 -0.04 0.07 -0.04 0.05 -0.02 -0.21 0.01 -0.01 0.04 -0.14 0.14 0.02 0.07 -0.01 0.04 0.06

46.99% 10.34% 8.53% 29.20% 26.70% 1.30% 11.40% 10.29% 28.05% 28.01% 84.85% 20.22% 51.30% 86.28% 47.09% 17.67% 17.72% 138.59% 139.76% 71.28% 40.34% 289.42% 7.13% 34.59%

68.55% 32.15% 29.20% 54.04% 51.67% 11.38% 33.77% 32.07% 52.96% 52.92% 92.11% 44.97% 71.63% 92.89% 68.62% 42.03% 42.09% 117.72% 118.22% 84.43% 63.51% 170.12% 26.70% 58.81%

0.05 0.06 0.06 0.06 0.04 0.01 0.05 0.03 0.07 0.05 0.08 0.07 0.05 0.11 0.09 0.08 0.12 0.11 0.32 0.17 0.28 0.10 0.01 0.08

115.27% 62.83% 55.38% 91.97% 93.93% 23.35% 61.64% 63.74% 113.97% 84.38% 145.46% 90.86% 95.47% 183.23% 104.16% 76.39% 69.81% 147.66% 199.56% 137.16% 98.95% 258.56% 43.76% 83.01%

251.49% 140.62% 108.35% 232.62% 173.77% 57.48% 131.49% 134.57% 172.16% 168.77% 248.34% 169.44% 258.57% 339.52% 258.31% 145.15% 144.79% 442.97% 305.20% 310.09% 202.02% 594.68% 147.20% 249.03%

45.83% 44.68% 51.11% 39.53% 54.05% 40.63% 46.88% 47.37% 66.20% 50.00% 58.57% 53.62% 36.92% 53.97% 40.32% 52.63% 48.21% 33.33% 65.38% 44.23% 48.98% 43.48% 29.73% 33.33%

49.91% 7.10% 7.02% 29.67% 24.27% 0.60% 10.20% 7.47% 17.82% 32.04% 92.46% 14.06% 82.14% 64.73% 60.96% 16.06% 19.21% 254.88% 142.43% 86.93% 47.78% 367.34% 6.93% 52.01%

70.65% 26.65% 26.50% 54.47% 49.26% 7.75% 31.94% 27.34% 42.21% 56.60% 96.16% 37.49% 90.63% 80.45% 78.08% 40.07% 43.83% 159.65% 119.35% 93.24% 69.12% 191.66% 26.32% 72.12%

0.03 0.03 0.06 0.02 0.04 0.00 0.02 -0.01 -0.03 0.04 0.03 0.00 -0.12 0.00 0.02 0.01 0.06 -0.19 0.02 0.03 -0.15 -0.17 0.03 0.02

The table above shows the calculations that were done prior to formalizing the CAPMs. The first four co‐/moments and the R squared, the lower partial moments and the mean excess gain, the upper partial moments and the mean excess loss as well as the explicit volatility of the expected shortfall (denoted here as “downside” volatility) and the explicit volatility of the expected leftover (denoted as “upside” volatility”) are shown above. A MAR of 0% was used. The time series belong to the 67 securities previously mentioned (the 10 RASDAQ securities are COFI, CEON, ALBZ, TRAI, IPRU, RMAR, DAFR, AUCS, DUCL and ARAX). All figures are yearly continuous figures. The sample spans over 76 months from 01.2002 to 04.2008.

The adjacent figure plots the sum, for each security, of the shortfall and leftover probabilities which should theoretically sum up to 1. This does not happen as all the moments computed above are the unbiased moments of the samples. The probabilities would have summed up to one if the biased population moments were used.

