I need help calculating the volatility of the future price. The person who answered this has the number 0.4323. I don't understand how they got this number. Thanks!

A canola farmer wants to hedge her risk associated with next year's harvest, when she expects to harvest 200 tonnes of canola and sell it 6 months from now. The current spot price of canola is $250 per tonne and the convenience yield for canola is -10% per year and the return volatility of canola is 20% per year. The risk-free rate is 4% per year. She assumes that the volatility of her harvest is 50 tonnes and the correlation between quantity harvested and price is -0.5. How should she hedge her risk using 6-month futures contracts? I think this question has to do with the optimal hedging quantity or h that minimizes variance equation in the Derivative Securities & Risk Management Textbook Ch 3. Is there maybe a theory way of answering this question if there is not enough data to find h? I originally thought that the question was missing the volatility, but I thought I would ask an expert in case I was missing something. But, if you think data is missing, is there a theoretical way to answer this question? Thanks! The current spot price is $ 250 pet ton & She needs to hedge for 150 tonnes seeing that 50 tonnes are in volatility as per given problem. Future price = spot price*e^(r - y)t Future price = 250*e((0.04 + .1)*0.5) Future price = 250* 1.07 = 267.5 Minimum hedge ratio =rho * (sigma(of spotprice)/sigma(of futureprice)) Minimum hedge ratio = 0.5*(0.447213595/0.432337701) = -0.517204022 No of optimal contracts = 0.5172*250/267.5 = 0.48 So ideally first one needs to determine the future price for canola. Once future price is determined, Computation of minimum hedge ratio should take place taking the squareroot of volatility of spot price and future price respectively. Correlation is already negative which means that commodity would be available in low amounts in future. So sell the canola commodity futures for now and long on it later & thereby selling the stock in hand at expected price. This enables hedge. Compute the optimal no of contracts that you need to short or go long for thereby enable hedge. A canola farmer wants to hedge her risk associated with next year's harvest, when she expects to harvest 200 tonnes of canola and sell it 6 months from now. The current spot price of canola is $250 per tonne and the convenience yield for canola is -10% per year and the return volatility of canola is 20% per year. The risk-free rate is 4% per year. She assumes that the volatility of her harvest is 50 tonnes and the correlation between quantity harvested and price is -0.5. How should she hedge her risk using 6-month futures contracts? I think this question has to do with the optimal hedging quantity or h that minimizes variance equation in the Derivative Securities & Risk Management Textbook Ch 3. Is there maybe a theory way of answering this question if there is not enough data to find h? I originally thought that the question was missing the volatility, but I thought I would ask an expert in case I was missing something. But, if you think data is missing, is there a theoretical way to answer this question? Thanks! The current spot price is $ 250 pet ton & She needs to hedge for 150 tonnes seeing that 50 tonnes are in volatility as per given problem. Future price = spot price*e^(r - y)t Future price = 250*e((0.04 + .1)*0.5) Future price = 250* 1.07 = 267.5 Minimum hedge ratio =rho * (sigma(of spotprice)/sigma(of futureprice)) Minimum hedge ratio = 0.5*(0.447213595/0.432337701) = -0.517204022 No of optimal contracts = 0.5172*250/267.5 = 0.48 So ideally first one needs to determine the future price for canola. Once future price is determined, Computation of minimum hedge ratio should take place taking the squareroot of volatility of spot price and future price respectively. Correlation is already negative which means that commodity would be available in low amounts in future. So sell the canola commodity futures for now and long on it later & thereby selling the stock in hand at expected price. This enables hedge. Compute the optimal no of contracts that you need to short or go long for thereby enable hedge