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Valuation of  Acme Investment Group June 2006 This sample valuation for is from an actual analysis.  Names, places and num...
Introduction
Introduction <ul><li>Market Overview   3 </li></ul><ul><li>Analytical Overview   9 </li></ul><ul><li>Valuation – Ratio Mod...
Market Overview <ul><li>There were 117 mergers or acquisitions of investment management firms in 2005.  For the largest tr...
Market Overview <ul><li>The following pages include data for the 17 firms to be analyzed: </li></ul><ul><li>Employees rang...
Market Overview Source: Reuters, Hoover’s, corporate web sites.
Market Overview Source: Reuters, Hoover’s, corporate web sites.
Market Overview Source: Reuters, Hoover’s, corporate web sites. These four graphs plot market capitalization for 17 firms ...
Market Overview According to Pensions and Investments, there were 117 mergers or acquisitions in the global investment man...
Analytical Overview Valuation models are far too sensitive to rely on a single approach.  Even a minute change in a discou...
Analytical Overview Broadly, there are four steps to complete the analysis. First, four different ratio sub-models are dev...
Analytical Overview Heritage Book Value Assets Under Management Book Value as % of AUMs Skill Revenue Profit Sales as % of...
Analytical Overview <ul><li>For the market-driven analysis, each model requires four steps: </li></ul><ul><li>Identify ind...
Valuation – Ratio Models Price-to-AUM Ratio Sub-Model The Price-to-AUM sub-model is part of the set of Ratio Models.  The ...
Valuation – Ratio Models Price-to-AUM Ratio Sub-Model Source: Reuters, Hoover’s, corporate web sites.
Valuation – Ratio Models Price-to-AUM Ratio Sub-Model Application of Sub-Model to Acme Investment Group The application of...
Valuation – Ratio Models Price-to-Sales Ratio Sub-Model The Price-to-Sales sub-model is part of the set of Ratio Models.  ...
Valuation – Ratio Models Price-to-Sales Ratio Sub-Model Source: Reuters, Hoover’s, corporate web sites.
Valuation – Ratio Models Price-to-Sales Ratio Sub-Model Application of Sub-Model to Acme Investment Group The application ...
Valuation – Ratio Models Price-to-Earnings Ratio Sub-Model The Price-to-Earnings sub-model is part of the set of Ratio Mod...
Valuation – Ratio Models Price-to-Earnings Ratio Sub-Model Source: Reuters, Hoover’s, corporate web sites.
Valuation – Ratio Models Price-to-Earnings Ratio Sub-Model Application of Sub-Model to Acme Investment Group The applicati...
Valuation – Ratio Models Price-to-Book Ratio Sub-Model The Price-to-Book sub-model is part of the set of Ratio Models.  Th...
Valuation – Ratio Models Price-to-Book Ratio Sub-Model Source: Reuters, Hoover’s, corporate web sites.
Valuation – Ratio Models Price-to-Book Ratio Sub-Model Application of Sub-Model to Acme Investment Group The application o...
Valuation – Ratio Models Composite Ratio Model The Composite Ratio Model comprises the four individual sub-models for Pric...
Valuation – Ratio Models Composite Ratio Model Source: Reuters, Hoover’s, corporate web sites. NOTE: For each investment f...
Valuation – Ratio Models Composite Ratio Model Compiling the Composite Ratio Model for Acme Investment Group from Four Sub...
Valuation – Volume Model The Volume Valuation Model seeks to forecast market capitalization directly – not a ratio, so its...
Valuation – Volume Model Source: Reuters, Hoover’s, corporate web sites.
Valuation – Volume Model Application of Volume Model to Acme Investment Group This valuation will be included as part of t...
Valuation – Discounted Cash Flow With these annual projections of EPS and the current stock price, an IRR can easily be ca...
Valuation – Discounted Cash Flow Source: Reuters, Hoover’s, corporate web sites. As described on the previous page, 200-ye...
Valuation – Discounted Cash Flow Using assumptions described for determining a discount rate and long-term EPS estimates, ...