EGcovar

1.0000 0.6674 0.6237 0.0026 0.5202 0.3853 0.2032 0.8369 0.8519 0.8351 0.8543 0.8533 0.3248 0.3104 0.2124 0.3599 0.1685 0.2116 0.1779 0.0714 0.0421 0.1458 0.1559 0.0959 0.0953 0.1617 0.1136 0.2077 0.0764 0.1492 0.1231 0.0568 0.0511

INDEX SNP TLV BIO IMP SCD PTR SIF1 SIF2 SIF3 SIF4 SIF5 PCL CMP ART ATB SOCP SNO OIL AZO AMO ARM BRM CBC COMI EPT PEI STZ SRT UAM ZIM DAFR ARAX

variance skewness beta beta 1.00 -0.46 1.02 -0.39 0.77 -0.57 -0.11 -0.23 1.11 -0.45 0.81 -0.31 0.73 -0.60 1.35 -0.54 1.35 -0.58 1.30 -0.56 1.32 -0.49 1.32 -0.57 0.74 -0.38 0.75 -0.45 0.82 -0.68 0.68 -0.47 0.57 -0.23 0.70 -0.39 0.62 -0.47 0.38 -0.17 0.38 -0.22 0.48 -0.13 0.57 -0.31 0.61 -0.42 0.53 -0.26 1.02 -0.42 0.46 -0.08 0.71 -0.47 0.37 -0.15 0.67 -0.42 0.50 -0.09 0.52 -0.61 0.44 -0.90

Higher Moments CAPM kurtosis systemat. expected beta risk return 1 0.01 1.47 48.36% 0.01 1.41 48.15% 0.02 1.35 41.67% 0.00 0.13 7.13% 0.01 1.58 52.25% 0.01 1.13 40.08% 0.02 1.35 40.75% 0.01 1.90 61.32% 0.02 1.95 62.07% 0.02 1.88 59.98% 0.01 1.81 59.70% 0.02 1.90 60.79% 0.01 1.12 38.26% 0.01 1.21 39.63% 0.02 1.52 44.90% 0.01 1.16 37.32% 0.00 0.80 30.52% 0.01 1.10 37.06% 0.01 1.10 35.35% 0.00 0.56 23.50% 0.00 0.60 23.80% 0.00 0.62 26.51% 0.01 0.89 31.83% 0.01 1.04 34.43% 0.00 0.80 29.55% 0.01 1.45 48.74% 0.00 0.55 25.12% 0.01 1.20 38.56% 0.00 0.52 22.69% 0.01 1.09 36.22% 0.00 0.59 26.59% 0.02 1.16 33.76% 0.04 1.38 34.25%

expected return 2 16.27% 16.37% 14.50% 7.35% 17.17% 14.70% 14.24% 19.06% 19.13% 18.70% 18.80% 18.86% 14.14% 14.29% 15.01% 13.74% 12.70% 13.84% 13.28% 11.22% 11.19% 11.99% 12.82% 13.18% 12.40% 16.44% 11.78% 14.01% 11.09% 13.60% 12.10% 12.60% 12.09%

expected return 3 9.64% 9.72% 8.39% 3.47% 10.26% 8.56% 8.20% 11.56% 11.61% 11.31% 11.39% 11.42% 8.16% 8.26% 8.73% 7.87% 7.19% 7.95% 7.56% 6.16% 6.14% 6.70% 7.26% 7.49% 6.97% 9.76% 6.56% 8.06% 6.08% 7.79% 6.79% 7.07% 6.67%

