Question

Suppose that a pencil cost $1 today and for certain will cost $1 in 1 year. This can happen, for example, if the supply of pencils is perfectly elastic. Suppose also that the continuously compounded interest rate is 10%.

a. What is the forward price of a toothpick to be delivered in 1 year? Clearly explain your logic in answering this question.

b. Show that the forward price you derived in the previous point does not admit arbitrage opportunities.

Answer 1

a.

S0 = $1

T = 1

r = 10% = 0.1

The forward price = S0 × erT

S0 is the spot Price, r is the rate of interest, T is the no of years till delivery

So, substituting I get forward price (F0) = 1× e0.1×1

= $1.11

The logic is that forward price is nothing but the price to be paid for an asset with spot price S0 which is compounded at an interest rate r, over a period T. For continuous compounding interests we use the exponential function.

b.

An arbitrage occurs when an investor hedges a future contract against exchange rate risk. This happens only in forward currency contract as the investors look out for higher yielding currency using interest differentials. In our case, we have an asset (a pencil). Hence, there is no opportunity for arbitrage.

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