Beyond Mean-Variance: Portfolios with Derivatives and Non-Normal Returns in Mental Accounts
32 Pages Posted: 10 Mar 2011
Date Written: December 3, 2009
Today's portfolios are often composed of mental accounts, one for each of an investor's goals. They often also contain derivative securities. We develop a methodology for optimizing mental accounting portfolios that contain derivatives and other securities with non-normal distributions of returns, including distributions with very fat tails. This methodology is especially urgent now, following the financial crisis of the last year which revealed that fat tails are indeed prevalent in return distributions. Derivatives oer protection from the disastrous losses of fat left tails.
Our approach is based on a simple preference metric, making it easy to implement. We consider puts, calls, collars, capital guaranteed notes, and other structured products. We show that employing derivatives in mental accounting portfolios results in material improvements in portfolios' risk and expected returns. We also show that some derivatives which are puzzling to mean-variance investors are attractive to mental-accounting investors.
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