<p>  CONVENIENCE YIELD </p><p> CONTANGO & BACKWARDATION </p><p> NORMAL CONTANGO & NORMAL BACKWARDATION</p><p>FUTURES PRICE AND RISK PREMIA</p><p>1) The No Risk Premium Hypothesis  “ If the futures price does not contain a risk premium, then speculators are not rewarded for risk. Futures prices will then be unbiased expectations of future spot prices.”  Rationale:  Theoretically, the futures price today equals the expected price of the futures contract at expiration because the expected futures prices at expiration equals the expected spot price at expiration.  So, it often says that the futures price is the market’s expectation of the future spot price. If one wishes to obtain a forecast of future spot price, one need only observe the futures price. In the language of economists, futures prices are unbiased expectations of future spot prices.</p><p>2) The Risk Premium Hypothesis  “If the futures price contains a risk premium, then speculators are rewarded for taking on risk. Futures prices will then be biased expectation of future spot prices.”  This risk premium is due to the position of hedgers. If hedgers have more or less the same expectations, they will not make contracts with each other, but with speculators. This explains normal backwardation and normal contango.  Rationale:  Keynes (1930) and Hicks (1939) argued that futures and spot markets are dominate by individuals who hold long positions in the underlying commodities. These individuals desire the protections in the underlying commodities.  That means they need traders who are willing to take long positions in futures. To induce speculators to take long positions in futures, the futures price must be below the expected price of the contract at expiration, which is the expected future spot future. Therefore, Keynes and Hicks argued, futures prices are biased expectations of future spot prices, with bias attributable to the risk premium.</p><p>CONTANGO AND BACKWARDATION</p><p> Contango – Futures price patterns in which the futures price will lie above that of spot price (due to positive costs of carry), i.e. securities that do not pay dividends or interest. In plain words, the futures price exceeds the spot price in a contango market.</p><p>Norman Cheung 1 Convenience Yield  Backwardation – price patterns in which the futures price lies below that of the spot price. </p><p> Convenience Yield (X) – offers an explanation of Backwardation. The convenience yield is the additional return earned by holding a commodity in short supply or a non-pecuniary gain from an asset. F = S +θ- X</p><p>Note: If f = S+θ and f < S, thenθ< 0. What type of market condition might produce a negative cost of carry? – Suppose the commodity is in short supply; current consumption is unusually high relative to supplies of good. This is producing an abnormally high spot price. The current tight market conditions discourage individuals from storing the commodity. If the situation is severe enough, the current spot price could be above the expected future spot price. If the spot price is sufficiently high, the futures price may lie below it. The x is simply a positive value that accounts for the difference between f and S+θ. (P.387, D Chance’s “Introduction to Derivatives”))</p><p>NORMAL BACKWARDATION AND NORMAL CONTANGO </p><p> Normal Backwardation – If hedgers have more or less the same expectations, they will not make contracts with each other, but with speculators. This explains normal backwardation and normal contango. Speculators will require a return for the risk that the hedgers pass onto them and the hedgers will be willing to pay a cost to transfer the risk. Therefore the futures price will be lower than the expected spot price at expiration, to compensate speculators for the risk of buying. Thus future price can be expected to rise over the life of a contract. This is referred to as normal backwardation. (nb: backwardation only refers a situation where the futures prices is less that of the current spot price at a given point in time). Note that this will occur if hedgers are net short in futures.</p><p> Normal Contango – When hedgers are net long in futures, the futures price will be higher than the expected spot price to compensate speculators for the risk of selling short (and buying back later). A market in which the futures price is above the expected future spot price is called normal contango.</p><p> Definitions: A market in which the futures price is below the expected future spot price is called normal backwardation, and one in which the futures price is above the expected future spot price is called normal contango.</p><p>Contango S < f </p><p>Backwardation S > f</p><p>Norman Cheung 2 Convenience Yield Normal Contango E(ST) < f</p><p>Normal Backwardation E(ST) > f</p><p>(nb: backwardation only refers a situation where the futures prices is less that of the current spot price at a given point in time)</p><p>Cash and Carry Arbitrage</p><p>Cash and Carry Arbitrage Reverse Cash and Carry Arbitrage</p><p>If the cost of carry model is violated such that: If the cost of carry model is violated such that: F > S +θ F < S + θ</p><p>Then we can: Then we can 1. Buy Spot Asset at S with borrowed money 1. Short sell Spot Asset at S 2. Short Sell Futures at f 2. Buy Futures at f 3. Pay Carrying Costθover futures contract life 3. Receive Carrying Costθover futures contract life</p><p>Norman Cheung 3 Convenience Yield 4. Use the Spot Asset to fulfil the futures contract 4. Obtain the Asset from the futures contract and at expiry use it settle the short spot position</p><p>At the outset, At the outset,</p><p> Borrow money to buy the cash asset  Short sell the cash asset</p><p> Short sell futures  Invest the money from Short selling </p><p>At maturity,  Buy a futures contract</p><p> Outflow: Pay the loan and interest expenses At maturity,</p><p> Inflow: Receive the proceeds from the future  Outflow: Buy the asset using the future contract upon the delivery of the spot asset. contract.</p><p> Inflow: Receive the P + I from the investment.</p><p>Implied Repo Rate</p><p> Definition: The cost of financing a cash-and-carry transaction that is implied by the relationship between the spot and futures price.</p><p> Put it in another way, the implied repo rate is the rate of return that a trader earns from buying the deliverable spot asset and simultaneously selling a futures contract. That is, the rate of return earned on cash and carry trades. 1  f  t rˆ    - 1 t = holding period in terms of fractions in yrs  S </p><p> Implied Repo Rate vs Financing Cost</p><p> If the implied repo rate exceeds the financing cost (i.e. the actual repo rate), then exploit a “Cash and Carry Arbitrage” opportunity: borrow fund; buy the cash asset; sell future; hold the asset and deliver against futures.</p><p> If the implied repo rate is less than the financing cost (i.e. the actual repo rate), then exploit a “Reverse Cash and Carry Arbitrage” opportunity: buy futures; sell asset short and invest proceeds until futures expires; take delivery in futures; repay short sale obligation.</p><p> A repurchase agreement, or repo, is an arrangement with a financial institution in which the owner of a security sells that security to the financial institution with an agreement to buy it back. More CFA info & materials can be retrieved from the followings: For visitors from Hong Kong: http://normancafe.uhome.net/StudyRoom.htm</p><p>Norman Cheung 4 Convenience Yield For visitors outside Hong Kong: http://www.angelfire.com/nc3/normancafe/StudyRoom.htm</p><p>Norman Cheung 5 Convenience Yield</p>