Consider a commodity purely held for investment purposes. Today, a company enter
ID: 2783083 • Letter: C
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
a) What is the 9-month forward price per unit of the commodity today?
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
b) Note that the price in (A) is the delivery price of the forward contract. What is the value of the long position today
Value of long position per forward=100*(1298.068-1250)*e(-0.04*9/12) =$4664.7
Total value=50*4664.7=$233235
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?
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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