Valuation – Discounted Cash Flow <ul><li>Assumptions for calculating the DCF Valuation </li></ul><ul><li>Data for AUMs, in...
Valuation – Discounted Cash Flow Valuation from DCF Model = USD 442 million This valuation will be included as part of the...
Valuation – Discounted Cash Flow
Composite: Volume, Ratio & DCF The Composite Model – which represents the last quantitative step in the analysis prior to ...
Composite: Volume, Ratio & DCF Source: Reuters, Hoover’s, corporate web sites. In determining the weights to be assigned t...
Composite: Volume, Ratio & DCF
Composite: Volume, Ratio & DCF Compiling Acme’s Composite Valuation from Three Models This Composite Model reflects all qu...
Adjustments to Valuations <ul><li>Large Buyer </li></ul><ul><li>Belgium versus world </li></ul><ul><li>Illiquid shares ver...
Adjustments to Valuations Is Belgium different? According to MSCI indices, there is not a substantial difference in the va...
Adjustments to Valuations Final Adjustments to Acme’s Composite Model This value reflects our recommendation for Acme’s va...
Recommended Acme Valuation Though a valuation recommendation necessarily must land on a single number, the chart at left i...
Notes Edward A. Strohbehn Ed Strohbehn has spent the past 25+ years on Wall Street -- a period that has seen no less than ...
Notes Custom Model Optimization with Constraints (CMOC) versus Standard Linear Regression Many multivariate models are dev...
Notes <ul><li>Standard Linear Regression </li></ul><ul><li>Choose coefficients using mathematical analysis of data points....
Notes This simple example compares the two techniques: regression and CMOC.  The dependent variable is the left-hand colum...
Notes <ul><li>Strohbehn, Hall, Olson & Evans LLC (SHOE LLC) is a private investment firm that assists firms in growth and ...
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SAMPLE Valuation of Acme Investment Group

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SAMPLE Valuation of Acme Investment Group

  1. 1. Valuation of Acme Investment Group June 2006 This sample valuation for is from an actual analysis. Names, places and numbers associated with any client have been modified to preserve confidentiality. However, all public market data remains unchanged.
  2. 2. Introduction
  3. 3. Introduction <ul><li>Market Overview 3 </li></ul><ul><li>Analytical Overview 9 </li></ul><ul><li>Valuation – Ratio Models 13 </li></ul><ul><ul><li>Price-to-AUM Ratio </li></ul></ul><ul><ul><li>Price-to-Sales Ratio </li></ul></ul><ul><ul><li>Price-to-Earnings Ratio </li></ul></ul><ul><ul><li>Price-to-Book Ratio </li></ul></ul><ul><ul><li>Composite Ratio Model </li></ul></ul><ul><li>Valuation – Volume Model 28 </li></ul><ul><li>Valuation – Discounted Cash Flow Model 31 </li></ul><ul><li>Composite Valuation using Volume, Ratio and DCF Models 36 </li></ul><ul><li>Adjustments to Composite Valuation 40 </li></ul><ul><li>Recommended Valuation for Acme 43 </li></ul>
  4. 4. Market Overview <ul><li>There were 117 mergers or acquisitions of investment management firms in 2005. For the largest transactions reported by Pensions and Investments – reflecting an aggregate transaction value of USD 13 billion -- prices ranged from 0.54% to 9.13% of AUMs. </li></ul><ul><li>The Reuters data base contains 103 companies in its “Investment Services” industry. MSCI lists 26 firms as “Asset Management and Custody Banks” in developed countries and one such firm in emerging markets. </li></ul><ul><li>From this overlapping universe, there are 17 “pure” investment management firms with public shares actively traded on a secondary market for which satisfactory information was available. Firms were eliminated from the original universe for several reasons: </li></ul><ul><ul><li>Firms that do significant business in others areas, such as brokerage, investment banking, or banking. Examples include Banca Fideuram, Julius Baer, Man Group, and Schroders. </li></ul></ul><ul><ul><li>Firms for which insufficient data was available. Examples include the Chilean manager Provida and DHIL. </li></ul></ul><ul><ul><li>Firms whose business was private equity or venture capital. </li></ul></ul>
  5. 5. Market Overview <ul><li>The following pages include data for the 17 firms to be analyzed: </li></ul><ul><li>Employees range from 70 to as many as 48,000. </li></ul><ul><li>Assets under management (AUMs) range from USD 20 billion to as high as USD 864 million. </li></ul><ul><li>Market capitalizations range from USD 700 million to USD 23 billion. </li></ul><ul><ul><li>Price-to-AUM ratios range from 0.93% to 4.52%. </li></ul></ul><ul><ul><li>Price-to-Sales ratios range from 1.40 to 6.02. </li></ul></ul><ul><ul><li>Price-to-Earnings ratios range from 14 to 36. </li></ul></ul><ul><ul><li>Price-to-Book ratios range from 1.48 to 15. </li></ul></ul><ul><li>The average reported beta is 1.31, but is as low as 0.09 and as high as 2.68. </li></ul>
  6. 6. Market Overview Source: Reuters, Hoover’s, corporate web sites.
