WO2011059460A2 - Computer system and method for ranking private equity fund managers - Google Patents

Abstract

The present invention is computer based system and method for ranking of Private Equity (PE) Fund Managers based upon publically available performance information of PE Funds from an external data base. In one embodiment, the computer based method comprises the steps of (a) providing a computer system comprising a storage device; (b) creating a first data base on the storage device comprising a list of PE Fund Managers and PE Funds from the external data base; (c) creating a second data base on the storage device comprising absolute performance data DPI%, IRR% and TVPI% for all available PE, Fund from the external data base, (d) creating a third data base on the storage device comprising absolute performance data DPI%, IRR%, and TVPI% for each year of all available PE Fund from the external data base, (e) creating a fourth data base on the storage device comprising weighting coefficient DPI, weighting coefficient IRR, and weighting coefficient TVPl based upon statistical analysis of said performance data DPI%, IRR% and TVPI% respectively, for each year of the PE Funds stored in the third data base, (f) creating a fifth data base on the storage device comprising PE Fund Managers from the first data base, (g) creating a sixth data base on the storage device comprising qualifying PE Fund Managers from the fifth data base, and (h) creating a ranking data base on the storage device comprising a ranking for each of the qualifying PE Fund Managers stored in the sixth data base using the weighting coefficient DPI, weighting coefficient IRR, and weighting coefficient TVPI stored in the fourth data base.

Description

TITLE OF THE INVENTION

Computer System and Method For Ranking Private Equity Fund Managers

CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to and the benefit of International Application No. PCT US09/64288 filed on November 12, 2009, which is hereby incorporated by reference into this application in its entirety, which claims priority to and the benefit of U.S. Provisional Patent Application Serial No. 61/113,986 filed on November 12, 2008, which is hereby incorporated by reference into this application in its entirety.

BACKGROUND OF THE INVENTION

The present invention relates to computer based financial analysis tools for private equity (PE) funds. Measuring the performance of a PE firm or PE Manager relative to other PE firms and PE managers is challenging. Performance is typically recorded at the fund-level (and not for the entire PE firm or for a particular PE Manager). Furthermore, three factors make the aggregation of performance to the firm-level and manager-level challenging. First, alternative, complementary performance measures are used to assess performance (e.g. Internal Rate of Return (IRR) vs. Return Multiple), so that it is not trivial to know what measure to examine. Second, people disagree whether firms should be assessed according to their absolute performance or based on the performance relative to a performance benchmark. Third, PE firms typically manage a number of limited-life funds raised at different vintage years simultaneously and the so- called J-Curve phenomenon makes it difficult to say, whether for example, a four (4) year old fund with a 15% IRR is better or worse than a seven (7) year old fund with a 20% IRR. There is a need for a computer based financial analysis tool to help investors access the performance of PE fund managers.

SUMMARY OF THE INVENTION

One object of the present invention is to provide a computer based system and method to combine publically available information on private equity (PE) Funds with a financial analysis program that allows investors to assess the attractiveness of an investment into a given PE Fund Manager with a much greater level of accuracy.

The present invention is computer based system and method for ranking of PE Fund Managers based upon publically available performance information of PE Funds from an external data base. In one embodiment, the computer based method comprises the steps of: (a) providing a computer system comprising a storage device; (b) creating a first data base on the storage device comprising a list of PE Fund Managers and PE Funds from the external data base; (c) creating a second data base on the storage device comprising absolute performance data DPI%; IRR%; and TVPI% for all available PE Fund from the external data base; (d) creating a third data base on the storage device comprising absolute performance data DPI%; IRR%; and TVPI% for each year of all available PE Funds from the external data base; (e) creating a fourth data base on the storage device comprising weighting coefficient DPI, weighting coefficient IRR, and weighting coefficient TVPI based upon statistical analysis of the performance data DPI%; IRR%; and TVPI%, respectively, for each year of the PE Funds stored in the third data base; (f) creating a fifth data base on the storage device comprising PE Fund Managers from the first data base; (g) creating a sixth data base on the storage device comprising qualifying PE Fund Managers from the fifth data base; and (h) creating a ranking data base on the storage device comprising a ranking for each of the qualifying PE Fund Managers stored in the sixth data base using the weighting coefficient DPI, weighting coefficient IRR, and weighting coefficient TVPI stored in the fourth data base.

