Short hedge

[frm_daniel]

Hi David,

Here is a past year question :
A trade sell $80 million worth of gold short for six weeks and buys $80 million worth of gold for six weeks delivery. This exposes the trader to a:
A. Rise in the price of gold
B. Fall in the gold borrowing rate
C.Fall in short-term interest rates
D. Rise in the volatility of gold price

Answer B: The trade is hedged against the spot price of gold and its volatilty, and is effectively borrowing gold and lending cash for a fixed term of six months. So the trader will lose if the gold borrowing rate falls and the short-term interest rates rise.

I thought we are selling forward gold and buy spot and borrowing. (cash and carry) I can't figure out the answer.What is the gold borrowing rate ?

Daniel

 

[David Harper CFA FRM]

Hi Daniel,

I think it's a devious question (can you source?). The borrowing rate is the "lease rate" (the lease rate is reviewed in Culp and is associated with gold).
You are right this is near to a cash and carry arbitrage but it's not quite because there is not a cash borrowing to fund the purchase of the spot.
I copied version of Culp's cash and carry here: http://sheet.zoho.com/public/btzoho/goldshort
(orange mimics the question's transaction: cash and carry without the cash borrowing)

Note right hand column has 2 panels:
1. The cash and carry arbitrage: short the forward and borrow at risk-rate to get the cash to buy the spot (gold) commodity; because cash is borrowed to purchase at spot, the net cost is zero at time 0
2. Below that, this scenario in this question: short the commodity and buy the spot; i.e., this is not costless at inception. Rather, the answer correctly treats as effectively lending cash to borrow the commodity

So, you'll notice in my illustration the short forward + buy commodity returns 4% (cell K17) under the assumptions (i.e., lending cash @ 4%). One risk, then, is that short rates rise while we have committed our cash @ 4%. Conversely, the lease rate is similar to interest on cash; except it's interest (dividend) on commodity. Under these assumption, we've borrowed at initial lease of 1% (my example) but we'll miss the opportunity for "cheaper" gold if the lease goes down. (IMO, this question is devious b/c the logic can be extended to the arb scenario ....)

...another way to look at this is, while the transaction is not exposures to the spot price of gold per se (i.e., we bought the gold today that we need to deliver in the future, the future spot price of gold will not impact us this way), we have invested ("lended") cash based on today's gold forward price and today's gold forward price is a function of the riskless rate and lease rate risk factors:

Culp 6.14: Forward (gold) = Spot * EXP[(riskless - lease)*T
.... an increase in riskless or a decrease in lease rate will increase the forward price, which is contrary to our short forward position
... this transaction is not exposed to the spot per but is short the forward, so in a difficult way, the transaction is exposed to the forward price

Hope that helps, IMO a difficult question

David