# Commodity forward price with lease payment

I’m confused by the arbitrage formulas for commodities in Schweser “The commodity borrower is willing to pay the lease rate = convenience yield - storage cost. The value of the forward to the commodity borrower” F >= S * (e^ (Rf - lease rate)*T) In the secret sauce book, it says “Treating the lease payment as a dividend (for investing in the commodity), the forward price for a commodity with an active lease market is:” F <= S * (e^ (Rf - lease rate)*T) This whole section is confusing to me. Can anyone explain it in the plain english?

Lease rate basically give you the net benefits received by holding the commodity. It’s on the similar lines to receiving dividends by holding the stocks. Lease rate is a netted number and comprise of convenience yield (benefit to holder) - storage cost (cost to holder) = net benefit. Since this is benefitting the holder of the commodity, it reduced the overall price of the forward. Hence FR < SR since lease rate is subtracted from the exponential term. Increase in LR would decrease the value of Forward.

not sure if this will help but the way i look at it is that the lease rate is a benefit to whoever is holding the commodity. in that case the seller of the forward is willing to accept a lower price on the conract as he gets to hold the commodity until expiratio of the forward. by reducing the exponent by the lease rate you are reducing the forward price to reflect the beefit received by the holder of the commodity/seller of the forward

grgkir001 Wrote: ------------------------------------------------------- > not sure if this will help but the way i look at > it is that the lease rate is a benefit to whoever > is holding the commodity. in that case the seller > of the forward is willing to accept a lower price > on the conract as he gets to hold the commodity > until expiratio of the forward. by reducing the > exponent by the lease rate you are reducing the > forward price to reflect the beefit received by > the holder of the commodity/seller of the forward This is exactly how I think about it. You basically need to consider two types of people selling the commodity forward. One type of person receives benefit of actually holding the asset and the other type of seller receives no benefit of holding the asset. Because there are two type of sellers of commodities forward, we know that we can have an upper and lower bound for the forward price. For those who receive no benefit from holding the asset, the commodity forward price will be higher than the forward price for a seller who does receieve a convenience yield from the asset. Hope this helps.

Let’s say you want to take advantage of Forward premium and would like to short the commodity (say gold)… by the way, you would do this only if the right side of your first inequality is less or equal to the Future’s price… your actions: 1.Sell the futures 2.Invest the proceeds to earn Rf 3.Since you don’t have any gold, borrow it at a lease rate that will be to your benefit 4.When the future date comes, sell your gold at Futures price If your Futures price> than what your proceeds are from investment (less leasing costs), then you earned a profit… This means, you took advantage of the arbitrage! Same goes with the second inequality… if this is true, you can take the opposite side to take advantage of this arbitrage… Therefore, Futures are priced in a way to eliminate any kind of arbitrage… So you will rarely see that Futures price does not equal to the right side of the formula… I hope this helps…