Abstract
The risk premium, is by standard definition a straightforward and simple concept that plays a central role in modern finance. This chapter, however, suggests that as extreme market events unfold, a new and heretofore unnoticed aspect of the risk premium ought to be taken into account.
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Notes
- 1.
As early as 1934, Graham and Dodd (1934, p. 12) wrote in their first edition, speculators are “most optimistic when prices are highest and most despondent when they are at bottom.”
Empirically, this can be seen from commercial surveys such as those of Investors Intelligence, in reports from Market Vane’s Bullish Consensus that measure percentages of bullish or bearish opinions, and in Shiller’s Crash Confidence Index, a monthly survey of individual and institutional investors as to their level of confidence that the market won’t crash in the next six months. Its all-time high was in 2006, according to Shiller in , “An Echo Chamber of Boom and Bust,” New York Times, August 30, 2009. At the tops, the percentages of bulls are always high: at the bottoms, bears predominate. For example, according to the Investors Intelligence surveys of more than 100 independent investment advisory newsletters, bullish readings of above 60% and bearish readings above 55% are rare. Bullish readings surged near the 1999 peak to above 60%, with a previous high prior to the crash in 1987. Two bearish readings above 55% were seen in 1994, just prior to the start of the late 1990s uptrend. See also Evans (2003, p. 4).
- 2.
Gjerstad and Smith (2014, p. 15).
- 3.
See Cochrane (2005, p. 480), consistent with Kahneman , who, in Schrage (2003) said, “What actually happens with fear is that probability doesn’t matter very much.” Prechter (1999, pp. 395–7) would add, “Hope tends to build slowly, while fear often crystallizes swiftly.” He has also said (Perspectives, 2004, Elliott Wave International, Gainesville, GA; www.elliottwave.com) that “Fear does not need a period of dissipation as does hope.” Greenspan (2008) makes the same point, writing, “The most credible explanation of why risk management based on state-of-the-art statistical models can perform so poorly is that the underlying data used to estimate a model’s structure are drawn generally from both periods of euphoria and periods of fear, that is, from regimes with importantly different dynamics…The contraction phase of credit and business cycles, driven by fear, have historically been far shorter and far more abrupt than the expansion phase, which is driven by a slow but cumulative build-up of euphoria.” From Greenspan (2009b): “Bubbles seem to require prolonged periods of prosperity, damped inflation and low long-term interest rates. Euphoria-driven bubbles do not arise in inflation-racked or unsuccessful economies. I do not recall bubbles emerging in the former Soviet Union.” Loewenstein (2000) suggests that “[V]isceral factors have important, but often underappreciated, consequences for behavior.”
- 4.
Bank of England Working Paper 283 by Gai and Vause (2005) appeared with a related concept that measures changes of investors’ risk appetites as distinguished from risk premiums and risk aversion. Their conclusion—that risk appetite fluctuates within a fairly narrow range during normal times but falls sharply during crises—is entirely consistent with the approach taken here. Their work seems particularly applicable to crash episodes.
- 5.
As in derivatives pricing, the drawing could be extended to a three-dimensional representation, which would show price ratios (e.g., P/E, P/S, or P/B) on one axis, the FRP on another, and the BRP on the third. References on volatility smiles include Wilmott et al. (1995), Neftci (2000), Hull (2003), and Gatheral (2006).
- 6.
Klingaman (1989, p. 263), concerning the Crash of 1929 (re: October 24), makes this clear: “The most horrifying hour came between 11:15 and 12:15 when numerous stocks could find no buyers at any price. These were the dreaded ‘air pockets,’ when prices shot straight down in a devastating free fall into an abyss that seemingly had no bottom.” Klingaman (p. 230) shows that just six weeks prior there had been great reluctance to sell. Absence of liquidity thus does not imply just low prices; it may imply that there is no price.
- 7.
Commodity markets may halt trading when daily “limit up” restrictions are reached, but the markets themselves remain open during those times. NYSE regulations for trading halts are asymmetrical as the halt-trading rules, which are adjusted regularly for changes in index levels, are designed to cushion crashes only. There are no equivalent rules to dampen steep rises, though there is a program-trading collar that says that in the event of a predetermined gain in the DJIA (150 points in Q4, 2005), all index arbitrage buy orders of the S&P 500 stocks must be stabilizing for the remainder of the day.
- 8.
The rules, installed in response to market breaks in October 1987, were first adopted in October 1988 and were designed to reduce market volatility and promote investor confidence. The revised halt provisions and circuit-breaker levels for a market-wide trading halt were set at 10%, 20%, and 30% of the DJIA calculated at the beginning of each calendar quarter.
- 9.
This idea, though independently arrived at, fits well with the findings of Jones et al. (1994), in which it is explained that volatility is correlated with the number of transactions but not as much with the size of each trading order. It also meshes with Derman (2002), who shows that “short-term stock speculators will expect returns proportional to the temperature of a stock, where temperature is defined as the product of the stock’s traditional volatility and the square root of its trading frequency.”
- 10.
All of this is equally applicable to individual stocks or other assets or sectors.
- 11.
- 12.
See Van Vliet (2017).
- 13.
