The recent years were hard for commodities, with most suffering of high losses. The uncertainty of the financial markets after the 2008 crisis has pushed in the interest of finding new way of diversification. With the Risk Parity or Equally Weighted Risk Contribution strategy, Maillard, Roncalli, and Teiletche (2008) suggested a method that maximize the diversification. These authors have applied this strategy to the volatility (standard deviation). In this chapter, the author describes how to apply Risk Parity to the Conditional Value at Risk using historical data estimation. Passing to CVaR, a coherent measure, the model can benefit from its properties with the needed assumptions. As a special case, the author has applied this method to an agricultural portfolio, compared the Risk Parity strategies with each other and with the Mean Variance and Conditional Value at Risk. An important part is the analysis of the riskiness, the diversification and the turnover. A portfolio with a certain numbers of agricultural commodities may have particular specified that an investor requires.
TopIntroduction
In recent years, the financial markets have been afflicted by high volatility, both equity and bond markets. After Markowitz (1952) with his first milestone work in modern portfolio theory, a number of other portfolio optimization models have been proposed in the literature. (Sharpe,1964) tried to linearize the portfolio optimization model. (Konno and Yamazaki 1991) introduced the Mean-Absolute Deviation (MAD), a different risk measure using linear programming model instead of a quadratic programming model.
The MiniMax approach, introduced by Young (1998), minimizes the worst-case scenario, which is used as risk measure. Risk Metrics introduced methods to quantify market risks, such as 
which is defined as the maximum potential change in value of a portfolio with a given probability over a certain horizon. Risk Management has used this instrument for many years, in order to evaluate the performance and regulatory requirements, and to develop methodologies to provide accurate estimates. 
does not allow diversification. There are many works on the alternative risk measure 
from the authors such as Andersson, Mausser and Uryasev (2000) that show why this is more preferred to 
.
The most important properties are that 
is a coherent and a convex measure shown in the model presented by (Artzner,1999), a model that allows diversification.
All these models have one problem in common: they need as an input the estimation of expected return for the assets. Models that need to estimate expected returns, produce extreme weights and have significant fluctuation over time. The Mean-Variance model is too sensitive to the input parameters, specially to the expected returns (Merton,1980). Thus, a significant variation of the input parameters can significantly change the composition of the portfolio, like in the Mean Variance portfolio. Models that rely on expected returns tend to be very concentrated on few assets and perform poorly out of sample (Merton,1980). The Black&Litterman model can be obtained using a Bayesian approach to change the estimated returns (Black, Litterman, 1990). With the passing of time, more sophisticated and advanced models were developed for the market forecasting, introducing different techniques and simulations. Thus, investors continue to use such simple allocation rules for allocating their capital across assets.
This chapter focuses on the models of portfolio selection under the Risk Parity criteria. More attention was focused on these models after the financial crisis of 2008 in the way they distribute the risk among the assets that compose the financial portfolio. The idea was introduced by Qian (2005) and it led to the creation of Risk Parity Portfolios, where we allocate an equal amount of risk to stocks and bonds in
order to capture long-term risk premium embedded within various assets. Risk Parity portfolios are more efficient than the traditional 60/40 portfolios and they are truly balanced in terms of risk allocation.
The first authors formulate and discuss this argument were Maillard, Roncalli and Teiletche (2009). They showed that the volatility of Risk Parity is located between that of the minimum variance and of the equally weighted portfolio. Also, they prove the uniqueness and the existence of the Risk Parity portfolio.