  7. 7. Market Overview Source: Reuters, Hoover’s, corporate web sites.
  8. 8. Market Overview Source: Reuters, Hoover’s, corporate web sites. These four graphs plot market capitalization for 17 firms against four different volumes: AUMs, revenue, earnings, and book value. As can be seen, earnings appears to have the greatest ability to predict market value. Earnings explains nearly 95% of the variability among firms, while the other three variables only explain 45-64% of the variability.
  9. 9. Market Overview According to Pensions and Investments, there were 117 mergers or acquisitions in the global investment management community in 2005. These 12 were listed as the most important. Though commentators often focus on the price paid for assets under management, the range of values – from 0.54% to 9.13% -- is stunning and indicates that Price-to-AUM ratios are insufficient in themselves for pricing a transaction.
  10. 10. Analytical Overview Valuation models are far too sensitive to rely on a single approach. Even a minute change in a discount rate or a modification of growth assumptions, for example, can yield significant changes. Consequently, it is wise to use several complementary methods, so that each is a check on the other. In this analysis, three quantitative models are included: (1) ratios models such as price-to-AUMs or price-to-earnings; (2) volume models, where market capitalizations are correlated against variables such as sales and AUMs; and (3) traditional discounted-cash-flow analysis, which often both the most reliable for a specific firm and the most sensitive – or volatile – to input changes. Finally, judgment is inevitably necessary to adjust model outputs for firm-specific situations, such as geography, lack of liquidity, or the relative size of the transaction. Professional Judgment Discounted Cash Flow Valuation Volume Models Ratio Models
  11. 11. Analytical Overview Broadly, there are four steps to complete the analysis. First, four different ratio sub-models are developed: (i) price-to-AUMs, (ii) price-to-sales, (iii) price-to-earnings, and (iv) price-to-book. After the sub-models are developed, Acme’s information is applied. Second, three different models are developed, each based on a different approach One uses strictly volume data, such as AUMs and sales. The second applied discounted cash flow analysis, and the third creates a composite ratio model from the component sub-models in the first step. When complete, Acme’s information is applied to each model. Third, the three models are combined into a composite model, and Acme’s results are also calculated, yielding a quantitative valuation. Finally, professional judgment is applied to Acme’s case, to consider such specific situations as difference in liquidity, the idiosyncrasies of the Belgian market, and the effect of having a single buyer of a significant block of stock.