BRIEF DESCRIPTION OF THE DRAWINGS

The following description of the invention will be better understood with reference to the accompanying drawings in which:

FIG. 1 is a high level block diagram showing the architecture of the computer system having a program module according to the present invention;

FIG. 2 is a high level flow chart showing the method of the program module according to the present invention;

FIGS. 3-6 are detailed flow charts showing the method of the program module according to the present invention;

FIG. 7 is an illustration of a Third Data Base 26 containing Performance Data (DPI%; IRR%, and TVPI%) for each year of a partial list of all available PE Funds; and

FIG. 8 is an illustration of a Fourth Data Base 28 containing Performance Weighting Coefficient DPI, Weighting Coefficient IRR, and Weighting Coefficient TVPI for each year of a partial list all available PE Funds by PE type and geography. DESCRIPTION OF THE INVENTION

Referring to FIG. 1 , where a computer system 10 according to the present invention is shown. Computer system 10 generally comprises an electronic computing device 12 such as a microprocessor. System 10 further comprises an input device 14 connected to computing device 12. Input device 14 may be a commonly available keyboard. System 10 further comprises a display device 16 connected to computing device 12. Display device 16 may be a commonly available display monitor. System 10 further comprises a storage device 18 connected to computing device 12. Storage device 18 may be a commonly available hard disk drive. System 10 further comprises a program module 20 stored on storage device 18. Program module 20 comprises a plurality of computer coded instructions or software configured to instruct computing device 12 to access the performance of the universe of PE Managers available from external PE fund data bases and provide a ranking of fund managers that is a better predictor of future performance than conventional systems or methods. Computer system 10 may access and download PE Fund Manager and PE Fund information from a First External Data Base 42 via Internet 40. Similarly, computer system 10 may access and download PE Fund performance data as well as vintage year, PE type (such as buy-outs, venture capital, and real estate), and geography from a Second External Data Base 44 via Internet 40. First External Data Base 42 may be a commercially available data base known as

VentureXpert® by Venture Expert LLC ( www.ventureexpert.com). Second External Data Base may be a commercially available data base known as Preqin

(www.preqin.com). Other external data bases may be employed to collect and download PE manager and PE fund performance information. The term DPI means the ratio of distributions made to investors by a PE fund compared to total capital paid-in to the PE fund by investors. The term IRR means the internal rate of return of a PE fund. The term RVPI means the ratio of the Residual Value of a PE fund to total paid-in capital. The term TVPI means the ratio of total value (namely, the sum of actual distributions to investors and undistributed value still held by the PE Fund) to total paid-in capital.

Referring to FIG. 2, and as indicated by block 202, program module 20 is generally configured to collect and store all world-wide available PE Manager and PE Fund performance data in First and Second Data Bases 22 and 24, respectively, from External Data Bases 42 and 44. As indicated by block 204, program module 20 is further configured to calculate and store in Fourth Data Base 28 a list of weighting coefficient DPI; weighting coefficient IRR; and weighting coefficient TVPI corresponding to fund performance data DPI%; IRR%; TVPI%, respectively, for each year of all available PE funds. As will be described more fully herein with reference to FIG. 4, the weighting coefficient DPI, weighting coefficient IRR, and weighting coefficient TVPI capture the accuracy of PE fund performance assessments as a function of the age of the fund. As indicated by block 206, program module 20 is further configured to identify and store in Sixth Data Base 32 a list of PE Managers that qualify to be ranked from the list of PE Managers stored in First Data Base 22 and/or Second Data Base 24. As indicated by block 208, program module 20 is finally configured to calculate and store the rank of each qualifying PE Manager in Ranking Data Base 38.

Referring to FIG. 3, where a more detailed flow chart shows the step of collecting and storing PE Manager and PE Fund performance data in Data Bases 22 and 24, respectively. As shown by block 302, program module 20 is configured to extract a list of all PE Managers, corresponding PE funds, and fund size from external VentureXpert® Data Base 42. As shown by block 304, program module 20 is configured to store the list of PE Managers, corresponding PE funds and fund size in First Data Base 22. As shown by block 306, program module 20 is further configured to collect a list of performance data (namely, DPI%; IRR%; and RVPI%) from external PREQIN Data Base 44 for each PE Manager and PE fund listed in First Data Base 22, as well as the vintage year, PE type, and geography. As shown by block 308, program module 20 is configured to calculate TVPI% for each PE fund. TVPI% equals DPI% minus RVPI%. As shown by block 309, program module 20 is configured to calculate the Fund Age for all available PE funds. Fund Age for a given PE fund equals the current calendar year minus the vintage year of the fund. For a PE fund having a vintage year of 2005, the Fund Age of the PE fund as of the calendar year 2009 would be four (4) years old. As shown by block 310, program module 20 is configured to store performance data TVPI% in Second Data Base 24.

