CFA Institute

"Sustainable Spending in a Lower-Return World": [Comment and Response]Author(s): Stephen L. Kessler and Robert D. ArnottSource: Financial Analysts Journal, Vol. 61, No. 2 (Mar. - Apr., 2005), pp. 17-18Published by: CFA InstituteStable URL: http://www.jstor.org/stable/4480650 .

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Letters to the Editor

"How to Value Employee Stock Options": Authors' Response We would like to thank Larry Johnson for his com- ment on our article. His perspective is a little differ- ent from ours. We regard the valuation of executive stock options to be analogous to the valuation of mortgage-backed securities. Both require a model of some aspect of human behavior. In the case of MBS, we are interested in prepayment behavior; in the case of executive stock options, we are interested in early exercise behavior. The issue is whether we assume we know nothing about human behavior (as is usual when prepayment functions are being derived empirically for the MBS market) or whether we assume that "behavior is optimal except. . .. We prefer the first approach.

Our model has the advantage that it is easy to implement. Also, it is compliant with FAS 123R, provided it is used in conjunction with a term structure of interest rates and a term structure of volatilities. At the time we wrote the article, we had limited data on the actual early exercise behavior of employees. Since then, we have had the oppor- tunity to develop proprietary models of early exer- cise behavior for two large U.S. companies from 10 years of history. These models are similar to the model in our article, in that "moneyness" (S/K, that is stock price/stock option price) is the key vari- able, but the proprietary models are more complex. The probability of early exercise for an employee depends on S/K, on time since vesting, and on the path followed by the stock price.

We find little difference, in most situations, between the model in our article and the model with Professor Johnson's adjustment to the early exercise rule. When dividend yields are less than 6 percent, the difference between the value found with Professor Johnson's model and the value found with our model is small. And few companies pay dividend yields in excess of 6 percent; a search of Yahoo! Finance produced only 214 of 8,692 equi- ties (about 2.5 percent) with dividend yields of 6 percent or higher. Most of those companies are real estate or similar investment trusts.

John Hull University of Toronto

Alan White University of Toronto

"Sustainable Spending in a Lower-Return World": A Comment Editor Robert D. Arnott's long-standing concerns about sustainable spending rates from pensions, endowments, and foundations are worth repeating often. I suggest that this concern would be ampli-

fied by using the full 200-year history of returns from 1802 rather than the portion that begins only in 1871 (although, of course, as Mr. Arnott points out, reliable earnings begin to be available only from 1871). So, I offer the following analysis of returns based on the 1802-2004 data.

As shown in the following table, the rates of return available through investing in stocks, long- term bonds, cash, or a 60 percent stock/40 percent long bond mix differ markedly depending on whether the earlier 70 years are included:

Period Stocks Bonds Cash 60/40 Mix

1802-1871 5.91% 5.06% 5.23% 5.77%

1802-9/2004 7.81 4.98 4.27 7.01

1871-9/2004 8.76 4.90 3.74 7.61

1926-9/2004 10.03 5.33 3.80 8.65

Source: Based on Jeremy Siegel's data from Stocksfor the Long Run (New York: McGraw-Hill, 1994) updated through last month by the author.

The early 70 years of data reveal almost a com- plete lack of any equity risk premium, and bond investing was actually penalized. The cause could not be a lack of progress and innovation during the period. Transportation, communication, industri- alization, and expansion of U.S. borders were hall- marks of the time. From the Erie and Hudson canals to transcontinental railroads, the telegraph, the reaper, and the Louisiana purchase-all were opportunities for equity investing.

Although the low returns cannot be attributed to multiple contraction, note that productivity gains were lower prior to 1871 than afterward. GDP per person rose from $98 in 1800 to $220 by 1870, an annualized rate of 1.16 percent. Inflation during the period was 0.22 percent a year, leaving 0.94 percent yearly as the real productivity growth rate. Currently, GDP per person is about $39,000, a 134-year growth rate of 3.94 percent less 2.02 per- cent inflation, or 1.91 percent a year.

Investors who use an overly aggressive assumption of continuing 8.65 percent returns for equities are relying on 1926 (as in the Jbbotson Asso- ciates data) as their beginning date. One can only speculate what the return assumption would be had an lbbotson predecessor published a study based on the 70-year period ending 1871. So, using a 203-year history with present modeling techniques may tem- per the unrealistic enthusiasm about future returns by some investors. A 7 percent rate of return for 60/ 40 investors and a 3.5 percent risk premium are more in line with a 204-year history lesson.

Stephen L. Kessler Quantum Asset Management

Mercer Island, Washington

March/April 2005 www.cfapubs.org 17

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Financial Analysts Journal

"Sustainable Spending in a Lower-Return World": Author's Response Stephen Kessler raises a valuable point. Even a very long span (more than 130 years in this case) can be special. Going a step beyond Mr. Kessler's observa- tions, I would respond that perhaps the most important way the U.S. market returns for 1871- 2004 are special is "survivorship bias": The United States survived. Four of the fifteen largest stock markets in the world of 1900 experienced a 100 percent decline in value, through expropriation, at least once during the 20th century (Argentina, China, Egypt, and Russia). Several others experi- enced a 95 percent or larger decline in the wake of the two world wars. It would be difficult to say that the United States was "charmed" during this 130- year span but fair to say that we had an easier time than most countries over a like span both in recent history and since the dawn of civilization. I've writ- ten in the past that $1 of gold invested at a 5 percent real rate at the birth of Christ just over 2000 years ago would today buy a sphere of gold larger than the orbit of the earth around the sun and growing larger at roughly 400 miles per hour. A 5 percent real return is, in the broad sweep of human exist- ence, an anomaly, not a normal real return.

Robert D. Arnott

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The views expressed in Letters to the Editor are those of the letter authors, not of CFA Institute or the Financial Analysts Journal.

18 www.cfapubs.org ?2005, CFA Institute

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