Financial issues

Hedging

admin — Sun, 13 Dec 2009 20:06:41 +0000

We earlier discussed hedging using futures contracts in the context of a business protecting the value of its inventory. We now discuss some hedging strategies available to portfolio managers based on financial futures. Essentially, an investment portfolio is an inventory of financial securities, and futures can be used to reduce the risk of holding a securities portfolio.
We consider the specific problem of an equity portfolio manager wishing to protect the value of a stock portfolio from the risk of an adverse movement of the overall stock market. Here, the portfolio manager wishes to establish a short hedge position to reduce risk and must determine the number of futures contracts required to properly hedge a portfolio.
In this hedging example, you are responsible for managing a broadly diversified stock portfolio with a current value of $100 million. Analysis of market conditions leads you to believe that the stock market is unusually susceptible to a price decline during the next few months. Of course, nothing is certain regarding stock market fluctuations, but still you are sufficiently concerned to believe that action is required.
A fundamental problem exists for you, however, in that there is no futures contract that exactly matches your particular portfolio. As a result, you decide to protect your stock portfolio from a fall in value caused by a falling stock market using stock index futures. This is an example of a cross-hedge, where a futures contract on a related, but not identical, commodity or financial instrument is used to hedge a particular spot position.
Thus, to hedge your portfolio, you wish to establish a short hedge using stock index futures.
To do this, you need to know how many index futures contracts are required to form an effective hedge. There are three basic inputs needed to calculate the number of stock index futures contracts required to hedge a stock portfolio:
The current value of your stock portfolio,
The beta of your stock portfolio,
The contract value of the index futures contract used for hedging.
You should be familiar with the concept of beta as a measure of market risk for a stock portfolio. Essentially, beta measures portfolio risk relative to the overall stock market. We will assume that you have maintained a beta of 1.25 for your $100 million stock portfolio.
You decide to establish a short hedge using futures contracts on the Standard and Poor’s index of 500 stocks (S&P 500), since this is the index you used to calculate the beta for your portfolio. From the Wall Street Journal, you find that the S&P 500 futures price for three-month maturity contracts is currently, say, 1,300. Since the contract size for S&P 500 futures is 250 times the index, the current value of a single index futures contract is $250 × 1,300 = $325,000.
You now have all inputs required to calculate the number of contracts needed to hedge your stock portfolio.

Basics of Stock Index Futures

admin — Fri, 11 Dec 2009 20:05:24 +0000

The second contract listed, on the S&P 500 index, is the most important. With this contract, actual delivery would be very difficult or impossible because the seller of the contract would have to buy all 500 stocks in exactly the right proportions to deliver. Clearly, this is not practical, so this contract features cash settlement.
To understand how stock index futures work, suppose you bought one S&P 500 contract at a futures price of 1,300. The contract size is $250 times the level of the index. What this means is that, at maturity, the buyer of the contract will pay the seller $250 times the difference between the futures price of 1,300 and the level of the S&P 500 index at contract maturity.
For example, suppose that at maturity the S&P had actually fallen to 1,270. In this case, the buyer of the contract must pay $250 × (1,300 – 1,270) = $7,500 to the seller of the contract. In effect, the buyer of the contract has agreed to purchase 250 units of the index at a price of $1,300 per unit. If the index is below 1,300, the buyer will lose money. If the index is above that, then the seller will lose money.

More on Spot-Futures Parity

admin — Tue, 08 Dec 2009 20:03:45 +0000

In our spot-futures parity example just above, we assumed that the underlying financial instrument (the stock) had no cash flows (no dividends). If there are dividends (for a stock future) or coupon payments (for a bond future), then we need to modify our spot-futures parity condition.
For a stock, we let D stand for the dividend, and we assume that the dividend is paid in one period, at or near the end of the futures contract’s life. In this case, the spot-futures parity condition becomes
F = S(1+r)-D
Notice that we have simply subtracted the amount of the dividend from the future value of the stock price. The reason is that if you buy the futures contract, you will not receive the dividend, but the dividend payment will reduce the stock price.

