Hedging an Equity Portfolio with Options - Essay Example

? Hedging an Equity Portfolio Using Options Table of Contents Table of Contents 2 0 Introduction 3 2.0 Advantages and disadvantages of using options to hedge this scenario compared to using futures only 3 3.0 Explanation of how options could be used to hedge the risk faced by the fund manager 5 4. Explanation and discussion of how a zero cost collar could be used in this scenario 5 4.1 Explanation and discussion of the zero cost collar 5 4.2 Application of the zero collar cost shown with an example 6 5. Considerations of additional risks and considerations to be taken into account when using options to hedge a portfolio. 7 Reference: 9 1.0 Introduction A US equity fund manager holds €100m in a portfolio comprising the largest US stocks which perfectly replicates and benchmarks the S&P 500 index. The US Federal Reserve indicated that the programmed quantitative easing of purchasing $85 billion is not going to be carried out. The quantitative easing is used to stimulate the price when the corresponding interest rate decreases to 0%. The non execution of the quantitative easing is set to correct the equity market. The fund manager predicts that the reluctance of the US Federal Reserve to perform a quantitative easing is going have a profound effect on the performance of the portfolio. For this reason the fund manager as such wants to hedge the portfolio using option instead of futures. 2.0 Advantages and disadvantages of using options to hedge this scenario compared to using futures only Fund managers use both futures and options to order to hedge their portfolio. Though there are some marked differences in the two types of hedging tools. The choices of the hedging tools depend on the fund manager as well as the objective to hedge. In the present scenario, the fund manager has decided to use the options instead of futures (Reilly and Brown, 2000). This is because of the reason that the options provide certain leverage in comparison to futures. The most basic advantage is that an option gives the option holder the right and not an obligation. In case of the futures both the parties have equal obligations. The second advantage is that the amount of loss is limited to the buyer of option while in futures the losses can be unlimited. Option and future both provides same opportunity to the holder to minimize loss and at same time make profit. The US Federal Reserve has decided to stop quantitative easing. The quantitative easing techniques are supposed to create a stimulant which helps to ease the pressure on prices of funds. The price decreases when the interest falls or drops sharply. The sharp drop of interest is associated with a corresponding decrease in the price level. This means if the fund manager wants to invest in various funds, then the increase in the price of the various funds will limit the ability of the fund manager to invest effectively (Hearth and Zaima, 1998). The fund manager is not sure what will happen in the future but the non execution of the quantitative easing program indicates that the fund manager can only invest in limited fund with the present value of the equity portfolio, since the price of the funds have increased. If the fund manager anticipates that the share price will increase then he can buy a future. The sudden growth in the share price of equity may not find enough buyers. The problem with buying a future contract is that if the price of the funds drop then the fund manager is obliged to sell the future at the decreased price. So the future holder is in a risk, if the anticipated increase in price does not take place and instead of that the price actually decreases. So on one hand there is chance to make profit while on the other hand there is chance to incur loss. There are no restrictions to the limit of profit or loss. This is one of the greatest disadvantages of using the future contract. The advantage of the options with respect to future can be explained with the help of an example. As already explained the find manager is anticipating in increase in the price of the funds so the fund manager takes a call option. The call option gives the fund manager the right to buy the option at the agreed price although is not obligated to do anything if the price of the fund decreases from the strike price (Lo, 2001). In case the price of the fund becomes less than the strike price then the only loss that occurs is the premium paid while entering the contract. This loss is explained from the point of view of the option buyer. On the other hand the option writer can suffer significant loss that can very well exceed the premium received from the buyer. This benefit is not present in future. 3.0 Explanation of how options could be used to hedge the risk faced by the fund manager The fund manager can use various kinds of options like the call option and the put option to control the risks. For example the fund manager can use the slightly out of the money S&P 500 index puts. While at the same time the fund manager can resort to selling S&P 500 index calls which are slightly out of the money. The slightly out of the money calls are expiring within a time of 2 months. It is mentioned that the present index level of the S&P 500 is 1622, while the December 1575 SPX put contracts cost X and the December 1750 SPX cal contracts cost X+5. At the same time it can be assumed that the contract multiplier is $ 100. From this it can be easily found out the number of contacts that are needed to be purchased and written at the same time. The net premium can be calculated by deducting the total premium collected from total cost of the put options (Hobson, 1998). As the index value starts decreasing the call option starts decreasing in value whereas the put option value starts increasing. In the reverse way as the index value starts increasing the put option value starts decreasing while the call option value starts decreasing even more. 4. Explanation and discussion of how a zero cost collar could be used in this scenario 4.1 Explanation and discussion of the zero cost collar The cost less collar or the zero cost collars is applied through buying of a protective put and at the same time writing an out-of-the money call. This entails a covered call, since the investor holds a long position and at the same time writes/sells call options on the same asset, so that increased income can be generated from the asset.. Here the premium got is equal to the premium of the protective put purchased (Derman and Kani, 1995). The existing long stock position can be fully protected by incurring little or no cost. This is because of the reason that in zero cost collars the same premium received in lieu of the protective puts is offset by the same premiums got by writing the covered calls. 