  In this paper, we study the Black-Litterman (BL) asset allocation model
(Black and Litterman, 1990) under the hidden truncation skew-normal
distribution (Arnold and Beaver, 2000). In particular, when returns are assumed
to follow this skew normal distribution, we show that the posterior returns,
after incorporating views, are also skew normal. By using Simaan three moments
risk model (Simaan, 1993), we could then obtain the optimal portfolio.
Empirical data show that the optimal portfolio obtained this way has less risk
compared to an optimal portfolio of the classical BL model and that they become
more negatively skewed as the expected returns of portfolios increase, which
suggests that the investors trade a negative skewness for a higher expected
return. We also observe a negative relation between portfolio volatility and
portfolio skewness. This observation suggests that investors may be making a
trade-off, opting for lower volatility in exchange for higher skewness, or vice
versa. This trade-off indicates that stocks with significant price declines
tend to exhibit increased volatility.
