Covered interest rate parity

The following common approximation is valid when S is not too volatile :


An example
In short, assume that

This would imply that one dollar invested in the US < one dollar converted into a foreign currency and invested abroad. Such an imbalance would give rise to an arbitrage opportunity, where in one could borrow at the lower effective interest rate in US, convert to the foreign currency and invest abroad.

The following rudimentary example demonstrates covered interest rate arbitrage (CIA). Consider the interest rate parity (IRP) equation,


Assume:

the 12-month interest rate in US is 5%, per annum
the 12-month interest rate in UK is 8%, per annum
the current spot exchange rate is 1.5 $/£
the forward exchange rate implied by a forward contract maturing 12 months in the future is 1.5 $/£.
Clearly, the UK has a higher interest rate than the US. Thus the basic idea of covered interest arbitrage is to borrow in the country with lower interest rate and invest in the country with higher interest rate. All else being equal this would help you make money riskless. Thus,

Per the LHS of the interest rate parity equation above, a dollar invested in the US at the end of the 12-month period will be,
$1 · (1 + 5%) = $1.05
Per the RHS of the interest rate parity equation above, a dollar invested in the UK (after conversion into £ and back into $ at the end of 12-months) at the end of the 12-month period will be,
$1 · (1.5/1.5)(1 + 8%) = $1.08
Thus one could carry out a covered interest rate (CIA) arbitrage as follows,

1.Borrow $1 from the US bank at 5% interest rate.
2.Convert $ into £ at current spot rate of 1.5$/£ giving 0.67£
3.Invest the 0.67£ in the UK for the 12 month period
4.Purchase a forward contract on the 1.5$/£ (i.e. cover your position against exchange rate fluctuations)
At the end of 12-months

1.0.67£ becomes 0.67£(1 + 8%) = 0.72£
2.Convert the 0.72£ back to $ at 1.5$/£, giving $1.08
3.Pay off the initially borrowed amount of $1 to the US bank with 5% interest, i.e $1.05
The resulting arbitrage profit is $1.08 − $1.05 = $0.03 or 3 cents per dollar.

Obviously, arbitrage opportunities of this magnitude would vanish very quickly.

In the above example, some combination of the following would occur to reestablish Covered Interest Parity and extinguish the arbitrage opportunity:

US interest rates will go up
Forward exchange rates will go down
Spot exchange rates will go up
UK interest rates will go down

Interest rate parity

Interest rate parity, or sometimes incorrectly known as International Fisher effect, is an economic concept, expressed as a basic algebraic identity that relates interest rates and exchange rates. The identity is theoretical, and usually follows from assumptions imposed in economic models. There is evidence to support as well as to refute the concept.

Interest rate parity is a non-arbitrage condition which says that the returns from borrowing in one currency, exchanging that currency for another currency and investing in interest-bearing instruments of the second currency, while simultaneously purchasing futures contracts to convert the currency back at the end of the holding period, should be equal to the returns from purchasing and holding similar interest-bearing instruments of the first currency. If the returns are different, an arbitrage transaction could, in theory, produce a risk-free return.

Looked at differently, interest rate parity says that the spot price and the forward or futures price of a currency incorporate any interest rate differentials between the two currencies.

Two versions of the identity are commonly presented in academic literature: covered interest rate parity and uncovered interest rate parity.

Cost of carry

The cost of carry is the cost of " carring " or holding a position. If long , the cost of carry is the cost of interest paid on a margin account. Conversely, if short, the cost of carry is the cost of paying dividends, or opportunity cost the cost of purchasing a particular security rather than an alternative. For most investments, the cost of carry generally refers to the risk-free interest rate that could be earned by investing currency in a theoretically safe investment vehicle such as a money market account minus any future cash-flows that are expected from holding an equivalent instrument with the same risk (generally expressed in percentage terms and called the convenience yield). Storage costs (generally expressed as a percentage of the spot price) should be added to the cost of carry for physical commodities such as corn, wheat, or gold.

The cost of carry model expresses the forward price (or, as an approximation, the futures price) as a function of the spot price and the cost of carry.


where F is the forward price, S is the spot price, e is the base of the natural logarithms, r is the risk-free interest rate, s is the storage cost, c is the convenience yield, and t is the time to delivery of the forward contract (expressed as a fraction of 1 year).

The same model in currency markets is known as interest rate parity.