  12. 12. Analytical Overview Heritage Book Value Assets Under Management Book Value as % of AUMs Skill Revenue Profit Sales as % of AUMs Profit Margin Return on Equity (ROE) Potential EPS Growth Estimates Revenue Growth Estimates When building a statistical model, it is important to have a logical framework and not simply rely on the statistical techniques themselves, for models must make sense. For these valuations models, we will seek to include – unless the data do not support it – at least one variable from each of three categories: (1) heritage, (2) skill, and (3) potential. These variables tend to reflect different qualities of a firm. As “orthogonal” qualities, it is useful to evaluate each dimension. P S H
  13. 13. Analytical Overview <ul><li>For the market-driven analysis, each model requires four steps: </li></ul><ul><li>Identify independent variables: </li></ul><ul><ul><li>Market capitalization </li></ul></ul><ul><ul><li>Price-to-AUM Ratio </li></ul></ul><ul><ul><li>Price-to-Sales Ratio </li></ul></ul><ul><ul><li>Price-to-Earnings Ratio </li></ul></ul><ul><ul><li>Price-to-Book Ratio </li></ul></ul><ul><li>For each independent variable, identify possible dependent variables, including: </li></ul><ul><ul><li>AUMs </li></ul></ul><ul><ul><li>Book Value </li></ul></ul><ul><ul><li>Profit Margin </li></ul></ul><ul><ul><li>Future Earnings </li></ul></ul><ul><li>To choose optimal coefficients for various models (or weights for composite models), use Custom Model Optimization With Constraints (CMOC). See Notes for an explanation of this methodology and why we use it instead of standard linear regression techniques. </li></ul><ul><li>The methodology for the Discounted-Cash-Flow Model is separate. </li></ul><ul><li>Apply Acme’s data to each model. </li></ul>
  14. 14. Valuation – Ratio Models Price-to-AUM Ratio Sub-Model The Price-to-AUM sub-model is part of the set of Ratio Models. The constrained model optimization selected five independent variables, including at least one each from the three dimensions of Heritage, Skill and Potential. The model explains 55% of the variability among the firms in the data set, good but not a strong showing. For only 5 of the 17 firms was the forecast within ±10%. Though on average, the model was calibrated to hit its target, the mean absolute error was 19%. Its largest error was for Waddell & Reed, where it understated that firm’s ratio by 57%.
  15. 15. Valuation – Ratio Models Price-to-AUM Ratio Sub-Model Source: Reuters, Hoover’s, corporate web sites.
  16. 16. Valuation – Ratio Models Price-to-AUM Ratio Sub-Model Application of Sub-Model to Acme Investment Group The application of Acme’s data to this sub-model yields one estimate of Acme’s market value. This result will be included in the Composite Ratio Model that follows.
  17. 17. Valuation – Ratio Models Price-to-Sales Ratio Sub-Model The Price-to-Sales sub-model is part of the set of Ratio Models. The constrained model optimization selected four independent variables, including at least one each from the three dimensions of Heritage, Skill and Potential. The model explains 68% of the variability among the firms in the data set. For 7 of the 17 firms was the forecast within ±10%. Though on average, the model was calibrated to hit its target, the mean absolute error was 18%. Its largest error was for Gamco, where it overstated that firm’s ratio by 55%.
  18. 18. Valuation – Ratio Models Price-to-Sales Ratio Sub-Model Source: Reuters, Hoover’s, corporate web sites.
  19. 19. Valuation – Ratio Models Price-to-Sales Ratio Sub-Model Application of Sub-Model to Acme Investment Group The application of Acme’s data to this sub-model yields one estimate of Acme’s market value. This result will be included in the Composite Ratio Model that follows.
  20. 20. Valuation – Ratio Models Price-to-Earnings Ratio Sub-Model The Price-to-Earnings sub-model is part of the set of Ratio Models. The constrained model optimization selected three independent variables, including at least one each from the three dimensions of Heritage, Skill and Potential. The model explains only 30% of the variability among the firms in the data set. For 7 of the 17 firms was the forecast within ±10%. Though on average, the model was calibrated to hit its target, the mean absolute error was 15%. Its largest error was for Henderson Global Investors, where it overstated that firm’s ratio by 35%.
  21. 21. Valuation – Ratio Models Price-to-Earnings Ratio Sub-Model Source: Reuters, Hoover’s, corporate web sites.
