Hedging, Speculation and Arbitrage

The distinction between hedging, speculation, and arbitrage comes up when a company considers hedging with futures, or when a portfolio manager clarifies the purpose of a futures trade.

The same price move gives different results

Hedging, speculation, and arbitrage produce different gains and losses when the market moves, even when all three use the same futures. Futures are used in three ways: outright trading (speculation), hedging, and arbitrage¹.

Consider a hypothetical example in which the index is now at 20,000 and the contract unit of equity index futures is 1,000 times the index. If the index rises to 22,000 or falls to 18,000, the three trades give the following results.

Each row is a separate situation. Under the hedge, the gains and losses on the stocks and the futures offset each other, and the total is 0 whichever way the index moves. Under speculation, a rise in the index gives a profit and a fall gives a loss. Under arbitrage, if dividends come in as expected and there are no trading costs, a profit set by how overpriced the futures were at the start remains whichever way the index moves. However, if dividends are lower than expected or costs arise, the profit shrinks and can become a loss. How futures work is covered in Forwards and Futures.

You can tell the three purposes apart by applying the opening definition. For a question that asks "other than", answering "no" means the definition applies.

Figure description

A single trade can come close to more than one definition, so the figure is a guide for applying the definitions in order.

In the three situations in the table above, hedging meets its definition at the first question, arbitrage at the second, and speculation at the third. The speculation situation has no asset whose losses it limits and no second instrument to pair with. It is a trade on a view that the index will rise, so the first and second answers are yes, and the third is yes as well.

Hedging limits losses from price moves with an opposite trade

Hedging is a trade that limits losses from price moves in assets you hold, or plan to hold, by taking an opposite position in futures or options². Take an investor who holds 200 million yen of stocks and, to protect against a fall, sells 10 futures contracts at 20,000 when the index is at 20,000. The size of 10 futures contracts is 20,000 times 1,000 times 10, or 200 million yen, the same as the value of the stocks. To keep the example simple, the futures price is assumed to equal the index at 20,000 and to move by the same amount as the index afterward. The stocks are assumed to move in the same proportion as the index, and interest, dividends, and fees are ignored.

If the index falls to 18,000, the stocks go from 200 million yen to 180 million yen, a loss of 20 million yen. The investor sold the futures at 20,000 and buys them back at 18,000, so the futures make 2,000 times 1,000 times 10, a profit of 20 million yen that covers the loss on the stocks. If the index instead rises to 22,000, the 20 million yen gain on the stocks is wiped out by a 20 million yen loss on the futures. A hedge limits losses at the cost of also giving up the gain from a rise.

A hedge that sells futures to protect stocks you hold against a fall is called a short hedge, and a hedge that buys futures to protect against a rise when you plan to buy stocks later is called a long hedge. In a long hedge, the profit on the futures when prices rise is added to the funds for buying the stocks³. Besides selling futures, buying put options is another way to protect against a fall².

Real stocks do not move exactly with the index, so the loss may not disappear completely. The method of offsetting an option's price moves by trading the underlying asset is covered in Delta Hedging.

Speculation aims to profit from a view on price moves

Speculation is a trade that takes a position in futures or other contracts based on a view of whether the market will rise or fall, aiming to profit by closing it out with an offsetting trade if prices move as expected⁵. Suppose you expect a rise and buy one futures contract at 20,000 when the index is at 20,000. The size of the trade is 20,000 times 1,000, or 20 million yen. If the index rises to 22,000 and you sell the contract, you make 2,000 times 1,000, a profit of 2 million yen, but if your view is wrong and the index falls to 18,000, you lose 2 million yen. For someone who expects a fall and sells futures, the result is the reverse. Fees are ignored.

Futures are traded by depositing margin that is smaller than the size of the trade. As a result, both profits and losses are large compared with the margin⁶. Depending on market moves, you may have to deposit additional margin, or the loss may exceed the margin⁷.

Speculators take on the risk that hedgers want to pass on. Speculating investors play two roles in the market. By trading on their own judgment, they improve the market's price discovery, and they take on the risk that hedgers want to transfer⁵. In the stockholder example in the hedging section, if an investor expecting a rise buys the futures that the stockholder sold, the risk of a fall moves from the stockholder to the investor who bought the futures.