For example, a US investor buying a Standard and Poor's 500 e-mini futures contract on the Chicago Mercantile Exchange could expect the cost of carry to be the prevailing risk-free interest rate (around 5% as of November, 2007) minus the expected dividends that one could earn from buying each of the stocks in the S&P 500 and receiving any dividends that they might pay, since the e-mini futures contract is a proxy for the underlying stocks in the S&P 500. Since the contract is a futures contract and settles at some forward date, the actual values of the dividends may not yet be known so the cost of carry must be estimated.

Carrying charge

A carrying charge is the cost of storing a physical commodity, such as grain or metals , over a period of time. The carrying charge includes insurance , storage and interest on the invested funds as well as other incidental costs. In interest rate futures markets, it refers to the differential between the yield on a cash instrument and the cost of the funds necessary to buy the instrument. Also referred to as cost of carry.

The interest expense on money borrowed to finance a margined securities position.

Why should a convenience yield exist?

Users of a consumption asset may obtain a benefit from physically holding the asset (as inventory ) prior to T (maturity) which is not obtained from the futures contract. These benefits include the ability to profit from temporary shortages, and the ability to keep a production process running.

One of the main reasons that it appears is due to availability of stocks and inventories of the commodity in question. Everyone who owns inventory has the choice between consumption today versus investment for the future. A rational investor will choose the outcome that is best.

When inventories are high, this suggests an expected relatively low scarcity of the commodity today versus some time in the future. Otherwise, the investor would not perceive that there is any benefit of holding onto inventory and therefore sell his stocks. Hence, expected future prices should be higher than they currently are. Futures or forward prices Ft,T of the asset should then be higher than the current spot price, St. From the above formula, this only tells us that r − c > 0.

The interesting line of reasoning comes when inventories are low. When inventories are low, we expect that scarcity now is greater than in the future. Unlike the previous case, the investor can not buy inventory to make up for demand today. In a sense, the investor wants to borrow inventory from the future but is unable. Therefore, we expect future prices to be lower than today and hence that Ft,T < St. This implies that r − c < 0.

Consequently, the convenience yield is inversely related to inventory levels.

Convenience yield

A convenience yield is an adjustment to the cost of carry in the non -arbitrage pricing formula for forward prices in markets with trading constraints.

Let Ft,T be the forward price of an asset with initial price St and maturity T. Suppose that r is the continuously compounded interest rate for one year. Then, the non-arbitrage pricing formula should be

Ft,T = Ster(T − t).

However, this relationship does not hold in most commodity markets, partly because of the inability of investors and speculators to short the underlying asset, St. Instead, there is a correction to the forward pricing formula given by the convenience yield c. Hence

Ft,T = Ste(r − c)(T − t).

This makes it possible for backwardation to be observable.

Example: A trader in derivatives market, has observed that the price of 6 month gold futures price is Rs.12,000 per 10 grams and the spot price is Rs.13,710 per 10 grams. The annualized borrowing rate is 12.5% and storage cost is negligible. In this regard, the convenience yield:



12000 = 13710 + (13710 x 0.125 x 6/12 - convenience yield)

CY = Rs. 2566.875; as a percentage of spot price = 18.72%

Known Risks

The 2008-2009 Icelandic financial crisis has among its origins the undisciplined use of the carry trade. The US dollar and the yen have been the currencies most heavily used in carry trade transactions since the 1990s. There is some substantial mathematical evidence in macroeconomics that larger economies have more immunity to the disruptive aspects of the carry trade mainly due to the sheer quantity of their existing currency compared to the limited amount used for FOREX carry trades.

Currency

The term carry trade without further modification refers to currency carry trade: investors borrow low- yielding currencies and lend (invest in) high-yielding currencies. It tends to correlate with global financial and exchange rate stability, and retracts in use during global liquidity shortages.

The risk in carry trading is that foreign exchange rates may change to the effect that the investor would have to pay back more expensive currency with less valuable currency. In theory, according to uncovered interest rate parity, carry trades should not yield a predictable profit because the difference in interest rates between two countries should equal the rate at which investors expect the low-interest-rate currency to rise against the high-interest-rate one. However, carry trades weaken the currency that is borrowed, because investors sell the borrowed money by converting it to other currencies.

By early year 2007, it was estimated that some US$1 trillion may be staked on the yen carry trade. Since the mid-90's, the Bank of Japan has set Japanese interest rates at very low levels making it profitable to borrow Japanese yen to fund activities in other currencies. These activities include subprime lending in the USA, and funding of emerging markets, especially BRIC countries and resource rich countries.

Interest rates

For instance, the traditional income stream from commercial banks is to borrow cheap ( at the low overnight rate, i.e., the rate at which they pay depositors) and lend expensive (at the long-term rate, which is usually higher than the short-term rate).

