Thought Viruses and Asset Prices

Abstract

We develop a tractable model in which asset prices are driven by the epidemic spread of certain investment ideas. Once an idea “goes viral,” equilibrium prices exhibit a pattern of boom and bust. In turn, we identify a timeline of symptoms, which indicate whether a boom is in its early or later stages. Moreover, we find that prices start to decline while the number of infected agents, who buy the asset, is still rising. The presence of rational agents, who correctly anticipate the cycle, accelerates booms, lowers peak prices and tends to produce broad, drawn-out, market tops.

Keywords:

• Thought viruses
• Booms
• Busts
• Recessions
• Depressions

JEL:

• D53
• E10

Acknowledgments

I would like to thank the referee for very helpful comments. I also thank Dominik Grafenhofer, Alexander Ludwig, Vincenzo Merella, Carl Christian von Weizsäcker as well as participants at a macroeconomics workshop of Frankfurt University and seminars in Prague and Hangzhou for helpful comments. The term “thought virus” can be found in several other disciplines, and is used here without specific reference. First arxiv version: 29.12.2018.

Notes

1 Similar arguments can be found in Soros (1994, 27–141), Graham (1973, 188–213), or Fisher (2003, 266–75).

2 See also Kindleberger (2000, 15), who notes that “there is nothing so disturbing to one’s well-being and judgement as to see a friend get rich,” and Ash (1955) for the effects of peer pressure.

3 See e.g., Hirsch et al. (2003, 235–39).

4 To simplify notation, we suppress the holdings of agents I₀, who are infected in t = 0. Accounting for these holdings adds one term, which depreciates exponentially over time, and does not change results.

5 We have discussed how investors push prices higher, when they infect each other with euphoria. This argument works in reverse during a “depression.” That is, we may model an infected agent as someone who is selling rather than buying. This would create a U-shaped price pattern, where prices bottom earlier than sentiment.

6 Period t₂ therefore does not coincide with $t_P^{*}.$ Indeed one can show that $t_P^{*}<t_2$ (see Remark 3).

7 Prices are taken from Yahoo Finance. December 23rd highs and lows were roughly 15,000 and 13,000.

8 To see this we write $X_I=\beta \gamma {\int }_0^t\frac{I_v{S}_v}{P(v)}{e}^{-\gamma \left(t-v\right)}dv<\gamma \frac{I}{P_0}$ and recall that $\underset{t\to \infty }{\mathit{lim}}I=0.$

9 Lemma 2 shows that a peak in $I$ requires $S_0>\frac{\gamma }{\beta }.$ Moreover, we need only a small number of initially infected agents to start an epidemic, i.e., we can pick an arbitrarily small number $I_0$ for the number of initially infected agents.