Another popular approach is called the "Life Style Allocation", which simply puts the same percentage in fixed income as your age, e.g., if you are 40 years old, put 40% in fixed income. It is understandable that unsophisticated users want something that is simple to use. But that doesn't mean the underlying methodology has to be simple minded. The Life Style approach makes the ludicrous assumption that all 40 year olds have the same goals and the same amount of wealth to achieve the goal. FinancialEngines is proof that it is possible to hide complex statistical methodology from the end user while letting them benefit from rigorous analytics. While we profer a different methodology than Bill Sharpe, we respect the work he has done. For our approach to asset allocation, see the article titled "The Dutch Triangle"in the Journal of Portfolio Management, Fall 1999.
This paper assumes the asset allocation decision has already been determined in SetSAM. The question to be addressed is how to make the choice between active and passive equity managers. The most popular tool for making this decision is the ratio shown in Exhibit 1.
Exhibit 1
At first glance, this seems to solve the problem nicely. The numerator measures the excess return the active manager earned over a passive index. In CAPM terms this is the manager’s alpha. The term in the denominator is the standard error of the alpha. But what does that mean? If the manager’s portfolio looks exactly like the index, there will be no tracking error. But, there will also be no excess return in the numerator. In this instance, the information ratio would identify a closet indexer who is not worth the active management fee. This information appears valuable for reducing costs.
Suppose a manager was astute enough to avoid investing in Japanese banks in the ‘90’s. That manager could have beat the index for Japan by an average of 800 basis points per year. However, the tracking error would have been huge, which would have made the information ratio smaller than that of managers who held weak companies in a weak industry all the way to the bottom. Could this happen? It did. Could this cause a pension investment officer with an expensive consultant to reject such a manager? It did. The manager in question works with Invesco. He beat the Japan index every year for eight years; sometimes by as much as 1300 basis points, and sometimes by as little as 300 basis points. The result was a very large tracking error caused by excellent management.
Would replacing the S&P 500 with a blend of indexes solve the problem? There is a more fundamental problem with the information ratio. It is not directly related to the goal of the investor. If your goal is to retire at age 65, then investing in a market portfolio is merely one investment vehicle you might choose to accomplish your goal. Beating the market is not your goal. Beating the market may or may not accomplish your goal. If you must earn 8% to accomplish your goal and the market is down 10%, but your manager is only down 5%, the manager still incurred risk of not accomplishing your goal. Given the assumptions of the CAPM, the information ratio appears to be relevant for everyone. For the investor who can identify an MAR that will accomplish his or her goal, looks can be deceiving.
THE SOLUTION
I. Focus on the manager’s style, not the manager’s returns.
II. Identify the upside potential of this style relative to its downside risk.
III. Find managers who can beat their style benchmarks.
IV. Base judgments on what could have happened, not what did happen.
Over 80% of the returns for almost all managers can be explained by a combination of passive indexes (a style benchmark) one could purchase at 1/10th the cost of active management. Data is available on these indexes for 20 years or more. This provides much more stable estimates than the short term results of the manager.
PERFORMANCE RELEVANT TO YOUR GOAL
As explained in "The Dutch Triangle" [1999], there is some return that must be earned at minimum in order to accomplish one’s goal. If that minimal acceptable return (MAR) is not in the equation, the equation is not relevant to your goal. One way to accomplish that is to use the Sortino ratio.
The R in the numerator is the realized return of the manager for some interval of time. In this study the interval is five years. The R in the denominator is only for returns lower than the MAR. Since this ratio uses the manager's data, estimates are limited to relatively short term intervals. We try to overcome this time sensitivity problem by using the bootstrap procedure developed by Bradley Efron at Stanford University. If the Sortino Ratio is used, one could then use the Omega excess return to see if the manager beat the passive benchmark.
Of course, one could substitute returns on the manager's style benchmark for the manager's data. Instead we propose a new performance measure based on behavioral finance studies. It is called the Upside Potential Ratio (U-P ratio). For Details see the article on this Web site.