This works with an upward-sloping yield curve, but it loses money if the curve becomes inverted. Many investment banks, such as Bear Stearns, have failed because they borrowed cheap short-term money to fund higher interest bearing long-term positions. When the long-term positions default, or the short-term money dries up, the bank cannot meet its short-term liabilities and goes under.

According to a popular anecdote, traditional commercial banking was characterized as a "3-6-3" business: borrow at 3%, lend at 6% (thus earning the 3% spread), be on the golf course by 3 pm.While this may have been close to the truth in the market of the 1950s to the 1970s, the modern competitive market ensures that profits are kept more in line with perceived risks.

Carry (investment)

The carry of an asset is the return obtained from holding it (if positive), or the cost of holding it (if negative).

For instance, commodities are usually negative carry assets, as they incur storage costs or may suffer from depreciation, but in some circumstances, commodities can be positive carry assets if the market is willing to pay a premium for its demand.

This can also refer to a trade with more than one leg, where you earn the spread between borrowing a low carry asset and lending a high carry one.

Carry trades are not arbitrages: pure arbitrages make money no matter what; carry trades make money only if nothing changes against the carry's favor.

Dollar versus euro

Not long after the introduction of the euro (€ ; ISO 4217 code EUR) as a cash currency in 2002, the dollar began to depreciate steadily in value.As U.S. trade and budget deficits continued to increase, the euro started rising in value. By December 2004, the dollar had fallen to new lows against all major currencies; the euro rose above $1.36/€ (under €0.74/$) for the first time, in contrast to previous lows in early 2003 (€0.87/$). In the first quarter of 2004 the U.S. dollar, with the advantage of Federal Reserve's policy of raising the interest rates, regained some standing against all major currencies, climbing from €0.78/$ to €0.84/$. However, all gains were lost in the second half of 2004, and the dollar stood at €0.74/$ at the end of 2004. Since 2002, the only year in which the dollar actually recovered against the euro was 2005. Although some analysts previewed the dollar dropping as far as $1.60/€ (€0.63/$), it finished 2005 with an increase against the euro, climbing to €0.83/$. An interest rate reduction by the Federal Reserve on September 18, 2007, raised the euro's value significantly and caused the dollar to fall below €0.70 one month later, to new record lows.Economists like Alan Greenspan suggest that another reason for the continued fall of the dollar is its decreasing role as the world's reserve currency. Jim Rogers declared that he thinks the dollar's value will fall even further, especially against the Chinese yuan. Chinese officials signaled plans to diversify the nation's $1.9 trillion reserve in response to a falling U.S. currency which also set the dollar under pressure. However, a sharp turnaround occurred in late 2008 with the global financial crisis, with the dollar and Japanese yen rising against most world currencies. One reason to this might be that the dollar was regarded as safe-haven and therefore got stronger during the initial phase of the global financial crisis. As a result of the recent global financial crisis, China, the biggest foreign owner of U.S. Treasury securities, and other countries such as India and Russia are backing away from the dollar to diversify their securities. The dollar has rebounded to near multi-year highs as of May 2010 on weakness in the European monetary union which has put pressure on central banks to reinvest in the dollar and away from euros.

Dollarization and fixed exchange rates

Other countries besides the United States use the U.S. Dollar as thier official currency, a process known as official dollarization.For instance , Panama has been using the dollar alongside the Panamanian balnoa as the legal tender since 1904 at a conversion rate of 1:1. Ecuador (2000), El Salvador (2001), and East Timor (2000) all adopted the currency independently. The former members of the U.S.-administered Trust Territory of the Pacific Islands, which included Palau, the Federated States of Micronesia, and the Marshall Islands, chose not to issue their own currency after becoming independent, having all used the U.S. dollar since 1944. Two British dependencies also use the U.S. dollar: the British Virgin Islands (1959) and Turks and Caicos Islands (1973).

Some countries that have adopted the U.S. dollar issue their own coins: See Ecuadorian centavo coins, Panamanian Balboa and East Timor centavo coins.

Some other countries link their currency to U.S. dollar at a fixed exchange rate. The local currencies of Bermuda and the Bahamas can be freely exchanged at a 1:1 ratio for USD. Argentina used a fixed 1:1 exchange rate between the Argentine peso and the U.S. dollar from 1991 until 2002. The currencies of Barbados and Belize are similarly convertible at an approximate 2:1 ratio. In Lebanon, one dollar is equal to 1500 Lebanese pound, and is used inter­changeably with local currency as de facto legal tender. The exchange rate between the Hong Kong dollar and the United States dollar has also been linked since 1983 at HK$7.8/USD, and pataca of Macau, pegged to Hong Kong dollar at MOP1.03/HKD, indirectly linked to the U.S. dollar at roughly MOP8/USD. Several oil-producing Arab countries on the Persian Gulf, including Saudi Arabia, peg their currencies to the dollar, since the dollar is the currency used in the international oil trade.

