Methods and systems for providing an anti-benchmark portfolio
View Patent ↗In one aspect, the invention comprises a method comprising: (a) acquiring data regarding a first group of securities in a first portfolio; (b) based on said data and on risk characteristics of said first group of securities, identifying a second group of securities to be included in a second portfolio; and (c) calculating holdings in said second portfolio based on one or more portfolio optimization procedures. In another aspect, the invention comprises software for performing the steps described above (as well as steps of other embodiments), and in another aspect, the invention comprises one or more computer systems operable to perform those steps.
1. A computer-implemented method for providing an anti-benchmark portfolio, the method comprising:
acquiring, using a computer system, data regarding a first group of securities in a first portfolio, wherein the computer system comprises a computer processor and memory coupled to said processor;
identifying, using a computer system, a second group of securities to be included in a second portfolio based on said data and on risk characteristics of said second group of securities; and
providing, using a computer system, the individual weightings for each of the securities in said second portfolio according to one or more portfolio optimization procedures that maximizes the anti-benchmark ratio for the second portfolio wherein the anti-benchmark ratio is represented by the quotient of:
a numerator comprising an inner product of a row vector of said holdings in said second portfolio and a column vector of a risk characteristic of return associated with said holdings in said second portfolio; and
a denominator comprising the square root of a scalar formed by an inner product of said row vector of said holdings in said second portfolio and a product of a covariance matrix and a column vector of said holdings of said second portfolio.
2. The method according to claim 1 , wherein said risk characteristic in the numerator is based on calculating the standard deviation of the returns of the securities.
3. The method according to claim 1 , wherein said denominator is based on calculating the standard deviation of the returns of the portfolio.
4. The method according to claim 1 , the method further comprising:
providing, using a computer system, a combined portfolio consisting of a portion of said first portfolio and a portion of said second portfolio; and
providing, using a computer system, the individual weightings for each of the securities in said combined portfolio according to one or more portfolio optimization procedures that maximizes the anti-benchmark ratio for the combined portfolio.
5. The method according to claim 1 , wherein said second portfolio provides a full risk premium available in the pricing of the securities of said second portfolio.
6. The method according to claim 4 , wherein the combined portfolio has a higher expected return than said first portfolio while having a lower expected volatility than said first portfolio.
7. The method according to claim 4 , wherein the combined portfolio has a higher Sharpe ratio than said first portfolio.
8. The method according to claim 1 , the method further comprising:
providing, using a computer system, said individual weightings on a periodic basis.
9. The method according to claim 1 , the method further comprising:
transforming, using a computer system, said second portfolio into an equivariant portfolio via the Choueifaty Synthetic Asset Transformation and back-transforming said equivariant portfolio via the Choueifaty Synthetic Asset Back-Transformation.
10. A non-transitory computer readable medium having a computer program stored thereon which, when executed by a computer processor, performs a method for providing an anti-benchmark portfolio, the method comprising:
acquiring data regarding a first group of securities in a first portfolio, wherein the computer system comprises a computer processor and memory coupled to said processor;
identifying a second group of securities to be included in a second portfolio based on said data and on risk characteristics of said second group of securities; and
providing the individual weightings for each of the securities in said second portfolio according to one or more portfolio optimization procedures that maximizes the anti-benchmark ratio for the second portfolio wherein the anti-benchmark ratio is represented by the quotient of:
a numerator comprising an inner product of a row vector of said holdings in said second portfolio and a column vector of a risk characteristic of return associated with said holdings in said second portfolio; and
a denominator comprising the square root of a scalar formed by an inner product of said row vector of said holdings in said second portfolio and a product of a covariance matrix and a column vector of said holdings of said second portfolio.
11. The computer readable medium according to claim 10 , wherein said risk characteristic in the numerator is based on calculating the standard deviation of the returns of the securities.
12. The computer readable medium according to claim 10 , wherein said denominator is based on calculating the standard deviation of the returns of the portfolio.
13. The computer readable medium according to claim 10 , the method further comprising:
providing a combined portfolio consisting of a portion of said first portfolio and a portion of said second portfolio; and
providing the individual weightings for each of the securities in said combined portfolio according to one or more portfolio optimization procedures that maximizes the anti-benchmark ratio for the combined portfolio.
14. The computer readable medium according to claim 10 , wherein said second portfolio provides a full risk premium available in the pricing of the securities of said second portfolio.
15. The computer readable medium according to claim 13 , wherein the combined portfolio has a higher expected return than said first portfolio while having a lower expected volatility than said first portfolio.
16. The computer readable medium according to claim 13 , wherein the combined portfolio has a higher Sharpe ratio than said first portfolio.
17. The computer readable medium according to claim 10 , the method further comprising:
providing said individual weightings on a periodic basis.
18. The computer readable medium according to claim 10 , the method further comprising:
transforming said second portfolio into an equivariant portfolio via the Choueifaty Synthetic Asset Transformation and back-transforming said equivariant portfolio via the Choueifaty Synthetic Asset Back-Transformation.
19. A system for providing an anti-benchmark portfolio, the system comprising:
one or more computer processors;
memory, communicatively coupled to said one or more processors, which stores a computer program which, when executed by the one or more computer processors, performs a method for providing an anti-benchmark portfolio, the method comprising:
acquiring data regarding a first group of securities in a first portfolio, wherein the computer system comprises a computer processor and memory coupled to said processor;
identifying a second group of securities to be included in a second portfolio based on said data and on risk characteristics of said second group of securities; and
providing the individual weightings for each of the securities in said second portfolio according to one or more portfolio optimization procedures that maximizes the anti-benchmark ratio for the second portfolio wherein the anti-benchmark ratio is represented by the quotient of:
a numerator comprising an inner product of a row vector of said holdings in said second portfolio and a column vector of a risk characteristic of return associated with said holdings in said second portfolio; and
a denominator comprising the square root of a scalar formed by an inner product of said row vector of said holdings in said second portfolio and a product of a covariance matrix and a column vector of said holdings of said second portfolio.
20. The system according to claim 19 , wherein said risk characteristic in the numerator is based on calculating the standard deviation of the returns of the securities.
21. The system according to claim 19 , wherein said denominator is based on calculating the standard deviation of the returns of the portfolio.
22. The system according to claim 19 , the method further comprising:
providing a combined portfolio consisting of a portion of said first portfolio and a portion of said second portfolio; and
providing the individual weightings for each of the securities in said combined portfolio according to one or more portfolio optimization procedures that maximizes the anti-benchmark ratio for the combined portfolio.
23. The system according to claim 19 , wherein said second portfolio provides a full risk premium available in the pricing of the securities of said second portfolio.
24. The system according to claim 22 , wherein the combined portfolio has a higher expected return than said first portfolio while having a lower expected volatility than said first portfolio.
25. The system according to claim 22 , wherein the combined portfolio has a higher Sharpe ratio than said first portfolio.
26. The system according to claim 19 , the method further comprising:
providing said individual weightings on a periodic basis.
27. The system according to claim 19 , the method further comprising:
transforming said second portfolio into an equivariant portfolio via the Choueifaty Synthetic Asset Transformation and back-transforming said equivariant portfolio via the Choueifaty Synthetic Asset Back-Transformation.