The book that I wrote, published August 2010, is:
Navendu P. Vasavada, “Taxation of US Investment Partnerships and Hedge Funds,” New York, NY, Wiley, 2010.
This book is available at Amazon.
Among the various topics covered, the book includes a comprehensive analysis and description of partnership tax allocation methodologies of layering, full netting and partial netting.
A fairly good motivation and introduction as provided in the preface. I shall try to summarize it as briefly as possible in this blog-note. The first few chapters of the book describe U.S. onshore and offshore hedge fund and investment structuring, partnership entity formation and regulatory perspective. The next few chapters construct a formal representation of investment partnership accounting and tax reporting by codifying much of the relevant accounting into linear algebra. Offshore entities may apply the algebraic framework provided to track unit values and capital account value, disregard tax reporting. An entire chapter is subsequently devoted to performance presentation according to the Global Investment Performance Standards (GIPS) of the CFA institute.
A pivotal chapter in the book, Chapter 7, focuses on partner tax allocations required to be reported in the tax return of U.S. investment partnerships. Chapter 7 describes how the tax allocation problem is traditionally handled, and how an automated algorithm is formulated based on convex optimization to solve for tax allocations consistent with the U.S. tax regulations. Appendices 2 to 5 describe the tax allocation algorithm in greater detail based on a sample tax allocation test problem under the approaches of partial netting and full netting, along with the relevant computer code in Matlab and R. The previous chapters, Chapter 5 and 6, described in exhaustive detail the approaches of layering, partial netting and full netting for implementing tax allocations.
Users and readers may wish to explore their own tax allocation using the convex optimization algorithms discussed in the book. The input data are: book-tax disparities of partners before the current years’ tax allocations, and the various items of distributive income for the year to be allocated to partners. The algorithm allocates items of distributive income in such a manner so as to reduce (or minimize) the collective book tax disparities of the partners, while preventing distorted tax allocations that are forbidden by tax regulations. The solution to a 100-partner test problem with 8 items of distributive items of income to be allocated is solved in seconds, made possible due to the open-source algorithm SDPT3 for convex optimization, and the user-friendly open-source front-end named CVX made available by Dr. Stephen Boyd of Stanford University at http://cvxr.com/cvx/.
Users wanting clarification on full netting, layering, partial netting, partnership tax allocation, partnership taxation and implementing the convex programming algorithm may contact me by e-mail through my blog profile page.
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Erratum recorded by author on 06/18/2013
On page 119, the formula should have (1-ß^) replacing (ß^). I thank a kind reader Alan C. for pointing this out.
The formula on the middle of page 120, which verifies the sum of line item allocation (after performance fees) to GP+LPs = overall partnership profits, contains the correct version, with (1-ß^). [Page 120 does not carry the errant version with (ß^) shown on the previous page 119.]
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Author's note on 06/18/2013 -- on the relevance of ß^ distinct from ß:
The formula on page 119 should have (1-ß^) replacing (ß^), as explained in the erratum.
The formulae on the top part of page 109 are indeed entirely consistent with those on page 119 (duly corrected). What more, the notation of ß for limited partner and (1-ß) for the GP, is also consistent with the definition of ß on page 61. Note that ß deals with account values, and not profits (aggregate profits, or by line item). ß is the bifurcation factor that splits the LP’s account value before performance fees into what the LP retains going into the next year, the daughter capital account based on (1-ß). We do need ß for this, because at year end, after calculation of performance fee, the LP’s capital account is split, with the LP retaining the proportion (1-ß) and the remaining proportion (ß) being transferred to the GP.
So why does ß^ appear on page 119, and why is it not redundant? The formulae on pages 119-120 deal with division of profits and not account value. The following algebraic construction would clarify why ß and ß^ are needed. Let V.0 be start year partnership value, V.12 the end year value before performance fees. At year beginning, there is only 1 LP owning α, and the GP owns (1-α). There is only 1 line item of profit, say interest, which is p=V.12-V.0 for the partnership as a whole. The LP started with αV.0 in capital account value. The LP ended with αV.12 before performance fees. The LP’s account was then bifurcated, leaving the LP with αV.12(1-ß) of daughter capital account value after performance fees. The profit to the LP for the year is: p.LP=αV.12(1-ß)-αV.0. This has already become messy! It evaluates to p.LP=α(V.12-V.0-ßV.12). Define ß^=ßV.12/(V.12-V.0) and substitute to obtain p.LP=α(1-ß^)p. This is the formula on page 119 (after duly correcting with 1-ß^ replacing ß^).
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Erratum recorded by author on 06/18/2013
On page 119, the formula should have (1-ß^) replacing (ß^). I thank a kind reader Alan C. for pointing this out.
The formula on the middle of page 120, which verifies the sum of line item allocation (after performance fees) to GP+LPs = overall partnership profits, contains the correct version, with (1-ß^). [Page 120 does not carry the errant version with (ß^) shown on the previous page 119.]
*****************
Author's note on 06/18/2013 -- on the relevance of ß^ distinct from ß:
The formula on page 119 should have (1-ß^) replacing (ß^), as explained in the erratum.
The formulae on the top part of page 109 are indeed entirely consistent with those on page 119 (duly corrected). What more, the notation of ß for limited partner and (1-ß) for the GP, is also consistent with the definition of ß on page 61. Note that ß deals with account values, and not profits (aggregate profits, or by line item). ß is the bifurcation factor that splits the LP’s account value before performance fees into what the LP retains going into the next year, the daughter capital account based on (1-ß). We do need ß for this, because at year end, after calculation of performance fee, the LP’s capital account is split, with the LP retaining the proportion (1-ß) and the remaining proportion (ß) being transferred to the GP.
So why does ß^ appear on page 119, and why is it not redundant? The formulae on pages 119-120 deal with division of profits and not account value. The following algebraic construction would clarify why ß and ß^ are needed. Let V.0 be start year partnership value, V.12 the end year value before performance fees. At year beginning, there is only 1 LP owning α, and the GP owns (1-α). There is only 1 line item of profit, say interest, which is p=V.12-V.0 for the partnership as a whole. The LP started with αV.0 in capital account value. The LP ended with αV.12 before performance fees. The LP’s account was then bifurcated, leaving the LP with αV.12(1-ß) of daughter capital account value after performance fees. The profit to the LP for the year is: p.LP=αV.12(1-ß)-αV.0. This has already become messy! It evaluates to p.LP=α(V.12-V.0-ßV.12). Define ß^=ßV.12/(V.12-V.0) and substitute to obtain p.LP=α(1-ß^)p. This is the formula on page 119 (after duly correcting with 1-ß^ replacing ß^).
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