# Index Options Beginners Tutorial

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1 Index Options Beginners Tutorial 1

2 BUY A PUT TO TAKE ADVANTAGE OF A RISE A diversified portfolio of EUR 100,000 can be hedged by buying put options on the Eurostoxx50 Index. To avoid paying too high a premium, one will choose a strike price that is at the money or slightly out of the money. On august the 1st, with the underlying index at 2595, the premium for a put option with a strike price of 2575 and a September expiry is per contract or 169 Euros given the 10 Euros lot size. The number of put options to be bought is calculated as follows: If the value of the index at expiry is 2335,50 (-10 pct.), exercising the put options bought 47 days earlier provides a gain of Euros (( ,5) X 4 (number of contracts) X 10 Euros(multiplier)) which offsets the 10,000 Euros loss on the portfolio (100,000 EUR X -10 pct. = - 10,000 Euros.) Total: Euros (premium) + 9,580 Euros (gain on the put options) -10,000 Euros (loss on the portfolio) = - 1,096 Euros or -1,01 pct. as opposed as -10 pct. without the options hedge. If, on the other hand, the index closes at 3114 (+20 pct.), the options are not exercised and the portfolio is worth 120,000 Euros (100,000 Euros X (1+20pct)) less the premium paid for the options (676 Euros) Portfolio Strike price X multiplier = 100, X 10 = 3.88 Hedging a perfectly diversified euro-zone portfolio worth 100,000 Euros by buying 4 September put options with a strike price of 2575 thus costs 676 Euros. Unlike selling Futures, buying put options allows the hedger to profit from any rise in the index. 2

3 Selling covered calls An investor running a portfolio of European equities wants to achieve a higher return. His holdings have already posted gains, he is confident the current sluggish trend will continue, and he believes the uncertainty of future returns is sufficiently low that he can afford to take a short position in call options. He therefore decides to write call options on the Eurostoxx50 index. The option premiums provide immediate cash income today. The constraint is that if the stocks in his portfolio rise sharply, his gains will be limited. The options he writes are European options, which mean that he cannot be assigned before expiry. Strategy: For simplicity, the example below uses a portfolio composed of just two stocks, but the generalization to the case of n stocks is straightforward. A portfolio consist of two stocks, A and B, valued at 40 Euro and 60 Euro respectively. The manager holds shares of A, which has a beta of 1.20 relative to the Eurostoxx50 index, and 600 shares of B, which has a beta of (Beta: a measure of the sensitivity of an asset X to a benchmark index Y. His portfolio is therefore worth 80,000 Euro (1 100 X 40 Euro X 60 Euro). The Eurostoxx50 index is quoted at 2330 points. This portfolio is perfectly correlated with the index, since the combination of each stock s beta weighted by its capitalization in the basket gives an aggregate beta of For this portfolio, the number of call options to be sold is obtained in the following fashion: Portfolio Value Euro = Index value X multiplier 2330 X 10 = 3.43 The manager, being conservative, chooses the DEC Call at 38,70. Sell 4 eurostoxx50 Dec calls at 38,70 each for an immediate gain of Euro ( 38,70 X 4 (number of contracts) X 10 (multiplier)). Results: Depending on the case, having sold call options three months earlier enables the manager to: Limit losses on the portfolio when the eurostoxx50 index falls Make a profit when the eurostoxx50 index moves sideways 3

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