In the two years preceding the TMT mania’s peak of early 2000, Tiger Fund’s master, Julian Robertson, suffered such poor performance, in part from steadfast commitment to value stock investing, that he closed the fund and returned the remaining money (around $5 billion) to its outside investors. Gray and Vogel (2016, p. 35) posit that long-term value investing is better than growth investing but is often not feasible as a business model. Quantum Fund’s George Soros dumped 5000 S&P 500 futures contracts on October 22, 1987, just days after the “crash” of October 19. See “A Bad Two Weeks,” Barron’s, p. 35, November 2, 1987, in which the fund’s two-week loss was estimated at $840 million. Even legendary Warren Buffett’s Berkshire, according to Barron’s (October 13, 2008), apparently made at least a short-term mistake in the crash of 2008 by selling long-dated put options, a bullish bet, on some $40 billion of equity indexes that included the S&P 500. Lauricella (2008) recounts the errors made by fund manager William H. Miller in his Legg Mason Value Trust. See also Guerrieri and Kondor (2012). Tuckett (2011, pp. 78–9) describes how portfolio managers have to not only convince themselves that they are correct but also convince employers and clients “…your employer might panic or your clients might panic” even if you don’t…[M]any players in the market don’t have the luxury…of taking a long-term view, even if they think they ought to.” Futia (2009, p. 131) adds, “The social and financial pressure an investment crowd can exert on disbelievers cannot be overestimated.”
- 14.
- 15.
Qualitative investor surveys mentioned in Shiller (2000 [2005]) might be a possible source of behavioral data, as might studies of bullish and bearish sentiments published by several commercial-service vendors. For instance, the Daily Sentiment Index from MBH Commodity Advisors (www.trade-futures) for commodities. Huang et al. (2015) and Da et al. (2015) explore sentiment and asset pricing using different sentiment indicators.
- 16.
The Chicago Board Options Exchange’ s put-call option volatility index known as the VIX might provide another alternative: It is generally seen to be high, above 50 in crashes, and low, between 10 and 15, in complacent or bullish markets. The VIX is considered a leading benchmark of market sentiment and measures the market’s expectation of 30-day volatility implicit in the prices of near-term options. VIX options began trading in February 2006. VIX cannot be traded directly.
- 17.
- 18.
The closing of India’s market on May 18, 2009, after the Sensex had run up 17.3% in less than a minute of trading was a rare exception.
- 19.
By 2008, trading technology had improved to such an extent that on September 16, 2008, exchange transactions volume for the troubled insurance giant AIG reached a one-day record of 1.18 billion shares. That’s for a single listing and not counting trades in the other 2000 or so listed securities. A record of 10.27 billion shares was printed on the NYSE Composite on September 17, 2008. However, this was surpassed on October 10, 2008, its most volatile day ever, with a new record of 11.16 billion shares. Another high-volume (the “flash-crash”) day was on May 6, 2010, with 10.3 billion exchange shares (19 billion in all) traded. See Browning et al. (2008), Lauricella and Strasburg (2010), and Patterson (2010a), who writes of the parallels to October 1987; Peltz (2010), who describes high-frequency trading; and Lauricella and Patterson (2010). A joint report of the SEC and Commodity Futures Trading Commission, Findings Regarding the Market Events of May 6, 2010, was released on September 30, 2010. The more recent emergence of algorithmic private-trading dark pools, which provide anonymous and quick access to liquidity, further distorts TPUT data. As Patterson (2012, p. 6) writes, 10–15% of all trading in 2011 was in dark pools. See also Bowley (2011) and Levisohn (2017) on risks from algorithmic trading and dates of subsequent flash-crash episodes, for example, August 2007’s “quant quake” and one on August 24, 2015.
- 20.
- 21.
Only annual, not monthly, data on total NYSE shares listed are available prior to 1994 and, for the analysis that follows, these annual data have been interpolated, with a one-twelfth addition of the year-to-year difference added each month to provide monthly estimates prior to 1994.
- 22.
Periods of quasi -equilibrium exhibit, in terms of annualized monthly number of trades as a percentage of NYSE shares traded, much lower price variance than as measured over all bubble and non-bubble periods combined.
- 23.
For such estimates, it remains an open empirical question whether it is better to average the variances taken over the entire series or whether, because of technological and other changes, this behavioral variance benchmark ought to be based only on the most recent quasi -equilibrium periods that have been identified.
- 24.
Unlike the previously used ERP data from Ibbotson , these ERPs are based on a dividend-discount model taken from New York University Professor Damodaran’s website, www.Damodaran.com.
- 25.
More detail appears in Table 9.2 in this first edition of this book.
- 26.
The same data are further analyzed via a simple OLS regression (35 observations, 1968–2002) which takes the trailing five-year S&P 500 P/E ratio against the FRP and BRP. Both the FRP and BRP coefficients (–2.7 and 117.2, respectively) are significant with a p-value of 0,0. The adjusted R-sq. was 0.87 and the F-stat was 0.0, but with a DW statistic of 1.08, serial correlation is evident.
The negative sign of the FRP consistent with standard theory—the lower the FRP, the higher the P/E ratio. However, the positive sign for the BRP is more ambiguous given that a high BRP should lead to a high P/E ratio in bubbles (which is acceptable), but perhaps a bit less so in crashes given the trading cutoff limitations that would have a dampening effect on the available data. Much of this would also depend on whether the crash was accompanied or followed closely by a steep S&P 500-component earnings decline, in which case P/E ratios might also be high and ultimately infinite. That there are many more annual data points extending over bubble than crash periods might further distort the regression’s results.
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Vogel, H.L. (2018). Behavioral Risk Features. In: Financial Market Bubbles and Crashes, Second Edition. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-71528-5_9
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