Spot-Futures Parity

admin — Fri, 04 Dec 2009 20:02:47 +0000

We can be a little bit more precise concerning the relationship between spot and futures prices for financial futures. To illustrate, suppose we had a futures contract on shares of common stock in a single company (actually there are no such contracts in the U.S.). This particular stock does not pay dividends.
For concreteness, suppose the contract calls for delivery of 1,000 shares of stock in one year. The current (i.e., cash or spot) price is $50 per share. Also, 12-month T-bills are yielding 6 percent. What should the futures price be? To answer, notice that you can buy 1,000 shares of stock for $50 per share, or $50,000 total. You can eliminate all of the risk associated with this purchase by selling one futures contract. The net effect of this transaction is that you have created a risk-free asset. Since the risk-free rate is 6 percent, your investment must have a future value of $50,000 × 1.06 = $53,000. In other words, the futures price should be $53 per share.
Suppose the futures price is, in fact, $52 per share. What would you do? To make a great deal of money, you would short 1,000 shares of stock at $50 per share and invest the $50,000 proceeds at 6 percent. Simultaneously, you would buy one futures contract.
At the end of the year, you would have $53,000. You would use $52,000 to buy the stock to fulfill your obligation on the futures contract and then return the stock to close out the short position. You pocket $1,000. This is just another example of cash-futures arbitrage.
More generally, if we let F be the futures price, S be the spot price, and r be the risk-free rate, then our example illustrates that
F = S(1 + r)
In other words, the futures price is simply the future value of the spot price, calculated at the risk-free rate. This is the famous spot-futures parity condition. This condition must hold in the absence of cash-futures arbitrage opportunities.

Cash-Futures Arbitrage

admin — Fri, 27 Nov 2009 20:01:37 +0000

Intuitively, you might think that there is a close relationship between the cash price of a commodity and its futures price. If you do, then your intuition is quite correct. In fact, your intuition is backed up by strong economic argument and more than a century of experience observing the simultaneous operation of cash and futures markets.
As a routine matter, cash and futures prices are closely watched by market professionals. To understand why, suppose you notice that spot gold is trading for $400 per ounce while the two-month futures price is $450 per ounce. Do you see a profit opportunity?
You should, because buying spot gold today at $400 per ounce while simultaneously selling gold futures at $450 per ounce locks in a $50 per ounce profit. True, gold has storage costs (you have to put it somewhere), and a spot gold purchase ties up capital that could be earning interest. However, these costs are small relative to the $50 per ounce gross profit, which works out to be $50 / $400 = 12.5% per two months, or about 100% per year (with compounding). Furthermore, this profit is risk-free! Alas, in reality, such easy profit opportunities are the stuff of dreams.
Earning risk-free profits from an unusual difference between cash and futures prices is called cash-futures arbitrage. In a competitive market, cash-futures arbitrage has very slim profit margins. In fact, the profit margins are almost imperceptible when they exist at all.

Hedging With Futures

admin — Sat, 21 Nov 2009 19:53:45 +0000

Many businesses face price risk when their activities require them to hold a working inventory. For example, suppose you own a regional gasoline distributorship and must keep a large operating inventory of gas on hand, say, 5 million gallons. In futures jargon, this gasoline inventory represents a long position in the underlying commodity.
If gas prices go up, your inventory goes up in value; but if gas prices fall, your inventory value goes down. Your risk is not trivial, since even a 5-cent fluctuation in the gallon price of gas will cause your inventory to change in value by $250,000. Because you are in the business of distributing gas, and not speculating on gas prices, you would like to remove this price risk from your business operations. Acting as a hedger, you seek to transfer price risk by taking a futures position opposite to an existing position in the underlying commodity or financial instrument. In this case, the value of your gasoline inventory can be protected by selling gasoline futures contracts.
Gasoline futures are traded on the New York Mercantile exchange (NYM), and the standard contract size for gasoline futures is 42,000 gallons per contract. Since you wish to hedge 5 million gallons, you need to sell 5,000,000 / 42,000 = 119 gasoline contracts. With this hedge in place, any change in the value of your long inventory position is canceled by an approximately equal but opposite change in value of your short futures position. Because you are using this short position for hedging purposes, it is called a short hedge.
By hedging, you have greatly reduced or even eliminated the possibility of a loss from a decline in the price of gasoline. However, you have also eliminated the possibility of a gain from a price increase. This is an important point. If gas prices rise, you would have a substantial loss on your futures position, offsetting the gain on your inventory. Overall, you are long the underlying commodity because you own it; you offset the risk in your long position with a short position in futures.
Of course, your business activities may also include distributing other petroleum products like heating oil and natural gas. Futures contracts are available for these petroleum products also, and therefore they may be used for inventory hedging purposes.
The opposite of a short hedge is a long hedge. In this case, you do not own the underlying commodity, but you need to acquire it in the future. You can lock in the price you will pay in the future by buying, or going long in, futures contracts. In effect, you are short the underlying commodity because you must buy it in the future. You offset your short position with a long position in futures.