The R in the numerator is not the manager's realized return. It is calculated from the returns of the manager's style benchmark for 20 years or more. The returns are bootstraped to generate a distribution of returns that could have happened. Only those returns above the MAR are recognized in the numerator and only returns below the MAR are counted in the denominator. The implicit assumption is that investors should focus on the average return above the MAR for the manager’s style benchmark, because it should be a more reliable predictor of future performance. Consistency of results that are relative to your goal are what matters, not who had the highest return relative to other managers.
Empirical Results
Table 1
| Omega | 5 year | Sortino | |||||
| Fund | U-P Ratio | Excess | R-squared | Sortino Ratio Rankings | Return | Ratio | |
| Washington Mutual Investr | 189% | 3.0% | 96% | Janus Inv Twenty | 40.3% | 3.82 | |
| Vanguard Windsor II | 185% | -0.8% | 96% | Fidelity Aggressive Growth | 36.4% | 3.68 | |
| Vanguard Windsor | 184% | -3.3% | 87% | Fidelity Dividend Growth | 27.5% | 3.56 | |
| Putnam Growth & Income/A | 177% | -2.4% | 97% | T Rowe Price Science&Tech | 35.1% | 3.53 | |
| Fidelity Adv Grth Opp/T | 177% | -2.9% | 93% | Vanguard Instl Index/Ist | 27.5% | 3.33 | |
| MFS Mass Inv Trust/A | 177% | 0.0% | 96% | Vanguard 500 Index | 27.4% | 3.3 | |
| T Rowe Price Growth & Inc | 175% | 0.3% | 94% | BGI Masterworks S&P 500 | 27.0% | 3.26 | |
| Dreyfus Appreciation | 175% | -1.5% | 95% | Fidelity Spart US Eq Indx | 27.2% | 3.26 | |
| Amer Cnt Income & Gr/Inv | 174% | 1.1% | 98% | SSgA S&P 500 Index Fund | 27.2% | 3.26 | |
| BGI Masterworks S&P 500 | 174% | 0.0% | 100% | Vanguard Growth & Income | 27.5% | 3.25 | |
| Fidelity Dividend Growth | 173% | 4.3% | 89% | Amer Cnt Income & Gr/Inv | 26.8% | 3.25 | |
| SSgA S&P 500 Index Fund | 173% | 0.2% | 100% | T Rowe Price Eq Index 500 | 27.2% | 3.25 | |
| Investment Co of America | 173% | 0.3% | 98% | Dreyfus Basic S&P | 27.1% | 3.24 | |
| Vanguard Instl Index/Ist | 173% | 0.6% | 100% | Prudential Stock Index | 26.8% | 3.19 | |
| Vanguard Growth & Income | 173% | 1.6% | 98% | Dreyfus Appreciation | 26.0% | 3.15 | |
| Vanguard 500 Index | 172% | 0.4% | 100% | Putnam Investors/B | 28.1% | 3.14 | |
| Fidelity Spart US Eq Indx | 172% | 0.2% | 100% | MFS Mass Inv Growth Stock/A | 32.1% | 3.13 | |
| T Rowe Price Eq Index 500 | 172% | 0.2% | 100% | Washington Mutual Investr | 23.0% | 3.13 | |
| Fundamental Investors | 172% | 2.5% | 95% | Fidelity | 25.6% | 3.12 | |
| Aggressive Value_US | 172% | 0.0% | 100% | T Rowe Price Blue Chip Gr | 27.0% | 3 | |
| Prudential Stock Index | 172% | -0.1% | 100% | MFS Mass Inv Trust/A | 23.9% | 2.97 | |
| Dreyfus Basic S&P | 172% | 0.1% | 100% | Janus Inv Janus | 28.5% | 2.96 | |
| Fidelity Equity Income | 171% | -1.8% | 96% | Fidelity Grth & Inc | 23.9% | 2.95 | |