Referring to FIG. 4, where a more detailed flow chart shows the steps of calculating the weighting coefficient IRR, weighting coefficient DPI, and weighting coefficient TVPI, corresponding to fund performance data (IRR%, DPI%, and TVPI%), respectively, for each year of all PE fund types. The three weighting coefficients capture the accuracy of PE Fund performance assessments as a function of the age of the fund. In PE funds, performance measures for younger funds are less reliable, as these funds still have many unrealized investments in their portfolio. As funds approach the end of their life (10 years), performance can be assessed with increasing level of accuracy. As shown by block 402, program module 20 is configured to extract performance data IRR% from PREQIN Data Base 44 for all available PE Funds at each calendar year selected by user. As shown by block 404, program module 20 is further configured to store the list of performance data for IRR% in Third Data Base 26. FIG. 7 shows Third Data Base 26 with only performance data for IRR% for each year of PE funds 16124 - 16220. In practice, there may hundreds or thousand of PE funds. Third Data Base 26 contains performance data for IRR% for each year of all PE funds as well as performance data for DPI% and TVPI% for each year of each PE fund.

As shown by block 406, program module is configured to calculate the

Weighting Coefficient IRR for each year of each available fund using a statistical analysis known as the Pearson Coefficient of Correlation. As shown by block 408, program module 20 is further configured to store the weighting coefficient IRR for each year of PE Fund type in Fourth Data Base 28. FIG. 8 shows Fourth Data Base 28 having a list of calculated weighting coefficient DPI, weighting coefficient IRR, and weighting coefficient TVPI for years one (1) thru nine (9) of a given fund type with the weighting coefficient for year 10 being equal to one (not shown). Weighting Coefficient IRR for Year 1 equals the Coefficient of Correlation (Pearson) between columns 1 and 10 of FIG. 7. Weighting Coefficient IRR for Year 2 equals the Coefficient of Correlation (Pearson) between columns 2 and 10 of FIG. 7. Weighting Coefficient IRR for Year 3 equals the Coefficient of Correlation (Pearson) between columns 3 and 10 of FIG. 7. Weighting Coefficient IRR for Year 4 equals the Coefficient of Correlation (Pearson) between columns 4 and 10 of FIG. 7. Weighting Coefficient IRR for Year 5 equals the Coefficient of Correlation (Pearson) between columns 5 and 10 of FIG. 7. The Weighting Coefficient IRR for Year 6 equals the Coefficient of Correlation (Pearson) between columns 6 and 10 of FIG. 7. Weighting Coefficient IRR for Year 7 equals the Coefficient of Correlation (Pearson) between columns 7 and 10 of FIG. 7. Weighting Coefficient IRR for Year 8 equals the Coefficient of Correlation (Pearson) between columns 8 and 10 of FIG. 7. Weighting Coefficient IRR for Year 9 equals the Coefficient of Correlation (Pearson) between columns 9 and 10 of FIG. 7.

As shown by block 410, program module 20 is configured to extract performance data DPI% from Preqin Data Base 44 for all available PE Funds at each calendar year selected by user. As shown by block 412, program module 20 is further configured to store the list of performance data for DPI% in Third Data Base 26. As shown by block 414, program module 20 is configured to calculate the Weighting Coefficient DPI for each year of all PE funds of the same type and geography using the Pearson Coefficient of Correlation Program as previously described in connection with the calculation of the Weighting Coefficient IRR. As shown by block 416, program module 20 is configured to store the Weighting Coefficient DPI for each year of PE fund type in Fourth Data Base 28 as previously described in connection with the storing of the Weighting Coefficient IRR.