  22. 22. Valuation – Ratio Models Price-to-Earnings Ratio Sub-Model Application of Sub-Model to Acme Investment Group The application of Acme’s data to this sub-model yields one estimate of Acme’s market value. This result will be included in the Composite Ratio Model that follows.
  23. 23. Valuation – Ratio Models Price-to-Book Ratio Sub-Model The Price-to-Book sub-model is part of the set of Ratio Models. The constrained model optimization selected three independent variables, including at least one each from the three dimensions of Heritage, Skill and Potential. The model explains over 90% of the variability among the firms in the data set. For 10 of the 17 firms was the forecast within ±10%. Though on average, the model was calibrated to hit its target, the mean absolute error was 16%. Its largest error was for Gamco, where it overstated that firm’s ratio by 49%.
  24. 24. Valuation – Ratio Models Price-to-Book Ratio Sub-Model Source: Reuters, Hoover’s, corporate web sites.
  25. 25. Valuation – Ratio Models Price-to-Book Ratio Sub-Model Application of Sub-Model to Acme Investment Group The application of Acme’s data to this sub-model yields one estimate of Acme’s market value. This result will be included in the Composite Ratio Model that follows.
  26. 26. Valuation – Ratio Models Composite Ratio Model The Composite Ratio Model comprises the four individual sub-models for Price-to-AUMs, Price-to-Sales, Price-to-Earnings, and Price-to-Book. Given the jump in variability explanation, the Composite is far superior to the individual models. If the model optimizer had been unconstrained, the Composite would have included only the two sub-models for sales and earnings. However, it was a judgment call to require the Composite to include no less than a 10% weighting for each sub-model. The model explains 97% of the variability among the firms in the data set. For 8 out of 17 firms, the forecast is within ±10%, and the model’s mean absolute error is 13%. Its largest error is for Waddell & Reed, where it understates that firm’s value by almost 36%.
  27. 27. Valuation – Ratio Models Composite Ratio Model Source: Reuters, Hoover’s, corporate web sites. NOTE: For each investment firm, the blue-shaded box highlights which of the four sub-models came closest to forecasting market capitalization. As can be seen, each of the four models had a fair number of successes. The Price-to-Earnings Model had the lowest mean absolute error at 14.6%, while the other models ranged from 16-19%, which justifies its 50% weighting in the Composite Ratio Model. If there is a lesson, earnings is more important than AUMs, sales, or book value in determining market valuations.
  28. 28. Valuation – Ratio Models Composite Ratio Model Compiling the Composite Ratio Model for Acme Investment Group from Four Sub-Models This composite valuation of ratio models yields a model estimate that will be input into the Composite Model that follows.
  29. 29. Valuation – Volume Model The Volume Valuation Model seeks to forecast market capitalization directly – not a ratio, so its independent variable choices are straightforward variable such as sales, earnings, book value, and future earnings. The choice of earnings forecasted in 10 years is intended to include a measure of growth in the model, so that at least one variable would be included from the three dimensions of Heritage, Skill, and Potential. The model explains over 97% of the variability among the firms in the data set. For 10 of the 17 firms was the forecast within ±10%. Though on average, the model was calibrated to hit its target, the mean absolute error was 11%. Its largest error was for Gamco, where it overstated that firm’s ratio by 28%. Significantly, the variable AUMs was not included in the model, since its value was overshadowed by the others.
  30. 30. Valuation – Volume Model Source: Reuters, Hoover’s, corporate web sites.
  31. 31. Valuation – Volume Model Application of Volume Model to Acme Investment Group This valuation will be included as part of the Composite Model that follows, along with the results from the DCF Model and the Composite Ratio Model.