| Federated Amer Ldrs/A | 170% | 1.0% | 95% | Fundamental Investors | 23.2% | 2.93 | |
| Federated Equity Inc/A | 169% | 0.9% | 95% | Fidelity OTC Portfolio | 30.5% | 2.91 | |
| Fidelity Equity Income II | 168% | -4.6% | 94% | Investment Co of America | 22.6% | 2.88 | |
| Merrill Basic Value/A | 168% | 1.1% | 94% | Fidelity Advisor Equity Growth | 28.9% | 2.86 | |
| Fidelity Grth & Inc | 167% | -0.9% | 96% | Galaxy Eqty Growth/Tr | 25.8% | 2.85 | |
| Fidelity | 166% | -0.5% | 95% | Vanguard U#S# Growth | 28.9% | 2.83 | |
| AXP Stock | 165% | -6.5% | 95% | AXP New Dimensions | 26.5% | 2.82 | |
| Galaxy Eqty Growth/Tr | 165% | -1.7% | 95% | Fidelity Growth Company | 29.5% | 2.78 | |
| Amer Cnt Select/Inv | 163% | -3.1% | 92% | Fidelity Contrafund | 25.5% | 2.77 | |
| Norwest Growth | 163% | -2.9% | 93% | Amer Cnt Select/Inv | 25.0% | 2.77 | |
| Neuberger Partners Fund | 163% | -1.1% | 94% | Federated Equity Inc/A | 21.7% | 2.76 | |
| Scudder Growth & Income | 162% | -0.2% | 92% | Aggressive Growth_US | 35.1% | 2.7 | |
| Putnam Investors/B | 162% | -1.5% | 94% | Putnam OTC Emerg Grth/A | 29.2% | 2.68 | |
| Dodge & Cox Stock | 161% | 2.9% | 92% | Vanguard PRIMECAP | 29.4% | 2.67 | |
| Franklin Mutual | 160% | 0.7% | 84% | Putnam New Opportunity/A | 28.7% | 2.65 | |
| Fidelity Blue Chip Growth | 160% | -3.7% | 92% | Large Growth_US | 33.0% | 2.61 | |
| AXP New Dimensions | 160% | -1.9% | 96% | INVESCO Dynamics | 29.7% | 2.6 | |
| T Rowe Price Blue Chip Gr | 159% | 1.4% | 97% | Large Value_US | 27.0% | 2.59 | |
| T Rowe Price Growth Stock | 159% | -0.8% | 95% | T Rowe Price Growth Stock | 23.8% | 2.58 | |
| American Mutual | 158% | 1.4% | 95% | MFS Capital Opport Fund/A | 28.9% | 2.56 | |
| Fidelity Magellan Fund | 158% | -1.4% | 89% | Founders Growth | 26.6% | 2.53 | |
| Fidelity Retirement Growth | 156% | -7.4% | 87% | Fidelity Magellan Fund | 24.8% | 2.52 | |
| Prudential Equity Inc/B | 156% | -3.6% | 86% | Fidelity Blue Chip Growth | 24.1% | 2.51 | |
| Neuberger Guardian Fund | 155% | -10.5% | 85% | Fidelity Adv Grth Opp/T | 20.5% | 2.49 | |
| Neuberger Genesis Fund | 155% | -1.7% | 64% | AXP Growth | 27.1% | 2.44 | |
| MFS Research Fund/A | 154% | -2.7% | 92% | AIM Value Fund/A | 25.8% | 2.43 | |
| T Rowe Price Spect Growth | 154% | -1.7% | 91% | Putnam Vista/A | 27.0% | 2.41 | |
| T Rowe Price Equity Inc | 154% | 3.3% | 93% | Putnam Voyager/A | 27.1% | 2.4 | |
| Fidelity Disciplined Equity | 153% | -2.9% | 92% | Norwest Growth | 22.8% | 2.37 | |
| Janus Inv Janus | 153% | 0.9% | 83% | Amer Cnt Growth/Inv | 25.7% | 2.37 | |
| MAS Value/Inst | 153% | -2.1% | 88% | Amer Cnt Ultra/Inv | 26.5% | 2.34 | |
| Baron Asset Fund | 152% | -3.4% | 73% | New Economy | 24.8% | 2.3 | |
| Fidelity Value | 152% | -4.1% | 79% | Vanguard Windsor II | 20.7% | 2.28 | |
| Fidelity Advisor Equity Growth | 151% | 0.8% | 90% | MFS Research Fund/A | 23.7% | 2.26 | |
