Question

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A. Spot is $60 for a stock. The risk free rate at time of spot is 4%. And there is no convenience yield or carrying cost. What is the 18-month Forward price for the stock?

B. A barrel of oil  is trading in at $304. If the convenience yield is 12% and the bowing rate (risk free) is 4%, then what is the 6-month Futures price for this asset?

C.Using the information above, is this asset said to be trading in “contango” or backwardation

Answer 1

For Solution A, we can calculate using following formula

F = S * e ^ (r * t)

Here F = The contract forward price, S = the underlying asset spot price, e = it is fixed mathematical irrational constant by 2.7183, r = risk free rate, t = time period.

So inserting values into the formula we get following values,

F= $60 * 2.7183 ^ (0.04 * 18/12)

F = $63.71

So, forward price of the stock is $63.71

For Solution B, we can calculate using following formula

Here F = The contract future price, S = the underlying asset spot price, e = it is fixed mathematical irrational constant by 2.7183, r = risk free rate, s = the storage cost (expressed as a percentage of the spot price), c = convenience yield, t = time period.

F = Se^((r+s-c)*t)

Here storage cost is nnot given so excluding it and we get the values mentioned below.

F = $304 * 2.7183^((0.04-0.12)*6/12))

F = $292.07

So, we get future price of the asset is $292.07

C. The price is contango (forwardation) if the spot price is lower than forward price of a futures contract and backwardation if the spot price is higher than forward price of futures contract.

So, the the asset price is in backwardation