Learning Under Ambiguity

This paper considers learning when the distinction between risk and ambiguity (Knightian uncertainty) matters. Working within the framework of recursive multiple-priors utility, the paper formulates a counterpart of the Bayesian model of learning about an uncertain parameter from conditionally i.i.d. signals. Ambiguous signals capture responses to information that cannot be captured by noisy signals. They induce nonmonotonic changes in agent confidence and prevent ambiguity from vanishing in the limit. In a dynamic portfolio choice model, learning about ambiguous returns leads to endogenous stock market participation costs that depend on past market performance. Hedging of ambiguity provides a new reason why the investment horizon matters for portfolio choice.ambiguity, learning, noisy signals, ambiguous signals, quality information, portfolio choice, portfolio diversification, Ellsberg Paradox

Dynamic Consumption and Portfolio Choice with Ambiguity about Stochastic Volatility

We introduce ambiguity about the variance of the risky asset's return in the model of Chacko and Viceira (2005) for dynamic consumption and portfolio choice with stochastic variance. We find that, with investors being able to update their portfolio continuously (as a function of the instantaneous variance), ambiguity has no impact. To shed some light on the case in which continuous portfolio updating is not possible, we also evaluate the effect of ambiguity when investors must use their expectation of future variance for their portfolio decision. In the latter scenario, demand for the risky asset can be decomposed into three components: myopic and intertemporal hedging demands (as in Chacko and Viceira (2005)) and ambiguity demand. Using long-run US data, Chacko and Viceira (2005) found that intertemporal hedging demand is empirically small, suggesting a low impact of stochastic variance on portfolio choice. Using the same calibration, we find that ambiguity demand may be very high, much more than intertemporal hedging demand. Therefore, stochastic variance can be very relevant for portfolio choice, not because of the variance risk, but because of investors' ambiguity about variance.Asset Allocation, Stochastic Volatility, Ambiguity

Ambiguity in asset pricing and portfolio choice: a review of the literature

A growing body of empirical evidence suggests that investors’ behavior is not well described by the traditional paradigm of (subjective) expected utility maximization under rational expectations. A literature has arisen that models agents whose choices are consistent with models that are less restrictive than the standard subjective expected utility framework. In this paper we conduct a survey of the existing literature that has explored the implications of decision-making under ambiguity for financial market outcomes, such as portfolio choice and equilibrium asset prices. We conclude that the ambiguity literature has led to a number of significant advances in our ability to rationalize empirical features of asset returns and portfolio decisions, such as the empirical failure of the two-fund separation theorem in portfolio decisions, the modest exposure to risky securities observed for a majority of investors, the home equity preference in international portfolio diversification, the excess volatility of asset returns, the equity premium and the risk-free rate puzzles, and the occurrence of trading break-downs.Capital assets pricing model ; Investments

Asset allocation with multiple analysts’ views: a robust approach

Retail investors often make decisions based on professional analysts’ investment recommendations. Although these recommendations contain up-to-date financial information, they are usually expressed in sophisticated but vague forms. In addition, the quality differs from analyst to analyst and recommendations may even be mutually conflicting. This paper addresses these issues by extending the Black–Litterman (BL) method and developing a multi-analyst portfolio selection method, balanced against any over-optimistic forecasts. Our methods accommodate analysts’ ambiguous investment recommendations and the heterogeneity of data from disparate sources. We prove the validity of our model, using an empirical analysis of around 1000 daily financial newsletters collected from two top 10 Taiwanese brokerage firms over a 2-year period. We conclude that analysts’ views contribute to the investment allocation process and enhance the portfolio performance. We confirm that the degree of investors’ confidence in these views influences the portfolio outcome, thus extending the idea of the BL model and improving the practicality of robust optimisation

Robust portfolio management with multiple financial analysts

Portfolio selection theory, developed by Markowitz (1952), is one of the best known and widely applied methods for allocating funds among possible investment choices, where investment decision making is a trade-off between the expected return and risk of the portfolio. Many portfolio selection models have been developed on the basis of Markowitz’s theory. Most of them assume that complete investment information is available and that it can be accurately extracted from the historical data. However, this complete information never exists in reality. There are many kinds of ambiguity and vagueness which cannot be dealt with in the historical data but still need to be considered in portfolio selection. For example, to address the issue of uncertainty caused by estimation errors, the robust counterpart approach of Ben-Tal and Nemirovski (1998) has been employed frequently in recent years. Robustification, however, often leads to a more conservative solution. As a consequence, one of the most common critiques against the robust counterpart approach is the excessively pessimistic character of the robust asset allocation. This thesis attempts to develop new approaches to improve on the respective performances of the robust counterpart approach by incorporating additional investment information sources, so that the optimal portfolio can be more reliable and, at the same time, achieve a greater return. [Continues.

