Solvency Constraint, Underdiversification, and Idiosyncratic Risks

Abstract

Contrary to the prediction of the standard portfolio diversification theory, many investors place a large fraction of their stock investment in a small number of stocks. I show that underdiversification may be caused by solvency requirements. My model predicts that for quite general preferences and return distributions: (1) underdiversification decreases in discretionary wealth; and (2) expected return and covariance determine which stocks to invest in, but variance, higher moments, and Sharpe ratio do not matter for this choice. In addition, a less-diversified stock portfolio has a higher expected return, a higher volatility, and a higher skewness, and idiosyncratic risks are priced.

Why does junior put all his eggs in one basket? A potential rational explanation for holding concentrated portfolios

“…Underdiversification results similar to the ones we obtain in this paper are also obtained independently and contemporaneously in the paper by Liu (2010). Liu (2010), describes a model where investors engage in asset selection due to the combination of a desire to guarantee a minimum level of wealth and constraints on their ability to borrow and to short-sell risky assets.…”

“…1 also applies to other problems. For example, the framework described in Liu (2010) corresponds to the margin requirements becoming more stringent as the investor approaches the substinence level of wealth. In that case it is the shaded plane in Fig.…”

“…Liu (2010), describes a model where investors engage in asset selection due to the combination of a desire to guarantee a minimum level of wealth and constraints on their ability to borrow and to short-sell risky assets. The main difference between the paper by Liu (2010) and our paper is that we consider a dynamic framework that allows us to quantify the degree of underdiversification in investor portfolios through their lifetime, as well as the impact of approaching retirement to the degree of portfolio diversification, while the framework in Liu (2010) is static and does not offer any prediction regarding the age of an investor and the degree of portfolio underdiversification.…”

Repurchase behavior of individual investors, sophistication and regret

“…15 Other elements can also explain underdiversification: Liu (2012) shows that underdiversification may be caused by solvency requirement, while Korniotis and Kumar (2013) find that underdiversification may be driven by informational advantages. 16 The quintiles are the data values marking the boundaries between consecutive subsets.…”

The private equity premium puzzle: a behavioural finance approach

“…This result is consistent with Liu's model (2014) which shows that under-diversification can be optimal in case of solvency constraints for investors. According to Liu (2014), below a given level of wealth the optimal portfolio of investors is typically not diversified. According to Levine and Rubinstein (2013), entrepreneurs are not only skewness seeker.…”