  32. 32. Valuation – Discounted Cash Flow With these annual projections of EPS and the current stock price, an IRR can easily be calculated. These IRRs have been regressed against the betas for all the firms, as shown in the graph below. This “model” was used to estimate a model discount rate for each firm. Using this model rate, the Net Present Value of the EPS estimates was calculated to determine the Discounted Cash Flow Valuation for each firm. The chart on the next page contains the summary calculations described here. To determine the relative value of making a valuation using discounted cash flow, several steps were taken with the 17 publicly-listed firms: <ul><li>Year 1 EPS projections were the mean forecast made by Wall Street analysts, if available (15 of 17 firms had analyst estimates). Otherwise, current year EPS numbers were used. </li></ul><ul><li>Year 2 EPS estimates were also from Wall Street analysts, if available (15 had estimates). Otherwise, a growth rate was applied to Year 1 estimates. </li></ul><ul><li>Where available, the Long-Term Growth Rate from Wall Street was applied (for 15 firms, estimates were available). Otherwise, use the average of historical revenue and EPS growth rates. This growth rate was applied for years 3 through 10. </li></ul><ul><li>Beginning in year 11, a constant growth rate of 5.00% was used for all firms. </li></ul><ul><li>Rather than use a “terminal value,” as is often the case, the projections were extended through 200 years. This eliminates the need of assuming some sort of future PE ratio and also allows for slightly conservative – and known – growth assumptions. This is important, since roughly 40% of current value is determined by what happens after the tenth year. </li></ul>
  33. 33. Valuation – Discounted Cash Flow Source: Reuters, Hoover’s, corporate web sites. As described on the previous page, 200-year EPS estimates were calculated using Wall Street estimates for the first two years, Wall Street’s growth rates for the next eight years, and a flat 5% rate subsequently. A discount rate model was calculated, using the results from regressing IRR against Beta. Discount models are notoriously sensitive, and this approach seeks – among other things – to ascertain a good estimate of current market discount rates consistent with the growth assumptions. This discounting mechanism – and the long-term growth assumptions on which it is based – will be applied to Acme’s projected earnings.
  34. 34. Valuation – Discounted Cash Flow Using assumptions described for determining a discount rate and long-term EPS estimates, the resulting discounted-cash-flow numbers were relatively consistent with actual market capitalizations. When calculating Acme’s discount rate, we will use a beta of 2.50, which is at the upper end of the range for those firms studied. The model yielded a mean absolute error of 9.0% and explains 98% of the variability.
  35. 35. Valuation – Discounted Cash Flow <ul><li>Assumptions for calculating the DCF Valuation </li></ul><ul><li>Data for AUMs, income statement, balance sheet, and cash-flow statement were provided by Acme Investment Group. </li></ul><ul><li>Ten year projections of earnings were created in conjunction with Acme. </li></ul><ul><li>A beta of 2.50 was assumed. For the discount rate model developed earlier from market data, this equates to a discount rate of 14.70%. </li></ul><ul><li>The Terminal Value for the end of Year 11 was determined by extending 10 th year earnings at a 5% annual growth rate – the same as used in the analysis of publicly-listed firms. This equates to a P/E ratio of 10.3 as of year-end. </li></ul>
  36. 36. Valuation – Discounted Cash Flow Valuation from DCF Model = USD 442 million This valuation will be included as part of the Composite Model that follows, along with the results from the Volume Model and the Composite Ratio Model.
  37. 37. Valuation – Discounted Cash Flow
  38. 38. Composite: Volume, Ratio & DCF The Composite Model – which represents the last quantitative step in the analysis prior to professional adjustments being made -- comprises the three individual models: DCF, Volume, and the Composite Ratio. The model explains 98% of the variability among the firms in the data set. For 11 out of 17 firms, the forecast is within ±10%, and the model’s mean absolute error is 8%. Its largest error is for Cohen & Steers, where it understates that firm’s value by almost 22%. The analysis suggests the importance of the DCF methodology, since it comprises more than 60% of the composite weighting. Analysts often using ratios as a way of quickly comparing different firms, but the analysis suggests its value is considerably less than old-fashioned accounting.