Selection of Comparison Firms

admin — Mon, 16 Nov 2009 19:51:23 +0000

The single biggest problem with comparables may be the selection of appropriately comparable firms. Say, you own a little soda producer, the Your Beverage Corporation (YBC), with earnings of $10 million. You want to select public firms to use as your comparables from the universe of firms. Usually, this means publicly traded companies. So, which of the 10,000 or so publicly traded companies are most comparable to your firm (or project)? Are firms more similar if they are similar in assets, similar in their business products and services, similar in their geographical coverage, similar in their age, similar in their size and scale, etc.? Do they have to be similar in all respects? If so, chances are that not a single of the 10,000 firms will qualify!
Let us assume that after extensive research and much agonizing, you have identified the (same) three companies: KO, PEP, and CSG. Which one is most similar? You know that depending on which firm you select, your valuation could be $250 million (if Cadbury Schweppes, unlevered, was most similar), $410 million (if PepsiCo was most similar), or $500 million (if Coca Cola was most similar). Which shall it be?
Selecting comparables depends both on the judgment and on the motives of the analyst. In the YBC case, one analyst may consider all three firms (KO, PEP, and CSG) to be similar, but CSG to be most similar because it is the smallest comparison firm. She may determine a good P/E ratio would be 30. Another analyst might consider Coca Cola and Pepsi-Co to be better comparables, because they tend to serve the same market as YBC. He may determine a good P/E ratio would be 40. The owner of YBC may want to sell out and try to find a buyer willing to pay as much as possible, so she might claim Coca Cola to be the only true comparable, leading to a P/E ratio of 50. The potential buyer of YBC may instead claim Cadbury Schweppes to be the only comparable, and in fact attribute an extra discount to CSG: after all, YBC is a lot smaller than CSG, and the buyer may feel that YBC deserves only a P/E ratio of 10. There is no definitive right or wrong choice.
Another choice may be not to select either the P/E ratio of 10 or the P/E ratio of 45, but to “split the difference.” A reasonable P/E ratio that is better than either 10 or 45 may be 30. This might mean valuations of around $300 to $400 million. Unfortunately, though this may be the best solution, it is not a good solution.

Problems with Traditional Theories

admin — Thu, 12 Nov 2009 19:50:02 +0000

To illustrate some problems with traditional theories, we could examine the behavior of the term structure in the last two decades. What we would find is that the term structure is almost always upward sloping. But contrary to the expectations hypothesis, interest rates have not always risen. Furthermore, as we saw with STRIPS term structure, it is often the case that the term structure turns down at very long maturities. According to the expectations hypothesis, market participants apparently expect rates to rise for 20 or so years and then decline. This seems to be stretching things a bit.
In terms of maturity preference, the world’s biggest borrower, the U.S. government, borrows much more heavily short term than long term. Furthermore, many of the biggest buyers of fixed- income securities, such as pension funds, have a strong preference for long maturities. It is hard to square these facts with the behavior assumptions underlying the maturity preference theory.
Finally, in terms of market segmentation, the U.S. government borrows at all maturities. Many institutional investors, such as mutual funds, are more than willing to move maturities to obtain more favorable rates. Finally, there are bond trading operations that do nothing other than buy and sell various maturity issues to exploit even very small perceived premiums. In short, in the modern fixed- income market, market segmentation does not seem to be a powerful force.

Determinants of Nominal Interest Rates: A Modern Perspective

admin — Tue, 10 Nov 2009 19:49:02 +0000

Our understanding of the term structure of interest rates has increased significantly in the last few decades. Also, the evolution of fixed-income markets has shown us that, at least to some extent, traditional theories discussed in our previous series of articles may be inadequate to explain the term structure. We discuss some problems with these theories next and then move on to a modern perspective.

The Fisher Hypothesis

admin — Sun, 08 Nov 2009 19:48:54 +0000

The relationship between nominal interest rates and the rate of inflation is often couched in terms of the Fisher hypothesis, which is named for the famous economist Irving Fisher, who first formally proposed it in 1930. The Fisher hypothesis simply asserts that the general level of nominal interest rates follows the general level of inflation. According to the Fisher hypothesis, interest rates are on average higher than the rate of inflation. Therefore, it logically follows that short-term interest rates reflect current inflation, while long-term interest rates reflect investor expectations of future inflation.