Second Lower Partial Momnt CAPM Excess Loss Volatility CAPM shortfall expected expected expected SF/LO beta excess loss expected expected expected excess gain EL/EG beta leftover beta beta return 1 return 2 return 3 ratio beta return 1 return 2 return 3 beta ratio 1.00 42.80% 15.99% 9.50% 1.00 1.00 1.00 42.80% 15.99% 9.50% 1.00 1.00 0.92 39.86% 15.32% 9.03% 1.03 1.12 1.84 71.87% 22.62% 14.10% 1.83 0.99 0.41 22.37% 11.33% 6.26% 0.98 2.37 0.93 40.31% 15.42% 9.11% 1.24 1.33 -1.17 -32.48% -1.17% -2.42% 0.37 -0.32 -3.16 -101.59% -16.93% -13.37% 0.05 -0.02 0.89 38.86% 15.09% 8.88% 1.17 1.32 1.50 60.14% 19.94% 12.25% 2.02 1.35 49.35% 17.48% 10.54% 0.99 0.83 0.92 40.01% 15.35% 9.06% 0.75 0.82 1.19 0.54 26.72% 12.32% 6.95% 0.90 1.67 1.34 54.45% 18.64% 11.35% 0.84 0.63 1.25 51.42% 17.95% 10.87% 1.35 1.08 1.42 57.27% 19.29% 11.79% 2.11 1.49 1.21 50.16% 17.67% 10.67% 1.39 1.14 1.26 51.82% 18.04% 10.93% 1.71 1.36 1.15 48.00% 17.17% 10.32% 1.34 1.16 1.66 65.65% 21.20% 13.12% 1.86 1.12 1.29 52.75% 18.26% 11.08% 1.28 1.00 1.55 61.76% 20.31% 12.50% 1.82 1.18 1.15 47.98% 17.17% 10.32% 1.37 1.19 1.21 50.00% 17.63% 10.64% 1.66 1.38 0.62 29.57% 12.97% 7.40% 0.79 1.28 0.77 34.97% 14.20% 8.26% 1.18 1.52 0.73 33.32% 13.83% 8.00% 0.80 1.10 0.26 17.05% 10.12% 5.42% 0.61 2.37 0.52 26.14% 12.19% 6.86% 1.04 2.00 1.20 49.89% 17.60% 10.62% 1.16 0.96 26.14% 12.19% 6.86% 0.79 1.51 0.55 27.03% 12.39% 7.00% 0.78 1.44 0.52 -0.14 3.37% 7.00% 3.26% 0.80 -5.94 0.52 26.26% 12.22% 6.88% 1.39 2.65 0.71 32.70% 13.68% 7.90% 0.72 1.02 1.25 51.42% 17.95% 10.86% 0.70 0.56 0.62 29.53% 12.96% 7.40% 0.69 1.12 1.53 61.06% 20.15% 12.39% 0.19 0.12 0.05 9.81% 8.47% 4.28% 0.50 9.95 1.05 44.61% 16.40% 9.79% 0.60 0.57 -0.28 -1.67% 5.85% 2.46% 0.62 -2.23 0.56 27.49% 12.50% 7.08% 0.55 0.98 0.21 15.29% 9.72% 5.14% 0.55 2.64 0.60 28.96% 12.83% 7.31% 1.10 1.83 0.22 15.81% 9.83% 5.23% 0.72 3.22 0.17 14.10% 9.45% 4.96% 0.48 2.74 -0.06 5.83% 7.56% 3.65% 0.90 -14.04 -0.07 5.59% 7.50% 3.61% 0.86 -12.00 0.06 10.31% 8.58% 4.36% 0.70 10.80 0.80 35.84% 14.40% 8.40% 1.42 1.78 0.92 39.92% 15.33% 9.04% 1.04 1.14 1.73 68.06% 21.75% 13.50% 2.20 1.27 0.05 9.81% 8.47% 4.28% 0.56 11.13 0.79 35.65% 14.36% 8.37% 0.68 0.85 0.68 31.74% 13.47% 7.75% 0.78 1.14 1.65 65.41% 21.14% 13.08% 0.60 0.36 0.24 16.33% 9.95% 5.31% 0.41 1.71 0.85 37.68% 14.82% 8.69% 0.02 0.03 0.46 23.88% 11.67% 6.50% 0.78 1.72 1.18 49.02% 17.40% 10.48% 0.01 0.01 0.38 21.35% 11.10% 6.10% 0.49 1.28 0.48 24.75% 11.87% 6.64% 0.31 0.65 0.52 26.19% 12.20% 6.87% 0.67 1.28 0.79 35.34% 14.29% 8.32% 0.38 0.49 0.39 21.51% 11.13% 6.13% 0.72 1.85 2.70 101.69% 29.41% 18.83% -0.48 -0.18

actual return 1 42.80% 35.75% 56.25% 24.86% 42.27% 28.56% 58.72% 49.71% 54.29% 52.50% 44.23% 53.26% 36.26% 43.33% 65.96% 45.33% 21.11% 37.59% 45.64% 15.81% 20.41% 11.52% 29.80% 40.94% 24.78% 38.37% 5.91% 45.50% 13.13% 40.02% 6.60% 61.32% 91.41%

