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01-11-2015 | Research Article

Financial innovation and risk: the role of information

Author: Roberto Piazza

Published in: Annals of Finance | Issue 3-4/2015

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Abstract

Financial innovation has increased diversification opportunities and lowered investment costs, but has not reduced the relative cost of active (informed) investment strategies relative to passive (less informed) strategies. What are the consequences? I study an economy with linear production technologies, some more risky than others. Investors can use low quality public information or collect high quality, but costly, private information. Information helps to avoid excessively risky investments. Financial innovation decreases incentives to collect private information and deteriorates the quality of public information, so that the economy invests more often in excessively risky technologies. This changes the business cycle properties and can reduce welfare by increasing the likelihood of “liquidation crises”.

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To reduce notation, I normalize to zero the amount of systemic risk in the low risk technology technologies. This has no qualitative effect on the results. A case with systemic risk also in the low risk technology is presented in Sect. 4.

This gives rise to a constant return to scale for information collection. For a analysis of increasing returns technologies see Van Nieuwerburgh and Veldkamp (2008).

Having established the equilibrium values of the individual portfolio shares $\alpha ^*_{m, j}(I)$, the rest of the proof of Proposition 1 is straightforward and can be obtained upon request from the author. In particular, optimal saving rates $x^*_I$ are obtained from the first order conditions of the investor’s problem, and interior values for $\rho ^*$ are obtained by equating the resulting welfare accruing to informed and uninformed agents.

See “Appendix B”.

If ${\bar{L}}\simeq 0$ then the share $\eta ^*$ of active investors satisfies $\eta ^*\simeq 0$, so that A reflects the portfolio choice of only passive investors. This restriction has no qualitative consequence for our discussion, since the business cycle properties are linked to $\rho ^*$, which does not depend on ${\bar{L}}$.

The qualitative results presented do not depend on the logarithmic form. The full extension of utility (9) to a multiperiod case can be done using Epstein and Zin (1989) recursive preference. This more general setting is available upon request from the author.

There is no learning when $S_1=0$, since technologies have identical return at time 1.

This is the case if liquidity noises $L_t$ for $t=1,2$ are independent of each other.

Choose any reference market m and assume that an investor can observe the quantities y(m, 1) and y(m, 2). Then the investor deduces that the realization of the noise L satisfies $L\in \{L_1, L_2\}$. In this way, we associate to each realization $L\in \{L_1, L_2\}$ one and only one vector of types. More precisely, for any realization $\hat{\mathbf {y}}$ of the vector of quantities $\mathbf {y}$, call $\varTheta _j$ the unique vector of types associated with the joint event $\{L=L_j\} \cap \{\mathbf {y}=\hat{\mathbf {y}}\}$, with $j=1,2$. Using Bayes rule (for continuous variables) and the arguments above we have

$$\begin{aligned} \text {Prob}\left\{ \varTheta =\varTheta _{j}|\mathbf {y}=\hat{\mathbf {y}}\right\}&=\text {Prob}\left\{ L=L_{j}|\mathbf {y}=\hat{\mathbf {y}}\right\} \nonumber \\&=\frac{f(L_j)\text {Prob}\{\mathbf {y}=\hat{\mathbf {y}}|L_j\}}{f(L_j)\text {Prob}\{\mathbf {y}=\hat{\mathbf {y}}|L_j\}+f(L_{3-j})\text {Prob}\{\mathbf {y}=\hat{\mathbf {y}}|L_{3-j}\}}\nonumber \\&=\frac{f(L_j)F(\varTheta _j)}{f(L_j)F(\varTheta _j)+f(L_{3-j})F(\varTheta _{3-j})} \end{aligned}$$

Using (3) we obtain (31).

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Title: Financial innovation and risk: the role of information
Author: Roberto Piazza
Publication date: 01-11-2015
Publisher: Springer Berlin Heidelberg
Published in: Annals of Finance / Issue 3-4/2015
Print ISSN: 1614-2446
Electronic ISSN: 1614-2454
DOI: https://doi.org/10.1007/s10436-015-0267-z

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