The People's Republic of China's renminbi was informally and controversially pegged to the dollar in the mid-1990s at ¥ 8.28/USD. Likewise, Malaysia pegged its ringgit at RM3.8/USD in 1997. On July 21, 2005 both countries removed their pegs and adopted managed floats against a basket of currencies. Kuwait did likewise on May 20, 2007, and Syria did likewise in July 2007. However, after three years of slow appreciation, the Chinese yuan has been de facto re-pegged to the dollar since July 2008 at a value of ¥6.83/USD; although no official announcement had been made, the yuan has remained around that value within a narrow band since then, similar to the Hong Kong dollar.

Belarus, on the other hand, pegged its currency, the Belarusian ruble, to a basket of foreign currencies (U.S. dollar, euro and Russian ruble) in 2009.

In some countries such as Peru and Uruguay, the USD is commonly accepted although not officially regarded as a legal tender. In Mexico's border area and major tourist zones, it is accepted as if it were a second legal currency. Many Canadian merchants also accept US dollars, albeit sometimes only at face value. In Cambodia, US notes circulate freely and are preferred over the Cambodian riel for large purchases, with the riel used for change to break 1 USD. After the U.S. invasion of Afghanistan, U.S. dollars are accepted as if it were legal tender. Prices of most big ticket items such as houses and cars are set in U.S. dollars.

U.S. Dollar Index

The U.S.Dollar Index (Ticker :DXY) is the creation of the New York Board of Trade (NYBOT).It was established in 1973 for tracking the value of the USD against a basket of currencies,which,at that time,represented the largest trading partners of the United States. It began with 17 currencies from 17 nations, but the launch of the euro subsumed 12 of these into one, so the USDX tracks only six currencies today.

Euro 57.6%
Japanese yen 13.6%
Pound sterling 11.9%
Canadian dollar 9.1%
Swedish krona 4.2%
Swiss franc 3.6%

The Index is described by the NYBOT as "a trade weighted geometric average".The baseline of 100.00 on the USDX was set at its launch in March 1973. This event marks the watershed between the fixed-rate system of the Bretton Woods regime and the floating-rate system of the Smithsonian regime. Since then, the USDX has climbed as high as the 160s and drifted as low as the 70s.

The USDX has not been updated to reflect new trading realities in the global economy, where the bulk of trade has shifted strongly towards new partners like China and Mexico and oil-exporting countries while the United States has de-industrialized.

The dollar as international reserve currency

The U.S.dollar is an important international reserve currency along with the euro. The euro inherited this status from the German mark, and since its introduction, has increased its standing considerably, mostly at the expense of the dollar. Despite the dollar's recent losses to the euro, it is still by far the major international reserve currency, with an accumulation more than double that of the euro.

In August 2007, two scholars affiliated with the government of the People's Republic of China threatened to sell its substantial reserves in American dollars in response to American legislative discussion of trade sanctions designed to revalue the Chinese yuan. The Chinese government denied that selling dollar-denominated assets would be an official policy in the foreseeable future.

Former Federal Reserve Chairman Alan Greenspan said in September 2007 that the euro could replace the U.S. dollar as the world's primary reserve currency. It is "absolutely conceivable that the euro will replace the dollar as reserve currency, or will be traded as an equally important reserve currency."

International use

The dollar is also used as the standard unit of currency in international markets for commodities such as gold and petroleum ( the latter sometimes called petrocurrency is the source of the term petrodollar). Some non-U.S. companies dealing in globalized markets, such as Airbus, list their prices in dollars.

The U.S. dollar is the world's foremost reserve currency. In addition to holdings by central banks and other institutions there are many private holdings which are believed to be mostly in $100 denominations. The majority of U.S. notes are actually held outside the United States. All holdings of US dollar bank deposits held by non-residents of the US are known as eurodollars (not to be confused with the euro) regardless of the location of the bank holding the deposit (which may be inside or outside the U.S.) Economist Paul Samuelson and others maintain that the overseas demand for dollars allows the United States to maintain persistent trade deficits without causing the value of the currency to depreciate and the flow of trade to readjust. Milton Friedman at his death believed this to be the case but, more recently, Paul Samuelson has said he now believes that at some stage in the future these pressures will precipitate a run against the U.S. dollar with serious global financial consequences.