Actual Returns actual reg. slope return 2 15.99% 206.18 16.52% 0.01 14.94% 0.01 16.42% 0.01 42.34% 0.02 23.80% 0.02 27.65% 0.05 16.34% 0.05 9.29% 0.03 18.00% 0.03 26.14% 0.06 -0.18% 0.02 14.70% 0.05 16.00% 0.02 16.02% 0.60 16.71% 0.03 8.60% 0.00 13.08% 0.17 11.86% 0.01 8.76% 0.00 15.78% 0.00 15.31% 0.00 15.24% 0.03 11.67% 0.23 20.44% 0.02 10.18% 0.01 25.51% 1.40 12.16% 0.01 13.44% 0.00 14.84% 0.01 8.26% 0.03 19.15% 0.01 17.78% 0.00

reg. intercept -1,421.65 0.04 -0.14 -0.03 0.01 -0.34 -0.47 -0.56 -0.35 -0.25 -0.71 -0.09 -0.38 -0.16 -11.60 -0.31 0.08 0.03 -0.09 0.17 0.01 0.29 0.37 -2.58 -0.23 -0.10 34.81 -0.07 0.06 -0.04 1.09 -0.14 -0.10

APC TBM OLT ASA DUCL ARS TUFE CMF BRD PPL

0.53 0.36 0.85 0.34 0.32 0.24 0.27 0.23 0.66 0.40

-0.40 -0.25 -0.45 -0.07 -0.40 -0.30 -0.38 -0.22 -0.39 -0.60

0.01 0.00 0.01 0.00 0.01 0.01 0.01 0.01 0.01 0.02

0.95 0.61 1.31 0.42 0.73 0.55 0.66 0.45 1.05 1.02

31.56% 23.60% 42.99% 20.90% 24.11% 20.16% 22.24% 18.58% 35.53% 29.26%

12.56% 11.07% 15.07% 10.84% 10.86% 10.19% 10.48% 9.99% 13.50% 11.60%

7.06% 6.05% 8.80% 5.92% 5.88% 5.43% 5.62% 5.31% 7.72% 6.38%

0.22 0.25 0.47 0.01 0.26 0.18 0.31 -0.60 0.50 0.03

15.77% 16.69% 24.45% 8.45% 16.98% 14.36% 18.73% -12.82% 25.43% 9.05%

9.82% 10.03% 11.80% 8.16% 10.10% 9.50% 10.50% 3.31% 12.03% 8.29%

5.22% 5.36% 6.59% 4.06% 5.41% 5.00% 5.69% 0.69% 6.75% 4.15%

0.71 0.43 1.00 0.43 0.44 0.34 0.36 0.56 0.74 0.69

3.19 1.74 2.13 38.89 1.71 1.86 1.17 -0.94 1.49 24.42

0.39 0.62 1.42 0.73 0.95 0.82 1.60 0.32 1.46 1.12

21.49% 29.53% 57.31% 33.33% 40.91% 36.42% 63.74% 19.06% 58.89% 46.98%

11.13% 12.96% 19.29% 13.83% 15.56% 14.53% 20.76% 10.57% 19.66% 16.94%

6.13% 7.40% 11.80% 8.00% 9.20% 8.49% 12.82% 5.74% 12.05% 10.16%

0.61 0.11 0.61 0.09 0.04 0.24 0.28 0.74 0.75 0.48

1.58 0.18 0.43 0.12 0.04 0.29 0.17 2.35 0.51 0.43

39.58% 24.33% 42.45% 5.22% 40.49% 29.78% 38.08% 22.18% 37.01% 60.52%

13.09% 20.13% 12.53% 7.72% 15.13% 9.88% 14.14% -0.85% 14.64% 12.24%

0.01 0.01 0.01 0.00 0.02 0.02 0.01 0.01 0.36 0.06

-0.02 0.02 -0.12 0.30 0.00 -0.09 -0.15 3.58 -2.64 -0.84

MECF RRC BCC COTE BRK FLA VNC TEL IPRU EXC CEON ALR COS AUCS MPN EFO ELJ RMAR ALBZ TRAI ENP COFI ALT ALU

0.62 0.83 0.88 0.50 0.70 0.46 0.96 0.92 0.53 0.29 0.11 0.56 0.17 0.53 0.60 0.38 0.67 0.34 1.78 0.48 0.86 0.32 0.27 1.14

