ABSTRACT
This paper tackles the rather recent weekly period
from January 18, 2005 to February 28, 2018, encompassing 523 observations. The
portfolio is constructed from the perspective either of a US investor or of a
Lebanese one, since the US dollar foreign exchange rate was pegged during the
above whole period. The portfolio consists of an investment in the US S & P
500 stock market index and in three Rogers international commodity indexes:
agricultural, energy, and metals. The purpose of the paper is to estimate the
diversification benefits of the energy commodity index. These benefits arise
from the fall in the volatility of the investment portfolio when it is compared
to an investment in the energy index only, or in the S & P 500 only. The procedure follows the seminal
approach of Markowitz. The inputs of the model are the variance/covariance
matrix, the average log returns, and the condition that all investment shares
should sum up to 1. The outputs, obtained by matrix manipulation, are the
optimal investment shares in the four assets, the volatilities of the optimal
portfolios, the characteristics of the efficient frontier, the relation between
portfolio shares and the expected, or required return, and finally, the predicted
Capital Market Line (CML). The evidence shows that, by holding a portfolio
composed of the above four assets, the volatilities are substantially reduced.
Moreover, and since short sales are allowed in the model, all optimal
investment shares in the energy commodity asset are negative, meaning that in
the optimal portfolios the positions in the energy index are short positions.
The paper points to the significantly high relative riskiness of the energy
index, as a stand-alone asset, or as an aggressive and speculative investment
on the CML, and to the substantial portfolio benefits of shorting this index.