4.2 Application of the zero collar cost shown with an example The following discussion pertains to the use of put options that can be used by the fund manager to hedge the portfolio. The combined value of the portfolio is $ 100M. The fund manager decides to hedge the fund by purchasing slightly out of the money S&P 500 index put. At the same time the fund manager decides to sell an equal number of slightly out of the money S&P 500 index call. The calls are supposed to expire in two months. The current index level of S&P 500 is 1622. The DEC 1525 SPX put contract is available at a cost of $21, The DEC 1700 SPX call contract are available at $30 each. The contract multiplier of the SPX options is $150. This means that the number of contracts required to fully protect the holdings are $100,000,000/ (1622*150) = 411 put options need to be purchased and 411 call options need to be written. Total cost of the put options= 411*21*15= $12,94,650. The amounts of premium collected by selling the call options are 411*30*150 = $18,49,500. The total premium received is $18,49,500 - $12,94,650 =$5,54,850. S&P 500 Index Call Option Value Put Option Value Net Premium Received Un-hedged Portfolio Hedged Portfolio 1300 $0 89243000 554850 8952150 98750000 1400 $0 88445150 554850 97721660 98721660 1500 $0 88373480 554850 9760000 98688330 1622 $0 0 554850 100000000 100554850 1690 ($1,535,319) 0 554850 101952129 100971660 1750 ($9,869,799) 0 554850 131253279 121938330 Source: (www.cmegroup.com) The above table indicates the ability of the fund manager to counter the risks associated with the increase and decrease of the S&P index. The above table indicates the scenario that can happen ranging from S&P 1300 to S&P 1750. As the market starts declining the as indicated by the declining S&P 500 index, the value of the put options start increasing. At index level 1622, it is balanced. As the index level starts decreasing the value of the put options start increasing. The highest value is achieved at index level 1300. Again when the index value starts decreasing, the value of the put option starts increasing. Thus the fund manager has effectively decreased the risk associated with the increase and decrease of the index level through using options. Thus the fund manager has in effect applied the zero collar cost to limit the range of loss and at the same time earn profit. 5. Considerations of additional risks and considerations to be taken into account when using options to hedge a portfolio. Hedging is done to mitigate risks. Although hedging it is not devoid of risks. There are very specific types of risk that may arise, and one of them is basis risk. The basis risk occurs when the asset to be hedged and the underlying asset are not the same. For this reason the change in the price of the hedge does not match the change in the price of the asset which is hedged. Investment opportunities can be created due to the presence of imperfect correlation between two investments (Toft and Xuan., 1998). The basis risk arises if the fund manager decides to use futures contract instead of using options. In the preset context the fund manager is using the options instead of futures contract. So the occurrence of basis risk can be more or less ruled out. Apart from basis risk, there are also other kinds of risks, which are variable degree of risk, suspension or restrictions of trading and pricing relationship. A transaction in stock options carries with significant amount of risk. In some cases the purchaser of stock option may simply allow the stock option to expire or may simply exercise the stock option. When the stock option is exercised then it either results in settlement through cash or some cases the purchaser acquires the stock or some cases the purchaser delivers the stock. In case if the purchased stock option expires worthless, then the purchaser undergoes a total loss. The loss that occurs involves the stock option as well as the cost of premium and other transactions cost. In the present scenario, if the fund manager decides to purchase deep out of the money stock options, then it is highly unlikely that the stock option will become profitable. In the present scenario, the find manager decided to buy options as well as sell them. If the fund manager is not able to sell the stock options, then the fund manager has to undergo two kind of loses (Tompkins, 1999). One is the loss of premium and another is the cost of transaction. Even though the premium received by the seller is fixed but the seller can very well suffer loss if the loss is in excess of the premium received. Apart from this risk, the fund manager is also exposed to the risk if the purchaser exercises the stock option. Then the fund manager is obligated to either pay in cash or has to acquire or deliver the asset. There is another kind of risk that is the market risks. The market risks are sometimes also called as systematic risk. These kinds of risks cannot be diversified. Sometimes the market imposes certain kind of conditions or restrictions. This kind of restrictions and conditions increases the chance of loss. The chance of loss increases due to the difficulty or impossibility to carry out the transactions or even liquidate or offset the positions. If the investor has sold the options then the risk of loss increases even more. Reference: Derman, E. and Kani, I., 1995. Static Options Replication. Journal of Derivatives, 24(2), p. 78. Hearth, D. and Zaima, J. K., 1998. Contemporary investments in security and portfolio analysis. New York, The Dryden Press. Hobson, D., 1998. Robust Hedging of the Lookback Option. Finance and stochastic, 2(5), p.329. Lo, A., 2001. Risk Management for Hedge Funds: Introduction and Overview. Financial analysts journal, (58)2, p. 36. Reilly, F. K. and Brown, K. C., 2000. Investment analysis and portfolio management. New York, The Dryden Press. Toft K. and C. Xuan., 1998. How Well Can Barrier Options be Hedged by a Static Portfolio of Standard Options. The journal of financial engineering, 7(2), p. 147. Tompkins, R., 1999. Power options: hedging nonlinear risks. The journal of risk, 22(5), p. 29. Read More