  39. 39. Composite: Volume, Ratio & DCF Source: Reuters, Hoover’s, corporate web sites. In determining the weights to be assigned to the three “orthogonal” models, the data support assigning the highest weight to the DCF Model, with 63%. However, judgment suggests that this should be constrained to no more than 50?%, so the Optimizer was re-run with this requirements, even though it adds slightly to the fitted error. For each investment firm, the blue-shaded box highlights which of the three models came closest to forecasting market capitalization. As can be seen, each of the models had a fair number of successes. The Composite Model has a mean absolute error of 8.7%.
  40. 40. Composite: Volume, Ratio & DCF
  41. 41. Composite: Volume, Ratio & DCF Compiling Acme’s Composite Valuation from Three Models This Composite Model reflects all quantitative inputs to the Acme valuation. All that remains is to make appropriate adjustments for Acme’s unique situations that are not reflected in market data.
  42. 42. Adjustments to Valuations <ul><li>Large Buyer </li></ul><ul><li>Belgium versus world </li></ul><ul><li>Illiquid shares versus liquid shares </li></ul>
  43. 43. Adjustments to Valuations Is Belgium different? According to MSCI indices, there is not a substantial difference in the valuation ratios for markets in Belgium when compared to the rest of the world. Consequently, there appears to be no reason to add a premium or make a discount strictly on the basis of buying or selling a company in Belgium.
  44. 44. Adjustments to Valuations Final Adjustments to Acme’s Composite Model This value reflects our recommendation for Acme’s valuation and includes both quantitative and qualitative input. As with any forecast, there is a range of error that is unavoidable. We estimate that the statistical range for this forecast is ±15%.
  45. 45. Recommended Acme Valuation Though a valuation recommendation necessarily must land on a single number, the chart at left indicates that there can be varying viewpoints within a range. In this case, the valuation assigned by the Price-to-AUM model appears too far outside the range to be credible, so a reasonable range is probably from $34-51 million.
  46. 46. Notes Edward A. Strohbehn Ed Strohbehn has spent the past 25+ years on Wall Street -- a period that has seen no less than eight significant bear markets or market corrections -- gaining experience in each of its major areas: an investment firm, a bank, an insurance company, and a hedge fund. Though his education is in mathematics, his experience has tended to be broadly based, covering the areas of management, new product & business development, investment advice, marketing, sales support and operations, in addition to his interest in quantitative models. For the most part, his career has focused on international institutions, clients and distribution teams. INVESTMENT CAREER 1981-1991 -- Merrill Lynch & Co., including two years at Riyad Bank in Saudi Arabia 1991-1992 -- Oppenheimer & Company 1992-1996 -- Strohbehn & Co., Inc. 1996-1998 -- Coutts Bank 1998-2000 -- Consultant to 12 new businesses 2000-2004 -- Prudential Financial, Inc. 2004-2005 -- Calyx Financial LLC 2005+ -- Strohbehn, Hall, Olson & Evans LLC For additional information, please visit www.shoeLLC.com
  47. 47. Notes Custom Model Optimization with Constraints (CMOC) versus Standard Linear Regression Many multivariate models are developed using linear regression techniques. Sadly, regression often disappoints, especially when sample sizes are small or variables are highly correlated. In these situations, it is often observed that regression techniques over explain the data, yielding models that are less useful when applied to data outside the sample. This valuation project reflects limited sample sizes – the number of publicly-listed pure asset management firms with reliable data is less than two dozen. And the variables can sometimes reflect self-selecting management decisions, so that correlations are difficult to wade through. Consequently, SHOE LLC uses a customized methodology that seeks to achieve regression’s goals while being more robust – less affected by individual outliers, for example. Whereas regression seeks to choose a set of parameters so that the sum of the squares of the residuals (difference between model and actual values) is minimized. SHOE’s constrained model optimization works to choose a set of parameters as follows: (1) Minimize the average absolute residual, calculated by taking the absolute value of the difference between the model and actual values; (2) Establishing the constraint that all coefficients must be non-negative. Thus, any variable that seeks to over-explain its cohorts by being negative is automatically eliminated from the model; and (3) Establishing the additional constraint that the average residual is “close” to zero. That is, the average model result is never far from the average actual result. When using this methodology to create composite models, an additional constraint may be imposed that requires that all or most of the sub-models be included in the composite. Theoretically, this is sub-optimal. However, in a world where out-of-sample data is ultimately being analyzed, model “diversification” seems to have value that cannot easily be quantified. All these methods are put through a regression check when finished, to ensure that the relationship is statistically significant, even though tests are not available to confirm the statistical validity of each individual parameter.
