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So I was running a monte carlo simulation for two assets and a portfolio consisting of 1 quantity of the first asset and short a fraction x of the second asset to hedge, where the fraction is calculated as the minimum variance hedge ratio as correlation*volatility spot/volatility futures. Hence, this portfolio should have the lowest variance. However, when I run a monte carlo simulation (i.e. 5000 runs for 1 step f.e. 1 year), the portfolio with the minimum variance hedge ratio gets beat by other hedge ratios. I suppose that this might be due to the error happening in the simulation and the high input parameters and low correlation (I use volatility of 195% for the spot and 30% for the futures and a correlation of 0.1) Is there a way to correct for this error?

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