Mortality-Indexed Annuities

Longevity risk has become a major challenge for governments, individuals, and annuity providers in most countries, and especially its aggregate form, i.e. the risk of unsystematic changes to general mortality patterns, bears a large potential for accumulative losses for insurers. As obvious risk management tools such as (re)insurance or hedging are less suited to manage an annuity provider’s exposure to aggregate longevity risk, the current paper proposes a new type of life annuities with benefits contingent on actual mortality experience, and it also details actuarial aspects of implementation. Similar adaptations to conventional product design exist in investment-linked annuities, and a role model for long-term contracts contingent on actual cost experience is found in German private health insurance so that the idea is not novel in general, but it is in the context of longevity risk. By not or re-transferring the systematic longevity risk insurers may avoid accumulative losses so that the primary focus in an extensive Monte-Carlo simulation is on the question of whether and to what extent such products are also advantageous for policyholders in contrast to a comparable conventional annuity product

A RE-EXAMINATION OF EVENT STUDIES APPLIED TO CHALLENGED HORIZONTAL MERGERS

A growing body of empirical studies have been interpreted as support for a laissez-faire policy towards mergers. These "event studies" examine the reaction of stock market prices of firms that announce an agreement to merge. The type ~f reaction reveals whether a merger is motivated by a desire for market power or purely to improve market efficiency. In this paper, a version of the capital asset pricing model (CAPM) is applied to determine if abnormal returns are earned by rivals of 22 pairs of firms whose attempted horizontal mergers were challenged by the federal antitrust agencies. At most eight, and possibly only five, of the cases were found to be motivated by efficiency in seeking merger, and at most six, and possibly only one, were motivated by market power; the rest were inconclusive. The event-study technique is highly flawed for the study of business-regulation effects. Numerous unrealistic assumptions, inappropriate data constraints, and questionable interpretations hamper .the application of this technique to policy analysis.Industrial Organization,

Risk preference discrepancy : a prospect relativity account of the discrepancy between risk preferences in laboratory gambles and real world investments

In this article, we presented evidence that people are more risk averse when investing in financial products in the real world than when they make risky choices between gambles in laboratory experiments. In order to provide an account for this discrepancy, we conducted experiments, which showed that the range of offered investment funds that vary in their riskreward characteristics had a significant effect on the distribution of hypothetical funds to those products. We also showed that people are able to use the context provided by the choice set in order the make relative riskiness judgments for investment products. This context dependent relativistic nature of risk preferences is proposed as a plausible explanation of the risk preference discrepancy between laboratory experiments and real-world investments. We also discuss other possible theoretical interpretations of the discrepancy

Portfolio Optimization and Ambiguity Aversion

This thesis analyses whether considering ambiguity aversion in portfolio optimization improves the out-of-sample performance of portfolio optimization approaches. Furthermore, it is assessed which role ambiguity aversion plays in improving the portfolio performance, especially compared with the role of estimation errors. This is done by evaluating the out-of-sample performance of the approach of Garlappi, Uppal and Wang for an investor with multiples priors and aversion to ambiguity compared to other portfolio optimization strategies from the literature not taking ambiguity aversion into account. It is shown that considering ambiguity aversion in portfolio optimization can improve the out-of-sample performance compared to the sample based mean-variance model and the Bayes-Stein model. However, the minimum-variance model and the model of naïve diversification, which are both independent of expected returns, outperform the approach considering ambiguity aversion for most of the empirical applications shown in this thesis. These results indicate that ambiguity aversion does play a role in portfolio optimization, however, estimation errors regarding expected returns overshadow the benefits of optimal asset allocation. Keywords: portfolio choice; asset allocation; estimation error; ambiguity; uncertainty