As shown by block 418, program module 20 is configured to extract performance data RVPI% from Preqin Data Base 44 for all available PE Fund at each calendar year selected by user. As shown by block 420, program module 20 is further configured to store the list of Performance Data for RVPI% in Third Data Base 26. As shown by block 422, program module 20 is configured to calculate Performance Data for TVPI% by summing Performance Data (DPI%) and (RVPI%) for each year of all PE funds stored in Third Data Base 26. As shown by block 424, program module 20 is further configured to store the list of Performance Data for TVPI% in Third Data Base 26. As shown by block 426, program module 20 is configured to calculate the Weighting Coefficient TVPI for each year of all PE funds of the same type and geography using the Pearson Coefficient of Correlation Program as previously described in connection with the calculation of the Weighting Coefficient IRR. As shown by block 428, program module 20 is configured to store the Weighting Coefficient TVPI for each year of PE fund type in Fourth Data Base 28 as previously described. As will be more fully described with reference to FIG. 6, the three weighting coefficients are used to calculate the Weighted Average Performance (for all six different performance indicators) for each fund manager based on the six performance measures for each fund managed by a particular manager.

Referring to FIG. 5, where a detailed flow chart shows describes the process of selecting qualified PE fund managers to be included in the ranking. As shown by block 502, program module 20 is configured to create and store in Fifth Data Base 30 a list of all PE Fund Managers from First Data Base 22 along with corresponding PE fund Performance Data (DPI%; IRR%; and TVPI%) from Second Data Base 24. As shown by block 504, program module 20 is further configured to calculate and store in Fifth Data Base 30 the following variables for each PE Fund Manager:

(1) Number of PE Funds for each PE Fund Manager;

(2) Total sum of all PE Funds for each PE Fund Manager;

(3) Sum of all Ages for Each Fund;

(4) % Ratio of the number of funds of the PE Fund Manager stored in First Data Base 22 over the number of PE Funds of the PE Fund Manager stored in Second Data Base 24;

(5) % Ratio of the sum of Fund Sizes of the Fund Manager stored in First Data Base 22 over the sura of the PE Fund Sizes of the Fund Manager stored in Second Data Base 24; and

(6) % Ratio of the sum of the ages of all funds of the Fund Manager stored in First Data Base 22 over the sum of the ages of all funds of the Fund Manager stored in Second Data Base 24.

As shown by block 506, program module 20 is configured to select only those PE Fund Managers from Fifth Data Base 30 that meet the ranking criteria. By way of example only, the ranking criteria may be as follows: (1) at least $500 Million raised over a ten year period; (2) at least fifteen observation years (i.e., the sum of the age of all funds as of today); and (3) no known fund raised over selected period on which performance information is missing. Program module 20 is configured to limit the analysis to PE Firms that are of relevant scale in terms of their activities. Program module 20 is configured to make sure that "one-hit-wonders" are not reported; hence the requirement to have at least two (2) funds with full performance information and fifteen (15) observation years. Program module 20 does not consider funds raised after 2005, as their performance is still too unreliable to be judged at this point. Program module 20 further excludes PE managers that according to first and second data bases 22 and 24 raised funds between 1996 and 2005 but have no performance data available for these funds, as otherwise the performance for these PE manager could be unreliable.

As shown by block 508, program module 20 is configured to store the qualifying PE Fund Managers in Sixth Data Base 32. Referring to FIG. 6, where a detailed flow chart shows describes the process of ranking the qualified PE Fund Managers stored in Sixth Data Base 32.

As shown by block 602, program module 20 is configured to calculate a

Performance Bench-Mark Average (BM-DPI%, BM-IRR%, and BM-TVPI%) for Performance Data (DPI%; IRR%; and TVPI%) for a given vintage year, PE type, and geography measured over all funds stored in Second Data Base 24 meeting the same criteria. As such, BM-DPI% equals the sum of all Performance Data DPI% for a given vintage year, PE type and geography divided by the total number of funds stored in Second Data Base 24 meeting the same criteria. Similarly, BM-IRR% equals the sum of all Performance Data IRR% for a given vintage year, PE type and geography divided by the total number of funds stored in Second Data Base 24 meeting the same criteria. Finally, BM-TVPI% equals the sum of all Performance Data TVPI% for a given vintage year, PE type and geography divided by the total number of funds stored in Second Data Base 24 meeting the same criteria.

