2 In addition to the volatility of the return, the other factors which determine value under the Black-Scholes formula are the difference between the market and exercise prices, the time remaining before the expiration of the option, and the risk-free rate of interest. Among these, only volatility is normally subject to short-term changes, and it therefore dominates the value of options according to the formula.
3 Henry Kaufman, On Money and Markets: A Wall Street Memoir (New York: McGraw-Hill, 2000), 74.
4 A detailed description of the stock market’s volatility can be found in Derry Pickford and Andrew Smithers, “Stock Market Volatility,” Smithers & Co. Ltd. Report, no. 184 (November 11, 2002).
5 Andrew Smithers and Stephen Wright, “Stock Options: An Example of Catastrophic Myopia?,” Smithers & Co. Ltd. Report, no. 110 (October 7, 1997).
6 Kaufman, On Money and Markets, 74.
7 Tim Lee, Jamie Lee, and Kevin Coldiron, The Rise of Carry: The Dangerous Consequences of Volatility Suppression and the New Financial Order of Decaying Growth and Recurring Crisis (New York: McGraw-Hill, 2019), 65.
8 Kaufman, On Money and Markets, 77.
9 Lee, Lee, and Coldiron, Rise of Carry, 103–4.
10 Robin Wigglesworth, “Jane Street: The Top Wall Street Firm ‘No One’s Heard Of,’” Financial Times, January 28, 2021.
11 Lee, Lee, and Coldiron, Rise of Carry, 77.
12 Lee, Lee, and Coldiron, Rise of Carry, 73.
13 For the generally accepted view, see John Y. Campbell and Luis M. Viceira Strategic Asset Allocation: Portfolio Choice for Long-Term Investors (Oxford: Oxford University Press, 2002); Andrew W. Lo and A. Craig MacKinlay, A Non-Random Walk Down Wall Street (Princeton: Princeton University Press, 1999).
14 Lee, Lee, and Coldiron, Rise of Carry, 155.
15 This relationship is difficult to show graphically, as there are over twenty-three thousand data points for each data series.
16 See Chapter 4 of Andrew Smithers, The Economics of the Stock Market (Oxford: Oxford University Press, forthcoming), which shows how the dividend pay-out ratio varies with the growth of the economy and the change in leverage; the rise in the latter has recently outweighed the slowdown.
17 Paul Samuelson, “Science and Stocks,” Newsweek, September 19, 1966.
18 My regular updates on the level of the U.S. stock market by CAPE and q can be accessed at www.smithers.co.uk.