Price inflation

Price inflation is a rise in the general level of prices of goods and services in an economy over period of time.Ecomists view price inflation as a result or necessary outcome of monetary inflation .

A consumer price index (CPI) is a measure estimating the average price of consumer goods and services purchased by households. The United States Consumer Price Index is a measure estimating the average price of consumer goods and services in the United States. The following chart shows that the average price of consumer goods and services in the United States has been rising significantly since the 1970s.

Purchasing power of U.S. dollar

The following table shows the equivalent amount of goods that , in a particular year, could be purchased with $ 1.The table shows that from 1774 through 2009 the U.S. dollar has lost about 96.4% of its buying power.

The value of $1 over time, in 1776 dollars.Buying power of one U.S. dollar compared to 1774 USD Year Equivalent buying power Year Equivalent buying power Year Equivalent buying power
1774 $1.00 1860 $0.97 1950 $0.33
1780 $0.59 1870 $0.62 1960 $0.26
1790 $0.89 1880 $0.79 1970 $0.20
1800 $0.64 1890 $0.89 1980 $0.10
1810 $0.66 1900 $0.96 1990 $0.06
1820 $0.69 1910 $0.85 2000 $0.05
1830 $0.88 1920 $0.39 2007 $0.04
1840 $0.94 1930 $0.47 2008 $0.04
1850 $1.03 1940 $0.56 2009 $0.04

Value of U.S. dollar

The 5th paragraph of Section 8 of Article 1 of the U.S. Constitution provides that the U.S. Congress shall have the power to "coin money" and to " regulate the valu" of domestic and foreign coins. Congress exercised those powers when it enacted the Coinage Act of 1792. That Act provided for the minting of the first U.S. dollar and it declared that the U.S. dollar shall have "the value of a Spanish milled dollar as the same is now current".

Means of issue of U.S. dollar

New dollars are issued when the Federal Reserve elects to fund the purchase of debt, primarily U.S. Treasury Bonds , by creating new reserves rather than financing the purchase with existing reserves. When the bond issuer spends the money, new dollars enter circulation.

In theory, Federal Reserve Notes are like checks: liabilities drawn on the Federal Reserve Bank. The Fed offsets these liabilities by holding U.S. Treasury Bonds as assets, which are backed by the U.S. Government's ability to levy taxes and repay.

When compared to hard money backed by gold or silver, this debt-based approach has the advantage of making the currency elastic, giving the government a means of expanding or contracting the money supply in response to changing economic conditions. The disadvantage of this approach is inflation. The money supply must be continually expanded in order to finance interest payments on the debt by which it is issued. This devalues the currency, causing inflation.

Banknotes of U.S. dollar

The U.S. Constitution provides that Congress shall have the power to " borrow money on the credit of the United States".Congress has excercised that power by authorizing twelve private companies —the Federal Reserve Banks—to issue Federal Reserve Notes. Those notes are "obligations of the United States" and "shall be redeemed in lawful money on demand at the Treasury Department of the United States, in the city of Washington, District of Columbia, or at any Federal Reserve bank." Federal Reserve Notes are designated by law as "legal tender" for the payment of debts. Congress has also authorized the issuance of more than 10 other types of banknotes, including the United States Note and the Federal Reserve Bank Note. The Federal Reserve Note is the only type that remains in circulation since the 1970s.

The largest denominations of currency currently printed or minted by the United States are the $100 bill and the $100 one troy ounce Platinum Eagle.

$1 and $2 color: White and rich gray
$5 color: Gray and some purple
$10 color: Light yellow
$20 color: Light green
$50 color: Deep blue and purple
$100 color: Rich light blue (Series 2009 redesign is scheduled for release on February 10, 2011)
Currently printed denominations are $1, $2, $5, $10, $20, $50, and $100. Notes above the $100 denomination ceased being printed in 1946 and were officially withdrawn from circulation in 1969. These notes were used primarily in inter-bank transactions or by organized crime; it was the latter usage that prompted President Richard Nixon to issue an executive order in 1969 halting their use. With the advent of electronic banking, they became less necessary. Notes in denominations of $500, $1,000, $5,000, $10,000, and $100,000 were all produced at one time; see large denomination bills in U.S. currency for details. These notes are now collector's items and are worth more than their face value to collectors.

The design of the notes has been accused of being unfriendly to the visually impaired. A U.S. District Judge ruled on November 28, 2006 that the American bills gave an undue burden to the blind and denied them "meaningful access" to the U.S. currency system. The judge ordered the Treasury Department to begin working on a redesign within 30 days.