We show that a well-diversified portfolio of randomly chosen stocks must include at least 30 stocks for a borrowing investor and 40 stocks for a lending investor. This contradicts the widely accepted notion that the benefits of diversification are virtually exhausted when a portfolio contains approximately 10 stocks. We also contrast our result with the levels of diversification found in studies of individuals' portfolios.

When will borrowers choose fixed rate mortgages and when will they prefer index-linked mortgages? Baesel and Biger (BB) [1] proposed a model that answers this question. According to the BB model, a borrower's preference depends on the difference in interest rates between the fixed and index-linked mortgages, and on the covariance between the borrower's labor income and the rate of inflation. The purpose of this note is to propose a more complete model of borrower preferences. The novelty of the model lies in the inclusion of the value of the house (net of mortgage obligation) in the terminal wealth of the borrower. This inclusion leads to differences between this model and the BB model in the identification of the cases where borrowers will prefer fixed or index-linked mortgages.

We develop a positive behavioral portfolio theory (BPT) and explore its implications for portfolio construction and security design. The optimal portfolios of BPT investors resemble combinations of bonds and lottery tickets, consistent with Friedman and Savage's (1948) observation. We compare the BPT efficient frontier with the mean-variance efficient frontier and show that, in general, the two frontiers do not coincide. Optimal BPT portfolios are also different from optimal CAPM portfolios. In particular, the CAPM twofund separation does not hold in BPT. We present BPT in a single mental account version (BPT-SA) and a multiple mental account version (BPT-MA). BPT-SA investors integrate their portfolios into a single mental account, while BPT-MA investors segregate their port? folios into several mental accounts. BPT-MA portfolios resemble layered pyramids, where layers are associated with aspirations. We explore a two-layer portfolio where the low aspiration layer is designed to avoid poverty while the high aspiration layer is designed for a shot at riches.

This paper develops a capital asset pricing theory in a market where noise traders interact with information traders. Noise traders are traders who commit cognitive errors while information traders are free of cognitive errors. The theory includes the determination of the mean-variance efficient frontier, the return on the market portfolio, the term structure, and option prices. The paper derives a necessary and sufficient condition for the existence of price efficiency in the presence of noise traders and analyzes the effects of noise traders on price efficiency, volatility, return anomalies, volume, and noise trader survival.

We integrate appealing features of Markowitz’s mean-variance portfolio theory (MVT) and Shefrin and Statman’s behavioral portfolio theory (BPT) into a new mental accounting (MA) framework. Features of the MA framework include an MA structure of portfolios, a definition of risk as the probability of failing to reach the threshold level in each mental account, and attitudes toward risk that vary by account. We demonstrate a mathematical equivalence between MVT, MA, and risk management using value at risk (VaR). The aggregate allocation across MA subportfolios is mean-variance efficient with short selling. Short-selling constraints on mental accounts impose very minor reductions in certainty equivalents, only if binding for the aggregate portfolio, offsetting utility losses from errors in specifying risk-aversion coefficients in MVT applications. These generalizations of MVT and BPT via a unified MA framework result in a fruitful connection between investor consumption goals and portfolio production.