Figure description

This is the profit or loss at expiry for someone who bought a futures contract when the index was 20,000. The vertical axis is in index points; multiply by 1,000 to get the amount per contract. The gain grows by the amount the index is above 20,000, and the loss grows by the amount it is below. Someone who sold the same contract has the mirror image of this line, so the buyer's gain is exactly the seller's loss.

Arbitrage earns a profit from a price gap

Arbitrage is a trade that sells the more expensive and buys the cheaper of two instruments with the same character, and earns the price difference⁸. Investors carry out arbitrage between futures and the cash market (the stocks or other assets underlying the futures). They also do so between contract months (the months in which trading in each contract ends) of a futures contract and between different futures products⁸.

Arbitrage between equity index futures and the cash market compares the actual futures price with the theoretical price. The theoretical price is a guide to the futures price, calculated from the index, the interest rate, the expected dividend yield, and the number of days to expiry⁹¹⁰. Consider a hypothetical example in which the index is at 20,000, there are 73 days (0.2 years) to expiry, the interest rate is 2% a year, and the expected dividend yield is 1% a year. In index points, the interest is 20,000 × 2% × 0.2 = 80 and the dividends are 20,000 × 1% × 0.2 = 40. Adding the interest to the index and subtracting the dividends gives 20,040 as a guide to the theoretical price¹¹.

If the futures price is then 20,200, the futures are 160 above the theoretical price. Selling the futures and buying the underlying stocks when the futures price is above the theoretical price is called cash-and-carry arbitrage (kai-saitei in Japanese). Conversely, when the futures are below the theoretical price, buying the futures and selling the stocks is called reverse cash-and-carry arbitrage (uri-saitei)¹².

As an example of cash-and-carry arbitrage, you borrow 200 million yen at 2% a year, buy 200 million yen of stocks with the same composition as the index, and sell 10 futures contracts at 20,200. Over the 73 days you pay interest of 200 million yen × 2% × 0.2 = 800,000 yen and receive dividends of 200 million yen × 1% × 0.2 = 400,000 yen. For Osaka Exchange's equity index futures, a contract held to expiry is settled by paying or receiving the difference from the special quotation (SQ value), which is calculated from the prices of the stocks in the index¹³. Assuming the stocks can be sold at the same level as the SQ value, here are the results when the index at expiry is 22,000 and when it is 18,000.

If the index is 22,000, the stocks make a profit of 20 million yen and the futures lose (20,200 − 22,000) times 1,000 times 10, or 18 million yen. If it is 18,000, the stocks lose 20 million yen and the futures make 22 million yen. In both cases, after adding the dividends and subtracting the interest, the total is 1.6 million yen, the same as the initial overpricing of 160 times 1,000 times 10. If the futures had been sold at the theoretical price of 20,040, the total would be 0.

As in the hedging example, cash-and-carry arbitrage combines holding stocks with selling futures. The difference is that a hedge sells futures to protect stocks already held, whereas cash-and-carry arbitrage trades the stocks and the futures at the same time after spotting that the futures are overpriced. Instead of waiting for expiry, the arbitrageur may also close both positions with offsetting trades to lock in the profit once the price gap between the futures and the cash market returns to the level of the theoretical price¹².

The example assumed that dividends come in as expected, that the stocks can be put together to match the index, and that there are no trading costs. Real arbitrage involves fees and taxes. Timing losses, market impact, tracking error, and other items are also costs¹⁴. For this reason, investors carry out arbitrage when the gap between the actual futures price and the theoretical price grows beyond a certain level¹⁵.

If these assumptions do not hold, the total moves away from the 1.6 million yen in the example. For instance, if dividends come to only 200,000 yen, half of what was expected, the total falls from 1.6 million yen to 1.4 million yen. If fees and other costs add up to 2 million yen, the total is 1.6 million yen minus 2 million yen, a loss of 400,000 yen.

Because arbitrageurs sell the overpriced futures and buy the underpriced cash stocks, the gap between the futures and cash prices narrows. Arbitrage keeps futures prices at an appropriate level and increases liquidity in both the futures and cash markets¹⁶¹⁵. FX forward rates are also calculated from the current exchange rate and the interest rates of the two currencies, on the assumption that arbitrage links borrowing and lending in yen with borrowing and lending in the foreign currency¹⁷.

