Options, futures and swaps.
...blem is in the uncertainty of the spot price in September and in his expectations about it. If he expects the price to fall, it’s a good choice to sell the futures. Y, the baker, on the other hand, may think that the price is likely to rise. In his opinion, it would be wise to buy the futures. How can one determine the price of a futures? They usually use the following formula: Where Pf is the futures price (at the moment), Ps – spot price (current price) I – interest (one can sell the basis good at its spot price and buy interest-bearing securities). B – benefits of ownership (for example, if the basis good is a collection of pictures, one can organize an exhibition and make a profit by selling tickets) C – expenses of ownership (for example, insurance or renting the warehouse). DPs – difference between spot price on the delivery date and current price 9the effect is similar to benefits of ownership effect). The figure I – B + C is called “the cost of carry” of the futures. We have described the first type of futures – commodity futures. But a more recent financial instrument – financial futures (first appeared in the 70th) - accounts for much larger volume of transactions. There are two types of financial futures: currency futures and percentage (interest) futures. Currency futures are agreements about future transactions with foreign currencies. They are priced according to the interest rate parity principle. The following example will explain it. Imagine that you want to invest a certain sum of money for a year. You may buy Russian risk free J)) treasury bills, or exchange rubles for dollars, buy USA treasury bills and in a year sell them and exchange dollars for rubles. Both variants provide equal returns. 1+Rru – yield from investing in domestic securities Pf/Ps*(1+Rusa) – yield (in rubles) from investing in American bonds. Futures for securities or market indexes are often called interest futures, because their prices depend greatly on current and estimated interest rates. The futures price for treasury bills with the same date of maturity and delivery date equals: R – risk-free interest rate. The following table shows the advantages of investing in futures: it shows the average yields per year and risk (expressed as standard deviation) of portfolios with different proportions of stocks and future contracts. The share of stocks in the portfolio (%) The share of futures in the portfolio (%) Standard deviation (%) Avg. yield per year (%) 0 100 22,43 13,83 20 80 17,43 13,67 40 60 13,77 13,52 60 40 12,68 13,36 80 20 14,74 13,21 100 0 18,95 13,05 The yields don’t differ much, but the is a substantial difference in the risks of the portfolios. The forth portfolio (60% stocks, 40% futures), for example, carries a much better risk, then the others. Options. A contract between two investors that gives one of then the right (but not obliges to) buy from or (sell to) the other a certain asset at a fixed price up to certain date in the future is called option. There are two types of options – “call” and “put” options. The most widespread option contract is call option for stocks. It gives its buyer the right to call (buy) a certain number of stocks from the seller of the option at a certain price at any type up to a certain date in the future. The second type of option contracts is put option. It gives its buyer the right to sel a certain number of stocks to the seller of the option at a certain price at any type up to a certain date in the future. The contract determines the for basic items: 1. The company, whose stocks are the subject of the deal 2. The number of stocks that changes hands. 3. The price of the purchase, which is called exercise price. 4. The expiration date of the contract. Options help investors avoid risks even better than futures do. Let us see how they work. Imagine that investors X and Y want to sign a call option contract. The contract allows X to buy 100 shares of Widget from Y at the price of 50$ at any time within the following 6 month. The current price of widget shares is 45$ per share. X thinks that the price of the shares is likely to increase considerably in the following 6 month. Y – potential seller of the option, on the contrary, thinks that it will scarcely exceed 50$. By buying this option, X eliminates the risk at all: if spot price in 6 month is higher than 50$, he will buy the shares from Y at a price below the market price, and if the price is lower – he will just quit the option contract. Buy selling the option, Y undertakes all the risk, and to compensate for this risk X will have to pay Y a certain sum of money, which is called premium (for example, 3$ per share), also price would be a more suitable term. Another advantage of buying call options instead of shares is that X can use loan money, because he will need only 3$ per share to buy an option. To determine the price of call or put options, the Binominal Option Pricing Model can be used. Lets appreciate the intrinsic value of a call option. Imagine that current price of Widget shares (t=0) is 100$. In a year (t=T) the price will be either 125 or 80$. The risk free interest rate is 8%. The exercise price of the option is 100$. This all means that the value of the o...