| Oakmark Fund | 151% | -2.7% | 80% | Growth Fund of America | 26.5% | 2.25 | |
| Fidelity Contrafund | 150% | 2.2% | 81% | Fidelity Disciplined Equity | 23.0% | 2.25 | |
| Large Value_US | 150% | 0.0% | 100% | Vanguard Morgan Growth | 26.9% | 2.24 | |
| Amer Cnt Growth/Inv | 150% | -4.5% | 85% | Putnam Growth & Income/A | 19.8% | 2.18 | |
| Fidelity Low Priced Stock | 149% | -1.6% | 74% | MFS Emerging Growth | 25.4% | 2.15 | |
| Capital Income Builder | 149% | 0.3% | 79% | Federated Amer Ldrs/A | 21.3% | 2.15 | |
| Founders Growth | 148% | -0.1% | 88% | Merrill Basic Value/A | 20.1% | 2.11 | |
| AIM Value Fund/A | 147% | -1.3% | 86% | American Mutual | 17.9% | 2.07 | |
| Fidelity Growth Company | 147% | 1.8% | 82% | Franklin Stgc Sm Cap Gr/A | 27.3% | 2.07 | |
| Fidelity Aggressive Growth | 147% | 6.2% | 68% | Cap Research AMCAP | 23.3% | 2.04 | |
| T Rowe Price Science&Tech | 147% | 3.7% | 61% | T Rowe Price Growth & Inc | 18.3% | 2.04 | |
| MFS Mass Inv Growth Stock/A | 146% | 4.9% | 89% | Fidelity Equity Income II | 19.3% | 2.03 | |
| Income Fund of America | 146% | 1.5% | 94% | Fidelity Equity Income | 20.1% | 2 | |
| Fidelity OTC Portfolio | 146% | 2.6% | 74% | AXP Stock | 19.2% | 2 | |
| AXP Growth | 146% | -0.5% | 85% | T Rowe Price Equity Inc | 19.0% | 1.9 | |
| Amer Cnt Ultra/Inv | 146% | -4.2% | 82% | Dodge & Cox Stock | 20.8% | 1.89 | |
| Putnam New Opportunity/A | 145% | 0.7% | 74% | Fidelity Retirement Growth | 21.0% | 1.87 | |
| Small Value_US | 145% | 0.0% | 100% | Franklin Mutual | 17.7% | 1.84 | |
| Putnam Vista/A | 145% | 0.0% | 77% | Aggressive Value_US | 21.0% | 1.76 | |
| Vanguard U#S# Growth | 144% | -1.5% | 96% | T Rowe Price Spect Growth | 18.7% | 1.74 | |
| Putnam Voyager/A | 144% | 1.3% | 86% | Neuberger Partners Fund | 19.7% | 1.73 | |
| Amer Cent Value | 144% | 1.3% | 90% | T Rowe Price Mid-Cap Grth | 23.8% | 1.69 | |
| Putnam OTC Emerg Grth/A | 143% | -3.6% | 55% | Capital Income Builder | 14.5% | 1.69 | |
| Merrill Growth Fund/A | 143% | -9.5% | 44% | Baron Asset Fund | 20.2% | 1.66 | |
| PBHG Growth | 143% | -13.7% | 53% | Scudder Growth & Income | 18.1% | 1.63 | |
| Franklin Balance Sheet | 142% | -0.8% | 65% | Income Fund of America | 14.7% | 1.58 | |
| Cap Research AMCAP | 142% | -0.5% | 91% | Vanguard Windsor | 17.4% | 1.57 | |
| MFS Emerging Growth | 141% | -2.1% | 72% | Small Growth_US | 22.1% | 1.49 | |
| New Economy | 141% | 2.2% | 85% | Vanguard Idx Ext Mkt/Inv | 20.4% | 1.49 | |
| Vanguard Idx Ext Mkt/Inv | 141% | -2.0% | 86% | PBHG Growth | 19.9% | 1.44 | |
| Vanguard PRIMECAP | 141% | 5.2% | 82% | T Rowe Price New Amer Gr | 21.1% | 1.43 | |
| Growth Fund of America | 139% | 1.5% | 86% | AIM Constellation Fund/A | 19.7% | 1.32 | |
| INVESCO Dynamics | 139% | 5.3% | 78% | T Rowe Price New Horizons | 19.9% | 1.25 | |
| Janus Inv Twenty | 139% | 6.0% | 79% | Neuberger Genesis Fund | 16.3% | 1.22 | |