0.10 0.00 0.00 -0.02 0.00 0.00 0.00 0.00 0.11 0.12 0.19 0.11 0.08 0.02 0.01 0.00 0.00 0.01 0.10 0.03 0.00 0.02 0.02 0.00

0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.54 0.84 0.88 0.52 0.71 0.45 0.96 0.93 0.42 0.17 -0.07 0.46 0.09 0.51 0.59 0.37 0.66 0.32 1.68 0.46 0.86 0.31 0.25 1.15

28.61% 37.06% 38.78% 25.74% 32.53% 23.87% 41.37% 40.18% 25.10% 16.57% 9.64% 26.32% 12.95% 26.29% 28.84% 21.11% 31.15% 19.56% 68.64% 24.52% 38.08% 19.13% 17.31% 47.76%

12.94% 14.68% 15.07% 12.07% 13.64% 11.68% 15.66% 15.39% 12.18% 10.26% 8.82% 12.45% 9.35% 12.27% 12.83% 11.05% 13.34% 10.72% 22.08% 11.88% 14.91% 10.63% 10.22% 17.11%

7.40% 8.59% 8.86% 6.77% 7.87% 6.51% 9.27% 9.08% 6.87% 5.54% 4.55% 7.06% 4.90% 6.92% 7.31% 6.07% 7.66% 5.84% 13.75% 6.65% 8.75% 5.78% 5.50% 10.28%

0.58 0.92 0.98 0.26 0.67 0.61 0.89 1.04 0.43 0.14 -1.03 0.48 -0.10 0.29 -0.56 0.20 0.47 -0.59 0.31 -0.48 0.99 2.45 0.25 0.89

28.13% 39.87% 42.13% 17.14% 31.40% 29.39% 38.93% 44.24% 22.93% 13.00% -27.86% 24.73% 4.43% 18.18% -11.38% 14.95% 24.53% -12.56% 18.86% -8.69% 42.28% 93.13% 16.73% 39.02%

12.64% 15.32% 15.84% 10.14% 13.39% 12.93% 15.10% 16.32% 11.46% 9.19% -0.12% 11.87% 7.24% 10.37% 3.64% 9.64% 11.82% 3.37% 10.53% 4.25% 15.87% 27.46% 10.05% 15.13%

7.18% 9.04% 9.39% 5.44% 7.70% 7.38% 8.89% 9.73% 6.35% 4.78% -1.69% 6.64% 3.42% 5.60% 0.92% 5.09% 6.61% 0.73% 5.71% 1.35% 9.42% 17.47% 5.37% 8.90%

0.49 0.70 0.74 0.74 0.74 0.26 0.95 0.76 0.70 0.49 0.81 0.65 0.39 0.79 0.84 0.47 0.65 0.65 2.70 0.90 0.81 0.35 0.13 1.59

0.85 0.76 0.76 2.85 1.11 0.42 1.07 0.73 1.64 3.43 -0.78 1.36 -3.70 2.71 -1.50 2.35 1.37 -1.09 8.70 -1.87 0.82 0.14 0.50 1.78

3.32 1.29 1.17 1.08 0.30 0.88 0.66 1.00 -0.57 0.99 -0.57 0.83 -0.26 -5.58 0.21 -0.13 0.54 -3.06 1.97 0.02 1.47 -0.18 0.15 0.39

123.53% 52.84% 48.81% 45.45% 18.37% 38.74% 31.10% 42.64% -11.81% 42.45% -11.65% 36.89% -0.80% -185.86% 15.19% 3.41% 26.82% -98.04% 76.40% 8.63% 58.98% 1.68% 13.31% 21.73%

34.39% 18.28% 17.36% 16.59% 10.42% 15.06% 13.32% 15.95% 3.54% 15.91% 3.58% 14.64% 6.05% -36.14% 9.69% 7.01% 12.34% -16.12% 23.65% 8.20% 19.68% 6.61% 9.26% 11.18%

22.29% 11.09% 10.45% 9.92% 5.63% 8.86% 7.65% 9.48% 0.85% 9.45% 0.88% 8.56% 2.60% -26.71% 5.13% 3.26% 6.97% -12.81% 14.82% 4.09% 12.06% 2.99% 4.83% 6.16%

