Introducing arbitrage opportunities in commodity forwards

The author Robert McDonald introduced about some of the commodities, whose prices remain constant over a period of time.

When the prices remain constant, does it make any sense to store them? No, because traders or investors purchase or store commodities, expecting a price hike. If there is no price hike, it does not make sense to buy them and store them and to incur storage costs.

The above arguments are not applicable for financial assets.

The author introduced the prices of pencils, assuming that prices will remain constant.

Let us assume that 10 pencils will cost us $5.00 as of today.

Presently let us assume the risk-free rate in the market is 6% for one year maturity.(USD);

Let us calculate the forward price of these pencils after one year;

The forward price of any commodity is given by: S₀ x e^rT; S₀ = $5.00, r = 6% and T = 1 year

Therefore, the forward price of these pencils is expected to be: $5.00 x e^0.06x1 = $5.31;

The forward price formula says that after one year, the price of 10 pencils is expected to be $5.31

But do we enter into a forward agreement?

No..., because, the prices of pencils is expected to be constant. No one would buy at $5.31, when the pencils even after one year are available at $5.00;

Will there be any arbitrage, if the prices remain constant?

Yes... how?

Let us borrow 10 pencils from anyone for one year, who is holding them. Sell those 10 pencils today and get $5.00 and invest the proceeds for one year at the rate of 6%; after one year, we will get from the investment an amount of $5.31; then after one year get ten pencils from the market; return those 10 pencils to the holder of the pencils. Keep the profit of $0.31;

Or, borrow 10 pencils from the holder of pencils; Sell them in the cash market and get $5.00 and invest that $5.00 at 6%; and today only enter into a long forward agreement to buy at $5.00 after one year. After one year we will get $5.31 from our investment and buy 10 pencils at $5.00 as per long forward agreement and return those pencils to the lender. Keep the profit of $0.31;

This means, if the prices remain constant, there is an arbitrage opportunity. 

What does it mean and how to deal with such a situation? First of all prices cannot be constant. Secondly, even if the prices are constant, the lender who is lending 10 pencils for one year, is it possible that he will lend those pencils, without any benefit to him?... Let us discuss all these things in the next article.

Thanks a lot... Surya