READING 8: RISK MANAGEMENT APPLICATIONS OF FORWARDS AND FUTURES STRATEGIES Modifying a portfolio duration using futures: Number of future contract to be bought or (sold) (target duration bond portfolio duration) portfolio size = ( ) ( ) β(yield beta) future bond duration contract size A- Strategies and Applications for Managing Equity Market Risk 1- Measuring and Managing the Risk of Equities Beta (β), is the common risk measure for futures that are based on broadly diversified portfolios. It is formally measures as β = Cov(S,index) σ2 index As a risk measure, beta is similar to duration. If we wish to change the beta, we specify the desired beta as a target beta of β T. Because the value of the futures starts off each day as zero, the dollar beta of the combination of stock and futures if the target beta is achieved is β T S. The number of futures we shall use is N f, which is the unknown that we are attempting to determine. We set the target dollar beta to the dollar beta of the stock portfolio and the dollar beta of N f futures: We then solve for N f and obtain β T S = β S S + N f β f f N f = ( β T β S β f ) ( S f ) Equation 5 In the special case in which we want to completely eliminate the risk, β T would be zero and the formula would reduce to N f = ( β S β f ) ( S f ) Note: the futures contract will hedge only the risk associated with the relationship between the portfolio and the index on which the futures contract is based. Which means that pairs with different components or risk profiles should not be matched for this strategy 2- Managing the Risk of an Equity Portfolio To adjust the beta of an equity portfolio, an investment manager could use Equation 5 to calculate the number of futures contracts needed. She can use the formula to either increase or decrease the portfolio s systematic risk. The manager might increase the beta if she expects the market to move up, 1
or decrease the beta if she expects the market to move down. Also, the betas of equity portfolios change constantly by virtue of the market value of the portfolio changing.21 Therefore, futures can be used to adjust the beta from its actual level to the desired level. Also, be aware that increasing the beta increases the risk. Therefore, if the beta is increased and the market falls, the loss on the portfolio will be greater than if beta had not been increased. Decreasing the beta decreases the risk, so if the market rises, the portfolio value will rise less. 3- Creating Equity out of Cash Fundamental formula: Long stock + Short futures = Long risk free bond Long stock = Long risk free bond Short futures Long stock = Long risk free bond + Long futures a. Creating a Synthetic Index Fund Notations: V = amount of money to be invested f = futures price T = time to expiration of futures δ = dividend yield on the index r = risk free rate q = multiplier Steps for creating a synthetic index fund which is replicating owning the stock and reinvesting the dividends which means replicating long stock with a long risk-free bong and a long futures: 1- Determine the number of future contracts to be bought: V(1 + r)t N f = 2- Round N f to N f as a fraction of a futures contract can t be bought and determine the exact amount to be invested N V(1 + r)t f = rounded to an integer the amount actually invested is: V = N f (1 + r) T 2
3- Place the money in risk free bonds and capitalize at the risk free rate 4- Investing V in bonds and buying N f futures contracts at a price of f is equivalent to buying N f /(1 + δ) T units of stock. 5- At expiration the futures contract will pay off N f q(s t f) which will adjust your bond position for a payoff similar to that of owning the stock. b. Equitizing Cash The strategy of combining risk-free bonds and futures is used not only to replicate an index; it is also used to take a given amount of cash and turn it into an equity position while maintaining the liquidity provided by the cash. This type of transaction is sometimes called equitizing cash. There is one important aspect of this problem, however, over which the fund has no control: the pricing of the futures. Because the fund will take a long position in futures, the futures contract must be correctly priced. If the futures contract is over- priced, the fund will pay too much for the futures. In that case, the risk-free bonds will not be enough to offset the excessively high price effectively paid for the stock. If, however, the futures contract is underpriced, the fund will get a bargain and will come out much better. 4- Creating Cash out of Equity The objective is to construct a synthetic position in cash by selling futures against a long stock position. This is derived from the relation: Long risk free bond (or cash) = Long stock + Short futures Steps to create cash out of equity: 1- Determine the number of futures contracts to sell: N f = V(1+r)T 2- Round the number to an integer N f N f 3- Find out the exact amount of cash received (1+r) T 4- Capitalize it at the risk free rate 5- Calculate the number of units of stock at the beginning 6- And at expiration N f (1 + δ) T N f (1+δ) T 7- The payoff of the futures contract is N f q(s t f) will adjust your stock position for a payoff equal to that of the risk-free rate. 8- The overall position of the fund is an amount equal to investment in a risk free rate without having had to sell the stock B- Asset Allocation with Futures 3
