Commodity forward price with lease payment payment, forward, investing

yuoska

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?

jmh530

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..

wake2000

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