## Archive for the ‘Futures’ Category

### 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)]

### How futures price affect market price

Wednesday, May 28th, 2008

In our previous article, Who is to blame for surging food and oil prices?, we mentioned that institutional investors,

… through the futures market, affecting futures price, which in turn affected the spot prices (i.e. the real world market price).

Now that we have explained the basics of futures in Introduction to futures and Pricing of futures, we can now explain how those Index Speculators can affect real world market price through the futures market.

What happens, if the Index Speculators push up the price of a commodity futures above its theoretical price? When that happens, there will be an arbitrage opportunity.

Let’s say the price of a July futures is \$110 when its theoretical price is \$105 (i.e. spot price  of \$100 + carry cost of \$5). In that case, you can sell the overpriced July futures at \$110 and buy the underlying at \$100. When the futures expires in July, you can then sell the underlying at \$110. Your arbitrage profit will be \$5 (\$110 futures price – \$100 spot price – \$ carry cost).

What if the futures price is below its theoretical price? Let’s say, the futures price is now \$103 instead. You can short sell the underlying at \$100, earn the carry cost \$5 (e.g. interests) by holding the proceeds of the sale as cash. When the time comes to close out your short position in the underlying, you can buy the underlying at \$103 when the futures expires. Your arbitrage profit will be \$2 (\$100 short sell proceed + \$5 carry cost – \$103 close out short sell position).

All these are at least true in theory. In reality, for whatever reasons, futures price can veer out of its theoretical price. It can even fall below the spot price! That phenomenon is called “backwardation.”

And one last thing. Critics of Michael Masters’ theory that Index Speculators are behind the price inflation of commodity prices will point to the fact that inventory levels had not risen considerably as a result.

### 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!

### Introduction to futures

Sunday, May 25th, 2008

In our previous article, Who is to blame for surging food and oil prices?, we explained Michael Masters’ argument that the distortion of prices in the commodities futures market will affect the prices of commodities in the spot market (i.e. its real world market prices) and by extension, its inventory levels. If you can demolish that argument, you effectively demolish Michael Masters’ testimony.

We will not attempt to do that here. But today, we will introduce what futures is in order for you to have some understanding of the interaction between futures prices and spot prices.

First, what is a futures contract?

Basically, it is a contract to buy or sell something at a pre-determined price in the future. For example, if you buy a June futures contract for gold at \$1000, it means you have entered a contract that obliges you to buy gold at \$1000 in June. Conversely, if you sell a June futures contract for gold at \$900, you are obliged to sell gold at \$900 in June. In this example, gold is the “underlying” of the futures contract and June is the “expiry” of the futures contract. In the financial market, there are all sorts of “underlying” for futures, from stocks, bank bills, bonds, commodities and so on.

Thus, if you have an existing futures contract to obliges you to buy or sell an “underlying” in the future, you are said to have an open position. What if you want to absolve yourself from that future obligation? You need to enter an opposite futures position at the current market price to close out that position. For example, if you have already bought June futures for 100 ounce of gold, then you have to sell June futures for 100 ounce of gold at whatever the market price to close out your futures position. If you have already bought the futures at \$950 per ounce and sold the futures (to close out your position) at \$900 per ounce, then you have made a loss of \$50 per ounce.

That’s all for the introduction to futures. For those who are un-initiated to futures, isn’t it surprisingly simple? Next, we will cover the basics of futures pricing.