  48. 48. Notes <ul><li>Standard Linear Regression </li></ul><ul><li>Choose coefficients using mathematical analysis of data points. </li></ul><ul><li>Minimize the sum of the squares of the residuals. </li></ul><ul><li>No other constraints. </li></ul><ul><li>Custom Model Optimization with Constraints </li></ul><ul><li>Choose coefficients (a.k.a. parameters) using mathematical analysis of data points. </li></ul><ul><li>Minimize the sum of the absolute values of the residuals. </li></ul><ul><li>Subject to these constraints: </li></ul><ul><ul><li>All coefficients > 0 or automatically dropped from the model </li></ul></ul><ul><ul><li>Average residual = 0 (or close) </li></ul></ul><ul><ul><li>If choosing weights, then sum of the weights = 100%. </li></ul></ul>Notes “ Residuals” refers to the difference between model and actual values. In the usage here, there is no difference intended between a “coefficient” and a “parameter”. By minimizing the sum of the squares of the residuals, linear regression techniques tend to try to give extra weight to extreme data. This extra weighting is reduced through the objective function used in the Constrained Parameter Optimization, which treats all differences proportionately. Linear regression uses matrix algebra to compute its solutions. Constrained Model Optimization uses iterative numerical techniques; practically, the Solver Function in EXCEL is sufficient.
  49. 49. Notes This simple example compares the two techniques: regression and CMOC. The dependent variable is the left-hand column “Mkt Cap.” The independent variables are in the next four columns: sales, earnings, book value, and AUMs. The next section shows calculations for standard linear regression, while the final section shows the calculations for CMOC: the model forecast plus three measures of error. Blue shading indicates where one model seems superior. For regression, the coefficient for sales is negative, which immediately renders the model useless, since increasing sales should NOT cause market capitalization to go down. Looking at individual forecasts suggests the superiority of CMOC. Regression produced two superior forecasts, while CMOC prevailed in five. The other ten were similar. The regression approach generated forecasts that, in aggregate, were 2.1% away from actual values, while CMOC generated forecasts that were, in aggregate, not skewed. Finally, the mean absolute error was reduced to 14.4% for CMOC versus 15.2% for regression – in spite of a significant increase in the sum of the squares of the residuals. Regression: FCST = – .6984 * Sales + 18.136 * Earn + .5950 * Book + 0.52% * AUMs CMOC: FCST = 17.369 * Earn + .6222 * Book + 0.10% * AUMs
  50. 50. Notes <ul><li>Strohbehn, Hall, Olson & Evans LLC (SHOE LLC) is a private investment firm that assists firms in growth and transition, providing what Ed Strohbehn refers to as “tugboat services.” The firm is named for his four grandparents and is a single-member limited-liability corporation domiciled in New York state. Additional information is available at www.shoeLLC.com . </li></ul><ul><li>SHOC LLC is not registered as a broker-dealer with the National Association of Securities Dealers nor as an investment adviser with the United States Securities and Exchange Commission. </li></ul><ul><li>All forecasts and models have been prepared with strict, professional care; however, any forecast is subject to unknown influences and future forces beyond control, so no guarantee can be made by SHOE LLC that results will be as expected. Statistical or random errors can increase as projections are made outside the sample from which model parameters were estimated. </li></ul><ul><li>Information included in this report has been taken from sources believed to be reliable, including Reuters, Pensions & Investments, and Hoover’s; however, no information can not be guaranteed by SHOE LLC to be accurate beyond what is promised by the suppliers. </li></ul><ul><li>All securities prices as of close of business on May 31, 2006. </li></ul>

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