Consider a commodity purely held for investment purposes. Today, a company enter

Question

Consider a commodity purely held for investment purposes. Today, a company enters into a long position in 50 forward contracts (each on 100 units of the commodity) to hedge the purchase of 5,000 units of the commodity in 9 months. The spot price of the commodity is $1,250 per unit. The risk-free rate of interest is 4% per annum with continuous compounding. The 9-month storage cost per unit of the commodity is $10, payable at the end of the contract. A. What is the 9-month forward price per unit of the commodity today? B. Note that the price in (A) is the delivery price of the forward contract. What is the value of the long position today? C. Three months later, the spot price per unit of the commodity is $1,275. What is the forward price per unit of the commodity? What is the value of the long position?

Explanation / Answer

Now

Interest Cost=1250*e^(0.04*9/12)-1250=38.068

Storage Cost=10

forward price=spot price+interest cost+storage cost

=1250+38.068+10

=1298.068

So, 9-month price per unit of the commodity today=$1298.068

Forward price=1298.068*100=$129806.8

Value of long position per forward=100*(1298.068-1250)*e^(-0.04*9/12)=$4664.7

Total value=50*4664.7=$233235

Three months later

Interest Cost=1275*e^(0.04*3/12)-1275=12.81396

Storage Cost=10*3/9=3.33

3 month price per unit=spot price+interest cost+storage cost

=1275+12.81396+3.33

=$1291.144

Forward price=1291.144*100=$129114.4

Value of long position per forward=100*(1291.144-1275)*e^(-0.04*3/12)=$1598.336

Total value=50*1598.336=$79916.8

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