0.51 0.79 1.28 0.44 1.34 0.17 0.78 -0.23 -0.43 0.62 0.40 0.03 -1.61 -0.01 0.25 0.09 0.41 -1.49 0.22 0.03 -1.07 -0.20 0.05 0.03

0.15 0.61 1.09 0.41 4.52 0.20 1.18 -0.23 0.75 0.63 -0.70 0.04 6.30 0.00 1.24 -0.68 0.76 0.49 0.11 1.86 -0.73 1.09 0.34 0.06

-15.10% 2.18% 0.70% 40.34% 9.86% -13.18% -2.26% 7.18% 62.43% 55.13% 84.20% 43.66% 43.37% 98.05% 27.59% 33.82% 13.90% 67.93% 161.14% 89.93% 10.77% 159.92% -53.46% 11.32%

59.66% 9.22% 14.99% 19.56% 20.54% -30.49% 14.76% -20.69% 11.52% 9.32% 12.11% 12.59% 14.20% 11.65% 17.69% 14.55% 18.34% 12.98% 19.55% 14.38% 14.53% 20.09% #NUM! #NUM!

0.11 0.00 0.00 1.16 0.04 0.00 0.00 -0.36 0.10 0.03 0.22 0.12 0.11 0.38 0.01 0.03 0.01 0.35 0.01 0.59 0.11 0.02 -0.01 -0.25

1.08 0.07 0.36 -40.70 -1.01 0.58 0.02 61.23 -2.14 -0.35 -4.90 -1.79 -2.26 -11.03 0.01 -0.66 0.00 -11.83 -0.50 -21.06 -3.26 -0.86 0.59 24.38

The above table includes the five computed betas, their respective expected returns and the actual returns as well as the ratios of the shortfall (SF) and leftover (LO) betas and of the excess loss (EL) and excess gain (EG) betas. There are two important remarks to be made. The first one is that the expected returns were computed using different alternatives of the risk‐free rate and market‐risk premium. The first alternative uses the local risk‐free rate (the 10 year BUBOR rate) and a market return computed as the historical yearly log‐mean return. The second one uses the same risk‐free rate as the first one but a market rate computed as the “regressed” log‐return of the next 12 months (the regression is first done for the next 76 months and then computed back to one year). The third expected return uses the traditional combination of a risk‐free rate of 4% and a market return of 9.5% (i.e. a market risk premium of 5.5%). The second remark (implied by the first remark) is that there are also two alternative actual returns computed in accordance with the first two expected returns. The first actual return is the historical yearly log‐mean return of the security whereas the second actual return is the “regressed” log‐return for the next 12 months (performed as specified above). Please also note that positive skewness has a negative influence on the systematic risk, as it reduces it, and that the MRPs for the skewness and kurtosis betas where adjusted to be in accordance with the two higher moments.

Regarding the Shortfall beta to Leftover beta ratio please not that: Preferable scenarios when market is up‐trending: ‐ LO beta > SF beta => ratio<1 ‐ 1>LO beta>0 and 0>SF beta>‐1 => ratio<0 ‐ LO beta>1 and 1>SF beta>0 => 1>ratio>0 ‐ LO beta>1 and 0>SF beta>‐1 => 0>ratio>‐1 ‐ LO beta>1 and SF beta<‐1 => ratio<‐1 Preferable scenarios when market is down‐trending: ‐ SF beta > LO beta => ratio>1 ‐ 1>SF beta>0 and 0>LO beta>‐1 => ratio<0 ‐ SF beta>1 and 1>LO beta>0 => ratio>1 ‐ SF beta>1 and 0>LO beta>‐1 => ratio<‐1 ‐ SF beta>1 and LO beta<‐1 => 0>ratio>‐1

