Why Does Junior Put All His Eggs in One Basket? A Potential Rational Explanation for Holding Concentrated Portfolios (Digest Summary)

Empirical studies frequently find that household portfolios are underdiversified and concentrated in a small number of stocks. Although behavioral biases might explain this lack of diversification, the authors suggest a potential rational alternative approach. Faced with financial constraints, investors optimally choose to limit their holdings to a few assets. The ratio of financial wealth to income determines the extent to which investors concentrate their holdings. Young investors, who are typically characterized by a low ratio of financial wealth to lifetime labor income, hold portfolios that include only a few assets. As financial wealth increases relative to lifetime labor income, more assets are added to the portfolio.

The separation theorem suggests that investors should hold a combination of risky assets and risk-free assets and that the mix between the two should be determined by individual risk aversion. But empirical research on the composition of household portfolios has uncovered substantial deviations from this theory. Household portfolios are underdiversified and concentrated in a small number of risky holdings. Potential explanations for this result include small portfolio size and transaction costs, search and learning costs, investor demographics and financial knowledge, and investor behavioral biases.

A different and potentially rational explanation for underdiversification is proposed by the authors. Their approach highlights the importance of financial constraints, which are introduced in the form of margin requirements and borrowing restrictions. Faced with such constraints, investors rationally limit the number of assets in their portfolios. Investors’ decisions depend on the expected returns of the assets and their covariance with labor income. The ratio of financial wealth to labor income is a useful proxy for the existence of such constraints. The larger the ratio, the less likely that investors will be forced to eliminate assets from their portfolios.

The authors first develop a theoretical model and then present the numerical results from their study. They consider a continuous-time economic setting with an investor with an infinite life who derives utility from consumption, receives labor income, and is able to invest in a risk-free money market account and a number of risky securities. In this setting, the introduction of margin requirements can limit the investor’s ability to borrow against future income and thus influence portfolio composition.

The base case for the theoretical results assumes an infinite-life investor with constant relative risk aversion and an income stream with a stochastic growth rate. But the authors show that underdiversification can also result when an investor has a finite horizon, general preferences, and deterministic income stream.

In the special case of positive correlation between the asset returns and no shorting or borrowing, the authors show that the portfolio exhibits monotonic asset selection. In other words, assets are dropped from the portfolio at certain thresholds in the ratio of financial wealth to labor income.

To quantify the magnitude of the theoretical findings, the authors provide numerical results for the case of an investor who receives income until age 65 and then retires with an expected remaining life span of 20 years. The investor can choose from five risky assets, which have been calibrated to match the risk–return characteristics of five industry portfolios using data from 1927 to 2004. The numerical results show that young investors hold concentrated portfolios, whereas older investors hold better-diversified portfolios.

The authors make a convincing case for including the ratio of financial wealth to labor income as a control variable in studies about the composition of household portfolios. The theoretical results are derived rigorously, thus lending further support to an intuitively appealing idea.