| Vanguard Morgan Growth | 136% | 2.4% | 93% | Fidelity Low Priced Stock | 15.4% | 1.21 | |
| AIM Constellation Fund/A | 133% | -6.0% | 79% | Amer Cent Value | 17.3% | 1.12 | |
| T Rowe Price New Amer Gr | 133% | -4.1% | 78% | Prudential Equity Inc/B | 15.6% | 1 | |
| Vanguard Explorer | 130% | -9.1% | 71% | MAS Value/Inst | 15.7% | 0.97 | |
| Franklin Stgc Sm Cap Gr/A | 130% | 3.2% | 65% | Small Value_US | 16.2% | 0.95 | |
| T Rowe Price Mid-Cap Grth | 130% | 0.9% | 79% | Franklin Balance Sheet | 13.3% | 0.94 | |
| T Rowe Price New Horizons | 130% | -4.9% | 72% | Neuberger Guardian Fund | 14.9% | 0.91 | |
| Small Growth_US | 128% | 0.0% | 100% | Oakmark Fund | 14.1% | 0.81 | |
| Aggressive Growth_US | 127% | 0.0% | 100% | Vanguard Explorer | 15.4% | 0.78 | |
| MFS Capital Opport Fund/A | 124% | 9.9% | 86% | Fidelity Value | 13.9% | 0.72 | |
| Large Growth_US | 68% | 0.0% | 100% | Merrill Growth Fund/A | 12.6% | 0.61 | |
| Bond_US | 1% | 0.0% | 100% | US_Bond | 7.9% | -0.17 | |
| 3 Month T-bills_US | -99% | 0.0% | 100% | Money market | 5.2% | -1.99 | |
Washington Mutual earned 300 basis points (3%) more each year than its style benchmark after adjusting for downside risk. The negative returns in the Omega excess column support the view that most funds cannot beat a passive set of indexes. For example, Windsor fund is overweighted in finance stocks and tobacco, causing it to underperform the passive benchmark.
The performance analysis above does not indicate how much
should be allocated to each asset category, or how much should be allocated to active
versus passive management. The answer to
these questions requires an asset allocation model.
Table 2
Sam only allows those funds that are in the upper half and have an Omega excess of 100 basis points or more to be considered in the final solution. Suppose one allowed Janus to be considered in the asset allocation. The results are shown below.
Table 3
American Mutual is replaced by Janus and other positions are reduced to allow a 4.7% allocation to Janus. This demonstrates that SAM can accommodate both reversion-to-the-mean and momentum philosophies while maintaining a well diversified portfolio.
Although I believe strongly that international stocks should be a part of most portfolios, to simplify the analysis, I did not include them.
The style indexes in this analysis were provided by Independence International Associates (IIA) in Boston. Fund data was provided by LCG associates in Atlanta. The statistics were generated by SetSAM, a proprietary product of the Pension Research Institute that provides the input to SAM.
The purpose of this paper is to present research ideas. None of the information shown in this research paper should be considered an endorsement or recommendation of any mutual fund or investment strategy. Many assumptions were made that could invalidate the results. Anyone acting on the statistics shown here does so at their own risk.