Regarding the EL beta to EG beta ratio please not that: Preferable scenarios when market is up‐trending: ‐ EL beta > EG beta => ratio<1 ‐ 1>EL beta>0 and 0>EL beta>‐1 => ratio<0 ‐ EG beta>1 and 1>EL beta>0 => 1>ratio>0 ‐ EG beta>1 and 0>EL beta>‐1 => 0>ratio>‐1 ‐ EG beta>1 and EL beta<‐1 => ratio<‐1 Preferable scenarios when market is down‐trending: ‐ EL beta > EG beta => ratio>1 ‐ 1>EL beta>0 and 0>EG beta>‐1 => ratio<0 ‐ EL beta>1 and 1>EG beta>0 => ratio>1 ‐ EL beta>1 and 0>EG beta>‐1 => ratio<‐1 ‐ EL beta>1 and EG beta<‐1 => 0>ratio>‐1

1.3.2 Higher Moments CAPM

Higher Moments CAPM 1

risk = volatility ‐ skewness + kurtosis (actual return = historical yearly logmean return)

200.00%

150.00%

100.00%

Returns MRP1=34.73%

Return

MRP2=7.92% MRP3=5.5%

50.00%

Linear (MRP1=34.73%) Linear (MRP2=7.92%) Linear (MRP3=5.5%)

0.00% ‐0.50

0.00

0.50

1.00

1.50

2.00

2.50

‐50.00%

‐100.00% Systematic Risk

Higher Moments CAPM 2

risk = volatility ‐ skewness + kurtosis (actual return = regressed logreturn for next 12 months)

100.00%

80.00%

60.00%

Returns MRP1=34.73%

MRP2=7.92%

Return

40.00%

MRP3=5.5% Linear (MRP1=34.73%) 20.00%

Linear (MRP2=7.92%) Linear (MRP3=5.5%)

0.00% ‐0.50

0.00

0.50

1.00

1.50

2.00

2.50

‐20.00%

‐40.00%

Systematic Risk

1.3.3 Lower‐Partial‐Moment CAPM

LPM CAPM 1

risk = square root of second lower partial moment (i.e. shortfall volatility) (actual return = historical yearly logmean return) 200.00%

150.00%

100.00%

Returns MRP1=34.73%

Return

MRP2=7.92% MRP3=5.5%

50.00%

Linear (MRP1=34.73%) Linear (MRP2=7.92%) Linear (MRP3=5.5%)

0.00% ‐1.50

‐1.00

‐0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

‐50.00%

‐100.00% Systematic Risk

LPM CAPM 2

risk = square root of second lower partial moment (i.e. shortfall volatility) (actual return = regressed logreturn for next 12 months) 100.00%

80.00%

60.00%

Returns MRP1=34.73%

MRP2=7.92%

Return

40.00%

MRP3=5.5% Linear (MRP1=34.73%) 20.00%

Linear (MRP2=7.92%) Linear (MRP3=5.5%)

0.00% ‐1.50

‐1.00

‐0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

‐20.00%

‐40.00%

Systematic Risk

1.3.4 Excess Loss CAPM

Excell Loss CAPM 1

risk = volatility of excess loss (actual return = historical yearly logmean return) 200.00%

150.00%

100.00%

50.00%

Return

0.00% ‐7.00

‐6.00

‐5.00

‐4.00

‐3.00

‐2.00

‐1.00

0.00

1.00

2.00

3.00

4.00Returns MRP1=34.73%

‐50.00%

MRP2=7.92%

MRP3=5.5%

‐100.00%

Linear (MRP1=34.73%)

Linear (MRP2=7.92%) ‐150.00%

Linear (MRP3=5.5%)

‐200.00%

‐250.00% Systematic Risk

Excess Loss CAPM 2

risk = volatility of excess loss (actual return = regressed logreturn for next 12 months) 150.00%

100.00%

50.00%

‐7.00

Return

0.00%

‐6.00

‐5.00

‐4.00

‐3.00

‐2.00

‐1.00

0.00

‐50.00%

1.00

2.00

3.00

4.00 Returns MRP1=34.73% MRP2=7.92%

‐100.00%

‐150.00%

MRP3=5.5% Linear (MRP1=34.73%) Linear (MRP2=7.92%) Linear (MRP3=5.5%)

‐200.00%

‐250.00%

Systematic Risk

1.3.5 Market Efficiency Analysis

In this section a test to see if the market is efficient, in respect to the idiosyncratic return, was conducted. It is intuitive to assume that the higher the liquidity of a security the lower its idiosyncratic return. The first sample considers positive as well as negative idiosyncratic returns whereas the second sample comprises the modulus of these returns. The two types of expected and actual returns presented previously are taken into account. The p‐values and the normal and adjusted Rs squared are shown subsequently.