As shown by block 603, program module 20 is configured to calculate the Relative Performance Data (DDPI%; DERR%; and DTVPI%) for each PE Fund Stored in Second Data Base 24 as the difference between its absolute performance (DPI%; IRR%; TVPI%) and its performance bench-mark average (BM-DPI%; BM-IRR%; and BM- TVPI%) for all funds of the same vintage year, PE type, and geography. Relative Performance Indicator DDPI% equals DPI% minus BM-DPI%. Relative Performance Indicator DIRR% equals IRR% minus BM-IRR%. Relative Performance Indicator DTVPI% equals TVPI% minus BM-DTVPI%. As shown by block 604, program module 20 is configured to create and store in Seventh Data Base 34: (1) Absolute Performance Data DPI%; IRR%; and TVPI%; and vintage year and Fund Age for each PE fund stored in Second Data Base 24; (2) Relative Performance Data (DDPI%; DIRR%; and DTVPI%) for each PE fund; and (3)

Weighting Coefficient DPI; Weighting Coefficient IRR; and Weighting Coefficient TVPI From Fourth Data Base 28 for a given PE fund age.

As shown by block 606, program module 20 is configured to calculate Weighted Absolute Performance Data (WA-IRR%; WA-DPI%; and WA-TVPI%) for each qualified PE Fund Manager stored in Sixth Data Base 32 based upon: (1) Absolute Performance Data (DPI%, IRR%; and TVPI%) stored in Seventh Data Base 34; and (2) Weighting Coefficient DPI; Weighting Coefficient IRR; and Weighting Coefficient TVPI stored in Seventh Data Base 34. WA-DPI% = (Sum over all funds by fund manger of (fund DPI% x Weighting Coefficient DPI for fund age)) divided by (the Sum over all funds by fund manager of the Weighting Coefficient DPI for fund age). WA-IRR% = (Sum over all funds by fund manger of (fund IRR% x Weighting Coefficient IRR for fund age)) divided by (the Sum over all funds by fund manager of the Weighting

Coefficient IRR for fund age). WA-TVPI% = (Sum over all funds by fund manger of (fund TVPI% x Weighting Coefficient TVPI for fund age)) divided by (the Sum over all funds by fund manager of the Weighting Coefficient TVPI for fund age).

As shown by block 608, program module 20 is configured to calculate the Weighted Relative Performance Data (WAD-IRR%; WAD-DPI%; WAD-TVPI%) for each qualified PE Fund Manager stored in Sixth Data Base 32 based upon: (1) Relative Performance Data (DDPI%; DIRR%; and DTVPI%) stored in Seventh Data Base 34; and (2) Weighting Coefficient DPI; Weighting Coefficient IRR; and Weighting Coefficient TVPI) stored in Seventh Data Base 34. WAD-DPI% = (Sum over all funds by fund manger of (fund DPI% x Weighting Coefficient DPI for fund age)) divided by (the Sum over all funds by fund manager of the Weighting Coefficient DPI for fund age). WAD- IRR% = (Sum over all funds by fund manger of (fund DIRR% x Weighting Coefficient IRR for fund age)) divided by (the Sum over all funds by fund manager of the Weighting Coefficient IRR for fund age). WAD-TVPI% = (Sum over all funds by fund manger of (fund DTVPI% x Weighting Coefficient TVPI for fund age)) divided by (the Sum over all funds by fund manager of the Weighting Coefficient TVPI for fund age).

As shown by block 610, program module 20 is configured to store in Eighth Data Base 36 a list of the Weighted Absolute Performance Data (WA-IRR%; WA-DPI%; WA-TVPI%) and the Weighted Relative Performance Data (WAD-IRR%; WAD-DPI%; WAD-TVPI%).

As shown by block 612, program module 20 is configured to calculate and store in Ninth Data Base 37 Coefficient Matrix (COEFF-IRR; COEFF-DPI; COEFF-TVPI; and COEFF-DIRR; COEFF-DDPI and COEFF-DTVPI) using a statistical analysis commonly known as "Factor Extraction" (Principal Component Analysis) from the Weighted Absolute Performance Data (WA-IRR%; WA-DPI%; WA-TVPI%) and the Weighted Relative Performance Data (WAD-IRR%; WAD-DPI%; and WAD-TVPI%).