1- Adjusting the Allocation among Asset Classes To adjust allocation among different asset classes target beta and target duration are used. A target beta and a target duration of zero are used if the portfolio manager wishes to temporarily eliminate exposure. The different contracts to be purchased and sold are calculated one at a time and netted out to avoid duplicate transactions. 2- Pre-Investing in an Asset Class Now consider that the investor might not be in the market but wants to get into the market. The investor might not have the cash to invest at a time when opportunities are attractive. Futures contracts do not require a cash outlay but can be used to add exposure. We call this approach pre-investing, and the trick is to establish the position at the appropriate beta and duration. In this case, the fund is effectively borrowing against the cash it will receive in the future by preinvesting. Recall that Which means that Long underlying + Short futures = Long risk free bond Long underlying = Long risk free bond + Long futures In this example, however, the investor does not have the long position in the risk-free bond. That would require cash. We can remove the long risk-free bond in the equation above by off-setting it with a loan in which we borrow the cash. Hence, adding a loan to both sides gives31 Long underlying + Loan = Long futures An outright long position in futures is like a fully leveraged position in the underlying. C- Strategies and Applications for Managing Foreign Currency Risk Transaction exposure: risk of a foreign currency depreciating when the seller is about to receive a payment in foreign currency. Or of the foreign currency appreciating when the buyer is about to make a payment in foreign currency. Translation exposure: Accounting risk related to the translation of balance sheet items denominated in foreign currency. Economic exposure: Impact on business due to foreign currency fluctuations for example domestic products lose their international appeal when domestic currency strengthens. The reading focuses solely on transaction exposure. 4
1- Managing the Risk of a Foreign Currency Receipt To manage the risk of a foreign currency receipt the investor hedges by selling the currency forward. The exchange rate at expiration has no impact on the transaction as the investor is fully hedge and the cash are determined in advance. 2- Managing the Risk of a Foreign Currency Payment To manage the risk of a foreign currency receipt the investor hedges by buying the currency forward. The exchange rate at expiration has no impact on the transaction as the investor is fully hedge and the cash are determined in advance. 3- Managing the Risk of a Foreign-Market Asset Portfolio In hedging the returns of a foreign market the investor will only capture the foreign risk free rate In hedging both, the returns on a foreign market and the foreign exchange rate the investor will effectively only capture the domestic risk free rate. It is not possible to perfectly hedge currency risk on an international assets as returns because the future value of the asset is unknown. As a temporary and tactical strategy, hedging one or both risks can make sense. There are certainly periods when one might be particularly concerned about these risks and might wish to eliminate them. Executing this sort of strategy can be much easier than selling all of the foreign stocks and possibly converting the proceeds into domestic currency. But in the long run, a strategy of investing in foreign markets, hedging that risk, and hedging the exchange rate risk hardly makes much sense. D- Futures or Forwards The primary difference between futures and forwards are: 1) Futures contracts are standardized, with all terms except for the price set by the futures exchange. Forward contracts are customized. The two parties set the terms according to their needs. 2) Futures contracts are guaranteed by the clearinghouse against default. Forward contracts subject each party to the possibility of default by the other party. 3) Futures contracts require margin deposits and the daily settlement of gains and losses. Forward contracts pay off the full value of the contract at expiration. Some participants in forward contracts agree prior to expiration to use margin deposits and occasional settlements to reduce the default risk. 4) Futures contracts are regulated by federal authorities. Forward contracts are essentially unregulated. 5) Futures contracts are conducted in a public arena, the futures exchange, and are reported to the exchanges and the regulatory authority. Forward contracts are conducted privately, and individual transactions are not generally reported to the public or regulators. 5