For the first sample (A) one might expect no relation while for the second sample (B) a negative relation is reasonable. The liquidity is considered to be exogenous. The Rs squared are satisfactory for the first sample but not for the second one as they continue to point towards no explanatory power. The p‐values are only acceptable for the first type of idiosyncratic return in the first sample (Efficiency 1A). The coefficient of the liquidity for the second type of idiosyncratic return in the first sample (Efficiency 2A) is significant and should be rejected. The coefficient of the liquidity for the second type idiosyncratic return in the second sample (Efficiency 2B) is negative but insignificant. The other coefficient in the second sample (EFFICIENCY 1B) is also insignificant and points towards no negative relation. The results are therefore contradictory and cannot lead to a satisfactory conclusion. It would be interesting to further check what results are delivered if the sample is adjusted with the Skipped‐Huber‐Method.

2. Product Structuring and Derivatives (07.2007 to 06.2008) 2.1 Constant Proportion Portfolio Insurance This section presents different applications of the CPPI for the period of 06.2007 to 06.2008, in order to incorporate the impact of the undergoing financial crisis. The underlying security is the SNP, which is the mostly capitalized and highly liquid security listed on the BSE. The initial capital and the security are standardized to 100. The floor is set at 90%, the multiplier at 5 and the maximum acceptable stock quota at 80%. The money‐market‐account as well as the floor are compounded with the prevailing overnight interest rate. In some of the following applications transaction costs are also included (2% per transaction value). No‐load means that they are treated separately and as such subtracted from the final daily value of the portfolio. Loaded means that they are incorporated into the evolution of the portfolio (and therefore in the calculation of the stock quota) and consequently subtracted from the money‐market‐account on the day they occur.

2.2 Synthetic Put Hedge

This section, similarly to the previous section, presents different applications of the Synthetic Put Hedge strategy. The time span and underlying security used are the same. The illustrated floor is meant to be the strike price in the respective period. The interest compounding is done on an overnight basis. A dividend yield was also incorporated into the model, but it is in all applications set to zero. A transaction cost of 2% and a time to maturity of 365 calendar days should be the standard if not specified. The figure below refers to a time to maturity of the embedded put option of 365 calendar days.

The figure above refers to a time to maturity of the embedded put option of 10 calendar days.

The figure below refers to a transaction cost of 2% per transaction value.

The figure above refers to a transaction cost of 2% per transaction value.

The figure below refers to a transaction cost of 5% per transaction value.

The figure above refers to a transaction cost of 2% per transaction value.

Using the stock strike price instead of the portfolio strike price leads to a slightly less volatile portfolio but to more frequent portfolio shifts.

2.3 Synthetic Put and Synthetic Call

The evolution of the synthetic call is exactly the same as the one of the synthetic put hedge. The stock and money‐market accounts also follow the same path. This is due to the fact that the payoffs and the deltas of the two strategies are the same. Only the construction of the delta differs.

The figure below refers to a time to maturity of the put option of 365 calendar days.

The figure above refers to a time to maturity of the put option of 10 calendar days.

The figure below refers to a transaction cost of 2% per transaction value.

The figure above refers to a transaction cost of 2% per transaction value.

The figures below refer to an extreme transaction cost of 20% per transaction value.

Using the stock strike price instead of the portfolio strike price leads to a slightly less volatile portfolio but to more frequent portfolio shifts and an incapability of covering the initial capital.

3. Equity Valuation

This section provides a short insight into a corporate valuation model which uses the classical FCFF and FCFE methodologies. The model is constructed in such a way as to a have a flexible structure. For instance the individual cash flows can be estimated by using a logarithmic or linear regression conducted on values like a macroeconomic indicator or specific assets of the company or other relevant cash flows. Naturally, the model also checks for the explanatory power of the variables. Estimation can also be done to include different growth periods. Another flexibility arises for example from the different methods of estimating the cost of debt or the growth rate of the terminal value. The key ratios and financial information implicitly used in the valuation are extracted from the balance sheet, income statement and cash flow statement of the company.