stock market may play a significant role in financing food industries. Nowadays, people select an optimized portfolio with several shares instead of choosing only one in order to cope with the investment risk. For this, the systematic risk could be very important as the market is so fluctuating, especially in Iran. So in this paper, we enter a constraint for systematic risk that helps investors in making decision.

As we said, we want to enter systematic risk in the portfolio selection model. We use Extreme Downside Hedge (hereafter EDH) as the measure for the systematic risk of each company in the food industry. This measure relies on the argument that investors are able to hedge against extreme downside risk. The EDH can be estimated by regressing stock returns on a measure of market tail risk. We use Expected Tail Loss (ETL) to measure market tail risk. ETL is defined as the expected value of the loss given that the loss exceeds VaR. Then, the factor models are introduced to capture the systematic risk. In order to actively allocate the systematic risk, we use the definition of the marginal systematic risk introduced by Li et al (2018) to measure the systematic risk contribution of a risk contributor.  First, we choose some variables as factors that affect the return of each company. After that, we calculate the covariance between factors and then make an equation that shows the systematic risk for each company. We apply our methodology to the return time series of 11 companies and the index for the food industry, all listed on the Tehran Stock Exchange (TSE). The data covers the period from 2015 to 2019. Other variables include oil prices, gold prices and exchange rates extracted from the Economic and Financial Databank of Iran.

The results show the Behshahr Ind, Glucosan, Kalber, Margarin, Pars Mino, Pegah Fars and Salemin have positive EDH. This means for these companies the stock returns are affected by volatility of the market, in other words as the volatility increases, the stock returns decrease. It should be noted that the higher the EDH is, the greater the impact is. Also, Gorji Biscuit, Mahram Mfg, Minoo Co and Azar Pegah have negative EDH, indicating the reverse impactability of these companies' returns from market volatility. The higher the EDH, the lower the companies' volatility, also the higher the negative EDH, the higher the market volatility. After calculating the factor model and entering it in the portfolio model, we obtained the optimized result. According to the results, Azar Pegah and Pars Mino, with 86% and 12% have the highest percentage of the optimal portfolio, while Kalber, Pegah Fars and Salemin altogether have 2% of the portfolio, respectively. As the results show, the largest share belongs to the Azar Pegah Company, which is also according to the EDH of the company, in fact, the results show the company whose shares have the highest negative impact from the market has entered to the model. The presence of four other companies in the portfolio given the positive EDH is due to their high average return rather than other companies, since we consider the return as a constraint in the model because of its importance in decision making. It is also worth noting that, the two companies, kalber and behshahr Ind, with the highest positive EDH are not in the optimal portfolio. In order to investigate the effect of systematic risk the model was estimated without considering this constraint. The results show, without systematic risk constraint the optimal portfolio has shifted to companies with higher return and lower risk. Thus, the results of this study indicate that with systematic risk, based on expectations, portfolios will shift to companies with lower impactability from market volatility on the one hand and higher returns on the other.

Finally, the results of the study show, the systematic risk in the model shift the portfolio towards the stocks of companies that are less affected by market conditions. Therefore, given today's fluctuating conditions, it may be useful to apply a model that considers this part of the risk.