Posts Tagged ‘carry cost’

Pricing of gold forward rate

Wednesday, April 8th, 2009

Back in Pricing of futures, we discussed about the theoretical pricing of futures. But the futures price (or more technically correct, the forward price) of gold is calculated differently. This is because there is a lease rate for gold. As we mentioned before in Get paid to borrow gold and silver?,

But for a certain class of gold owners, they DO earn interests on gold. Right now, instead of receiving interest for lending out gold, they are paying people to borrow gold.

The best way to explain gold forward pricing is to use an example. To understand this, we assume that you have already read and understood Pricing of futures beforehand. Let’s suppose the spot price of gold is $1000 per ounce. The lease rate for 180 days is 2 percent per annum while the carry cost (which includes storage and interests) is 5% per annum.

So, we borrow $1000 for 180 days. At the carry cost of 5%, we have to repay $1000 * (1+.05(180/365)) = $1024.66 in 180 days time. With the borrowed $1000, we buy 1 ounce of gold and lease it out. At the end of the 180 days lease period, we expect to get back 1 * (1+.02(180/365) = 1 (1.01) = 1.01 ounce of gold.

Therefore, 1 ounce of gold has grown to 1.01 ounce in 180 days time at a value of $1024.66. Therefore, the forward price of gold will have to be $1024.66/1.01 = $1014.51. If the 180-day forward price of gold is not at $1014.51, then an arbitrage opportunity exists (see How futures price affect market price for more details).

To sum it all up with an equation, if the spot price is S, the forward price is F(T) for a time-horizon of T days, the carry cost is r, and the gold lease rate is r*, we have:

F(T) = S [1 + r (T/365)] / [1 + r* (T/365)]


Pricing of futures

Monday, May 26th, 2008

After having introduced futures yesterday in Introduction to futures, we will explain the basics of futures pricing. It must be noted that the pricing of futures is a theoretical concept, which is what the price shoud be. In real life, the actual price could deviate from its theoretical prices for various reasons.

The pricing of futures is very simple:

Futures price = spot price + carry cost

The spot price is the prices fetched by the underlying in the market.

Next, what is the carry cost? The carry cost is basically the cost to hold the underlying. One of the components that makes the carry cost is the opportunity cost of interest foregone when holding the underlying till expiry of the futures. For example, let’s say you want to hold 1000 stocks of a company at $1 (which is the spot price or market price) each for 12 months. What is the carry cost for holding those 1000 stocks? At 10% interest rate, the carry cost is $100 (or $0.10 per stock) over 12 months. Therefore, if a futures contract expires in 12 months time, then the futures price for that stock as underlying is:

$1 (spot price) + $0.10 (carry cost, which is the interests foregone for holding that stock over 12 months) = $1.10

If the stock pays dividend within the 12 months, then this dividend plus the interests associated with that dividend itself will be adjusted in the carry cost to arrive at the theoretical value of the futures.

For stocks, since it is an intangible thing, the carry cost is basically the interest foregone (and the dividends plus the interest on dividends). But for physical commodities (e.g. oil, gold, copper), the carry cost involves warehousing, insurance and other costs associated for physically holding them.

So, what if in actuality, the futures price deviates from its theoretical price? Keep in tune!