Most Popular ArticlesNovember 3, 2009
Monte Carlo simulations and the cost of alpha
David Loeper, the CEO of WealthCare Capital Management, is a pioneer in exposing the myths and risks of Wall Street’s performance game. He has written several books and white papers (referenced below), which are packed with data to make his case that the average investor is being under- and even ill-served by our industry.
Loeper’s work highlights the largely ignored danger of market-relative performance, or alpha. In his study, Loeper assumes that managers of active funds beat the market by an average of 2% annually over a period of 30 years. To calculate the variance in active approaches relative to the market, he bases his data on Ron Surz’ highly regarded Pipods universe of potential manager results. For his study, Loeper uses a simple case: A client has $2 million to invest and wants to generate $118,000 annually, adjusted for inflation, over 30 years without eroding his principal in real terms. Loeper’s Wealthcare Monte Carlo model shows that his 2% alpha assumption in a tax-efficient portfolio provides a 78% chance or degree of confidence that he can exceed his client’s required goal. That’s a fine portfolio.
But here’s the problem. Alpha, or market-relative performance, is not predictable. There is no way of knowing when a fund is going to outperform or by how much. This problem is known as timing risk. In his study, Loeper assumes that his portfolio will outperform the market by 2% annually on average (the implied promise of many actively managed funds). But to keep his model realistic, he does not force a constant 2% out-performance every single year. That feat cannot be realistically accomplished. The reality is that the extent and frequency of out-performance will vary each year, just as market returns do. Instead, Loeper selects only those theoretical managers from Surz’ data that beat the market by 2%, while recognizing that the timing of their relative out-performance is unpredictable.
What happens to the 78% confidence we saw earlier when timing risk is introduced into the model? Understanding that variability reduces confidence, one would correctly assume that confidence declines. In fact, confidence falls to 57% that our investor will be able to take $118,000 annually from his portfolio without violating his principal.
How would a passive S&P 500 index model do in comparison? To make it fair, Loeper assumes his index model will cost money to implement, so he assumes a negative alpha (or management cost) of .49%. He further handicaps his passive strategy by recognizing that there is some small tracking error even in an indexed portfolio. Under the same $2 million scenario as before, the passive portfolio provides a confidence of 54%, three points below our 2% alpha example.
Too many investors would walk out the door happy with the promise of 2% alpha and $118,000 to spend annually from their $2 million, unaware of the hidden dangers lurking in their uncertain future. Confidence of 57% is barely better than a coin flip. Would the client be better served if he understood that he faces an almost 50/50 chance of running out of money, even with a 2% market outperformance?
Let’s say our sample client was aware of the risks and therefore demands a higher confidence in his plan. He is also is willing to accept a lower level of income to keep his principal at $2 million. By reducing his income to $60,000 annually, he could achieve a confidence of 86% in a passive index model (burdened as before with costs and small tracking error) and a confidence of 84% in the 2% alpha portfolio.
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