Intermediate Financial Theory — 4th Edition
Errata
Danthine • Donaldson • Danthine — Academic Press / Elsevier
Corrections are listed chronologically within each chapter.
The most recent version of this page supersedes all earlier versions.
Chapter 5 — Risk Aversion and Investment Decisions, Part 1
Missing minus signs in the Arrow–Pratt measures
The expressions defining the Arrow–Pratt measures of risk aversion on p. 126
are missing a minus sign. As printed:
$$
\text{absolute risk aversion:}\quad
\frac{U”(Y)}{U'(Y)} \equiv R_A(Y)
$$
$$
\text{relative risk aversion:}\quad
\frac{YU”(Y)}{U'(Y)} \equiv R_R(Y)
$$
Both expressions should carry a leading minus sign:
$$
\text{absolute risk aversion:}\quad
-\frac{U”(Y)}{U'(Y)} \equiv R_A(Y)
$$
$$
\text{relative risk aversion:}\quad
-\frac{YU”(Y)}{U'(Y)} \equiv R_R(Y)
$$
The minus sign ensures $R_A(Y)>0$ and $R_R(Y)>0$ for a risk-averse agent
(for whom $U”<0$), in line with the convention of Arrow (1971) and Pratt (1964).
Chapter 6 — Risk Aversion and Investment Decisions, Part 2
Error in the numerator of Eq. (6.19)
Equation (6.19), which gives the optimal dollar investment in the risky asset
for a CARA investor facing smooth ambiguity aversion
(Klibanoff–Marinacci–Mukerji 2005),
is misprinted. As it appears in the text:
$$
a^{*} = \frac{\mu Y_0(1+r_f)}{\gamma\!\left(\sigma^2 + (1+\eta)\sigma_0^2\right)}
\tag{6.19, as printed}
$$
The numerator should be the excess return $\mu – r_f$, not $\mu Y_0(1+r_f)$.
The correct expression is:
$$
a^{*} = \frac{\mu – r_f}{\nu\!\left(\sigma^2 + (1+\eta)\sigma_0^2\right)}
\tag{6.19, corrected}
$$
where $\nu$ denotes the CARA coefficient (written $\gamma$ in the text).
Initial wealth does not appear in the solution—a hallmark of CARA utility.
A complete derivation is provided in Web Chapter wc6.
Summary Table of Corrections
| Chapter / Location | Description | Reported |
|---|---|---|
| Ch. 5, p. 126 | Missing minus sign in both Arrow–Pratt risk aversion measures. | [date TBC] |
| Ch. 6, p. 27, Eq. (6.19) | Numerator printed as $\mu Y_0(1+r_f)$; correct value is $(\mu – r_f)$. | April 2026 |
References
- Arrow, K.J. (1971). Essays in the Theory of Risk-Bearing. Markham Publishing.
- Gollier, C. (2011). “Portfolio Choices and Asset Prices: The Comparative Statics of Ambiguity Aversion.”
Review of Economic Studies, 78(4), 1329–1344. - Klibanoff, P., M. Marinacci, and S. Mukerji (2005). “A Smooth Model of Decision Making under Ambiguity.”
Econometrica, 73(6), 1849–1892. - Pratt, J.W. (1964). “Risk Aversion in the Small and in the Large.”
Econometrica, 32(1–2), 122–136.