Deep diveOsaka Exchange's formula for the theoretical price

The theoretical price of Nikkei 225 Futures is the Nikkei Stock Average multiplied by $e^{(r-\delta)T}$. Here $e$ is the base of the natural logarithm, $r$ is the interest rate, $\delta$ is the expected dividend yield, and $T$ is the number of days to expiry divided by 365¹⁰.

$$F = S \times e^{(r-\delta)T}$$

$S$ is the index and $F$ is the theoretical futures price. Applying this formula to the example in the text ($S$ = 20,000, $r$ = 2%, $\delta$ = 1%, $T$ = 0.2) gives 20,040.04. The guide of 20,040 in the text calculates the interest and dividends with simple interest, and in this example it differs from the formula's value by 0.04.

Notes

1. Pension Fund Association, "先物取引（用語集）" (Glossary: futures trading, in Japanese). ↩

2. Japan Exchange Group, "ヘッジ取引（用語集）" (Glossary: hedging, in Japanese). ↩ ↩²

3. Osaka Exchange, "先物取引のすべて" (All about futures trading, in Japanese; published August 2024), appendix "株価指数先物取引の利用方法" (How to use stock index futures), "（2）ヘッジ取引" ((2) Hedging), page 40. ↩

4. The same booklet, "ヘッジ取引の具体例" (Worked example of hedging), pages 40–41. ↩

5. Osaka Exchange, "利用方法（先物）" (How to use futures), Kitahama Investment School (in Japanese), "スペキュレーション" (Speculation). ↩ ↩²

6. Japan Exchange Group, "先物取引（用語集）" (Glossary: futures trading, in Japanese). ↩

7. Japan Exchange Group, "商品概要" (Product overview), Nikkei 225 Futures (in Japanese), the paragraph below "１単位あたりの例" (Example per unit) under "証拠金" (Margin). ↩

8. Japan Exchange Group, "裁定取引（用語集）" (Glossary: arbitrage, in Japanese). ↩ ↩²

9. Osaka Exchange, "先物取引のすべて" (All about futures trading, in Japanese), "裁定取引の具体例" (Worked example of arbitrage), page 42. ↩

10. Japan Exchange Group, "商品概要" (Product overview), Nikkei 225 Futures (in Japanese), the "理論価格" (Theoretical price) paragraph and its formula. ↩ ↩²

11. The simple-interest guide is 20,000 × (1 + (2% − 1%) × 0.2) = 20,040, the same value as "index + interest − dividends" in the text. The theoretical price calculated with the booklet's formula (see the deep dive) is 20,040.04. ↩

12. Osaka Exchange, "利用方法（先物）" (How to use futures), Kitahama Investment School (in Japanese), "理論価格と裁定取引" (Theoretical price and arbitrage). ↩ ↩²

13. Osaka Exchange, "先物取引のすべて" (All about futures trading, in Japanese), "建玉及び決済について" (Open positions and settlement), "（3）最終決済" ((3) Final settlement), page 38. ↩

14. Osaka Exchange, "先物取引のすべて" (All about futures trading, in Japanese), the paragraph following "（2）異なる限月間の裁定取引（スプレッド取引）" ((2) Arbitrage between contract months (spread trading)), page 42. ↩

15. Osaka Exchange, "先物取引のすべて" (All about futures trading, in Japanese), appendix "株価指数先物取引の利用方法" (How to use stock index futures), "（3）裁定取引" ((3) Arbitrage), page 41. ↩ ↩²

16. Osaka Exchange, "利用方法（先物）" (How to use futures), Kitahama Investment School (in Japanese), the second paragraph of "裁定取引（アービトラージ）" (Arbitrage). ↩

17. Bank of Japan Financial System and Bank Examination Department, Center for Advanced Financial Technology, "スポットレートとその応用" (Spot rates and their applications, in Japanese), "５．フォワード為替" (5. Forward exchange rates), page 14, and "フォワード為替の計算式" (Formula for the forward exchange rate), page 15. ↩