Academic journal article Journal of Applied Finance

Bayesian Networks: A Decision Tool to Improve Portfolio Risk Analysis

Academic journal article Journal of Applied Finance

Bayesian Networks: A Decision Tool to Improve Portfolio Risk Analysis

Article excerpt

This paper demonstrates how Bayesian networks, a graphical modeling tool, can improve analysts' forecasts, portfolio decision-making, and risk analysis. Bayesian networks combine historical quantitative information with qualitative information in a systematic way. Findings in behavioral finance show buying and selling investment behavior that indicates biased decision-making, but most behavioral finance literature is descriptive, not normative. Our goal is to improve rational financial decision-making by helping analysts eliminate bias from their probability assessments and systematically improve value-at-risk forecasts. [G11, G19, C4]

Portfolio management is a very special problem in engineering, of determining the most reliable and efficient way of reaching a specified goal, given a set of policy constraints, and working within a remarkably uncertain, probabilistic, always changing world of partial information and misinformation, all filtered through the inexact prism of human interpretation (Ellis 1985, p. 53).

Security analysts evaluate a variety of information to decide whether to buy, sell, or hold a security. Research on security analysis concentrates primarily on two different areas. The first is pricing and valuation models. The second is the relation between firm or economic variables and earnings forecasts. We use a Bayesian network to model economic relations to produce earnings forecast for each stock in a portfolio and a return distribution for the portfolio. The output of the model is a probability distribution that combines historical information with current news.

Traditional pricing models such as the capital asset pricing model (CAPM) or arbitrage pricing theory (APT) describe how economic variables and firm characteristics are related to stock returns. The models are based on historical and quantitative data, and the results are averages for a typical firm. Most analysts use this historical quantitative analysis as part of an overall approach that also includes a wider variety of information. Analysts typically concentrate on special situations and individual cases, not on the average. Their information includes historical data and qualitative, imprecise evidence that may affect a firm.

An analyst may consider, for example, how effective or trustworthy a firm's management is. Or, what is the effect of China's entry into the World Trade Organization on a particular line of business? How reliable are a firm's financial statements? We show how to integrate this type of information with historical quantitative data using a graphical decision-modeling tool, Bayesian networks.

In portfolio management, analysts must assess a large amount of sometimes conflicting data to make a decision based on uncertain information. We suggest that Bayesian networks are especially well suited for this task. They help experts represent uncertain, ambiguous, or incomplete knowledge that portfolio managers and analysts often deal with.

The output of the model is a probability distribution of portfolio value. As the entire distribution is modeled, measures of risk and value-at-risk (VAR) are modeled naturally. When new evidence is added its effects on other variables in the model and on risk are also computed.

There are two types of inputs to the model - the graphical relation, and a set of equations and conditional probability distributions described by the graph. The conditional probability relations can be estimated from historical data or from expert judgment. Shenoy and Shenoy (2000) show how traditional expected return models such as the CAPM and APT can be used to model relations in a Bayesian network.

Here we show how to combine quantitative data with qualitative or soft information in a systematic way. Our example demonstrates how to combine macroeconomic factors and firm-specific factors, but the methodology is flexible enough to reflect an individual analyst's decision-making process. …

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