As shown by block 614, program module 20 is configured to calculate a ranking score for each qualified PE Manager as follows: Ranking Score = (WA-IRR% x COEFF- IRR) + (WA-DPI% x COEFF-DPI) + (WA-TVPI% x COEFF-TVPI) + (WAD-IRR% x COEFF-DIRR) + (WAD-DPI% x COEFF DDPI) + (WAD-TVPI% x COEFF-DTVPI). As shown by block 616, program module 20 is configured to store the ranking score of each qualified PE Manager in Ranking Data Base 38. Program module 20 may be further configured to display the ranking scores on display device 16.

The preceding description is given merely by way of illustration only and not in limitation of the invention and that various modifications may be made thereto without departing from the spirit of the invention as claimed.

Claims

WHAT IS CLAIMED:

1. A computer based method for ranking of PE Fund Managers having PE Funds based upon information from an external data base, the method comprising the steps of:

(a) providing a computer system comprising a storage device;

(b) creating a first data base on said storage device comprising a list of PE Fund Managers and PE Funds from the external data base;

(c) creating a second data base on said storage device comprising absolute performance data DPI%; IRR%; and TVPI% for all available PE Fund from the external data base;

(d) creating a third data base on said storage device comprising absolute performance data DPI%; IRR%; RVPI%; and TVPI% for each year of all available PE Funds from the external data base;

(e) creating a fourth data base on said storage device comprising weighting coefficients DPI, IRR, and TVPI based upon statistical analysis of said performance data DPI%; IRR%; and TVPI%, respectively, for each year of said PE Funds stored in said third data base;

(f) creating a fifth data base on said storage device comprising PE Fund Managers from said first data base and absolute performance data DPI%; IRR%; and TVPI% from said second data base;

(g) creating a sixth data base on said storage device comprising qualifying PE Fund Managers from said fifth data base; and

(h) creating a ranking data base on said storage device comprising a ranking for each of said qualifying PE Fund Managers stored in said sixth data base.

2. The method of claim 1, further comprising the steps of:

(i) calculating performance bench-mark data BM-DPI%, BM-IRR%, and BM-TVPI% based upon absolute performance data DPI%, IRR%, and TVPI%, respectively, for a given vintage year, PE type, and geography based on said PE Funds stored in said second data base meeting the same criteria; and

(j) creating a seventh data base comprising relative performance data DDPI%, DIRR%, and DTVPI% for each of said PE Funds stored in said second data base as the difference between said absolute performance DPI%, IRR%, and TVPI% and said performance bench-mark data BM-DPI%, BM-IRR%, and BM-TVPI%, respectively, for all funds of the same vintage year, PE type, and geography.

3. The method of claim 2, further comprising the step of: (k) creating an eighth data base on said storage device comprising weighted absolute performance data WA-IRR%, WA-DPI%, and WA-TVPI% for each qualified PE Fund Manager stored in said fourth data base based upon said absolute performance data DPI%, IRR%; and TVPI% stored in said second data base and said weighting coefficients DPI, IR , and TVPI stored in said third data base.

4. The method of claim 3, further comprising the steps of: (1) storing in said eighth data base weighted relative performance data WAD-IRR%, WAD-DPI%, and WAD- TVPI% for each qualified PE Fund Manager stored in said fourth data base based upon said relative performance data DPI%, IRR%; and TVPI% and said weighting coefficients DPI, IRR, and TVPI stored in said third data base.

5. The method of claim 4, further comprising the step of: (m) creating a ninth data base on said storage device comprising COEFF-IRR, COEFF-DPI, COEFF-TVPI, and COEFF-DIRR, COEFF-DDPI, and COEFF-DTVPI using a statistical analysis based upon said weighted absolute performance data WA-IRR%, WA-DPI%, and WA-TVPI%, and said weighted relative performance data WAD-IRR%, WAD-DPI% and WAD- TVPI%, respectively.

6. The method of claim 5, wherein said step of creating a ranking data base on said storage device comprises the step of calculating said ranking of each PE Managers as being equal to said weighted absolute performance data WA-IRR%, WA-DPI%, and WA-TVPI% multiplied by said COEFF-IRR, COEFF-DPI, and COEFF-TVPI, respectively, plus said weighted relative performance data WAD-IRR%, WAD-DPI%, and WAD-TVPI% multiplied by said COEFF-DIRR, COEFF-DDPI, and COEFF- DTVPI, respectively.