On 3rd March 2020, Anuj, a Delhi based gold jeweller buys 12 kgs. of gold in the cash market as a raw material to make jewellery from it. Anuj wants to protect himself from a decline in the prices of gold till the jewell

CS Professional · Capital Commodity and Money Market · PYQS · June 2021
On 3rd March 2020, Anuj, a Delhi based gold jeweller buys 12 kgs. of gold in the cash market as a raw material to make jewellery from it. Anuj wants to protect himself from a decline in the prices of gold till the jewellery is ready for sale in 45 days. He decides to hedge by selling futures contract of gold. The standard deviations of the change in the cash price of gold and change in futures price of gold over the last 45 day period is 0.88 and 0.60 respectively. The coefficient of correlation between the change in cash price and the futures price of gold for 45 days is 0.87. Standardised futures contract size of gold is 1 kg. (i) Calculate Optimal Hedge Ratio

Answer & Explanation:

(i) Calculate Optimal Hedge Ratio The Optimal Hedge Ratio (h) is calculated using the formula: h = ρ * (σ ΔCP / σ ΔFP ) Where: ρ (rho) = Coefficient of correlation between change in cash price (ΔCP) and change in futures price (ΔFP) = 0.87 σ ΔCP = Standard deviation of the change in cash price = 0.88 σ ΔFP = Standard deviation of the change in futures price = 0.60 h = 0.87 * (0.88 / 0.60) h = 0.87 * 1.46666... h = 1.276 The Optimal Hedge Ratio is 1.276.

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