Notes
1 Chesterton's actual remark was, “Life is a trap for logicians because it is almost, but not quite, reasonable.
2 Perhaps the most famous example of the Rothschild family trading on early knowledge of world events occurred in connection with the Battle of Waterloo. Nathan Rothschild, then head of the English branch of the family, learned early in the day that Wellington had defeated Napoleon and that English securities would rise dramatically when the news was broadly known. You might imagine that Rothschild would use that news to buy. But he knew that Waterloo was a once-in-a-lifetime opportunity and he intended to make the most of it. Therefore, he began quietly to sell. Word gradually spread across the floor of the exchange that the Rothschilds were pulling out of the market. Astute traders began to sell also, assuming that Wellington had lost. Rothschild accelerated his selling and soon the exchange was in a panic. Finally, with prices at preposterously low levels, Rothschild swept in and bought, making a vast fortune in a few hours.
3 “Portfolio Selection,” Journal of Finance 7, no. 1 (March, 1952): 77 ff. Markowitz's breakthrough ideas about portfolio design actually had their origin in his earlier insight about the possibility of applying mathematical methods to the capital markets. It was from this inspiration that all else followed.
4 Like Markowitz, Einstein was virtually unknown when he published his seminal papers on the photoelectric effect, the special theory of relativity, and statistical mechanics. Indeed, he was not even a practicing academic, but an obscure clerk in the Zurich patent office.
5 Notice that the computer is not trying to solve a complex equation. Instead, it is conducting an iterative process of looking at each portfolio and discarding those that produce inferior results.
6 Modern mean variance optimizers employ algorithms designed to reduce—drastically—the number of asset combinations that must be reviewed. See, for example, Markowitz's own work on the fast computation of mean-variance frontiers in his book, Portfolio Selection: Efficient Diversification of Investments (New York: John Wiley and Sons, 1959), Appendix A. In addition, financial advisors almost always constrain the optimizer—by, for example, requiring that recommended portfolios have minimum or maximum exposures to certain desired assets.
7 There are many other problems with using MVO and similar asset allocation techniques. See, e.g., Gregory Curtis, “Asset Allocation,” in J.K. Lasser Pro Expert Financial Planning: Investment Strategies from Industry Leaders, edited by Robert C. Arffa (New York: John Wiley & Sons, 2001), 327–345. But the best and most popular book on the subject of asset allocation is Roger C. Gibson's Asset Allocation: Balancing Financial Risk, 3rd ed. (New York: McGraw-Hill Trade, 2000).
8 Private foundations do pay a small excise tax.
9 Yes, private equity is typically a riskier asset class than hedge, but even on a risk-adjusted basis most families would prefer the private equity return.
10 The name is unfortunate, as it connotes gambling. However, as we all know (I hope!), gambling statistics are biased in favor of the house, while Monte Carlo simulations produce a straight-up, unbiased series of possible outcomes.
11 Eugene F. Fama, “The Behavior of Stock-Market Prices,” Journal of Business of the University of Chicago 38, no. 1 (January 1965).
12 These calculations were prepared by Jens Carsten Jackwerth and Mark Rubinstein, “Recovering Probability Distributions from Option Prices,” Journal of Finance 51, no. 5 (December 1996): 1,612. Yale Professor Benoit Mandelbrot has calculated the odds of the three major daily market declines in August 1998 at 1 in 500 billion, and the odds of three large declines in July 2002 at 1 in 4 trillion. See Benoit Mandelbrot and Richard L. Hudson, The Misbehavior of Markets (New York: Basic Books, 2004), 4.
13 Necessary because mean variance optimization is a mathematical technique, not a psychoanalytical technique.
14 Our portfolios will also experience unexpected and very good performance, but we are unlikely to complain about that.
15 Many institutions, for example, state the objectives for their endowment portfolios roughly like this: “The objective of the endowment is to provide a steady and growing stream of revenue to support the institution's operations and mission.” There will also be metrics around this broad statement, such as, “The stream of revenue, and the return on the portfolio, should grow faster than inflation net of all costs over a long period of time.”
16 The issue of prudence is discussed later. See Satisfying Portfolio Claims Prudently.
17 This discussion is indebted to the insightful work of Ashvin B. Chhabra, whose signature article in The Journal of Wealth Management should be required reading for anyone involved in designing portfolios for family investors. See “Beyond Markowitz: A Wealth Allocation Framework for Individual Investors,” The Journal of Wealth Management 7, no. 4 (Spring 2005): 8–34. I have departed from Chabbra's terminology somewhat, given the nature of the audience for this book. I am also indebted to my partner at Greycourt, Jim Foster, who contributed substantially to this discussion.
18 Estate taxes also represent a significant headwind, albeit one that can be substantially reduced via competent estate, tax, and trust planning.
19 Treasury Inflation Protection Securities, which are Treasury bonds designed to pay a real (adjusted for inflation) yield.
20 In other words, cash held now but which is expected to be invested when interesting opportunities present themselves. Portfolios that are too illiquid lack optionality.
21 See Brett P. Hammond, Jr., and Martin L. Leibowitz, “Rethinking the Equity Risk Premium: An Overview and Some Ideas,” The Research Foundation of the CFA Institute (2011). Hammond and Leibowitz review the literature and come up with 19 estimates of the equity risk premium, ranging from 0 percent to 7 percent.
22 That is, family members typically succeed the prior generation by assuming stewardship of the portfolio when they reach their mid-40s and their parents are in the mid-60s. They will maintain oversight of the family's capital for about 20 years and then pass the mantle to the next generation. Thirty years' worth of upside-down capital markets returns means that an entire generation will have failed in its stewardship duties.
23 The background of the Black-Litterman model and how it is used is described on the website www.blacklitterman.org. See, also, Guangliang He and Robert Litterman, “The Intuition behind Black-Litterman Model Portfolios,” available at SSRN: ssrn.com/abstract=334304.
24 Fischer Black and Robert Litterman, “Global Portfolio Optimization,” Financial Analysts Journal (September–October 1992): 28–43.
25 Reported earnings are averaged in order to control for business cycle effects. See John Y. Campbell and Robert J. Shiller, “Valuation Ratios and the Long-Run Stock Market Outlook,” The Journal of Portfolio Management (Winter 1998).
26 Thomas M. Idzorek, “A Step-By-Step Guide to the Black-Litterman Model, Incorporating User-Specified Confidence Levels,” (working paper, draft of April 26, 2005, available on numerous websites).
27 I am indebted for this analogy to Chhabra, “Beyond Markowitz”, note 17.