2 covered and uncovered interest arbitrage 19 2.1 covered interest arbitrage without distortion 19 2.2 No-arbitrage condition with bid-spread 24 2.3 deviations from the CIP no-arbitrage condition 26 2.4 Combining covered arbitrage with three currencies 36. so ET, ET, et –1( St) is the expected value of the exchange rate that will prevail at t when the expectation is given at t – 1.
DEFINITION OF ARBITRAGE
TWO-CURRENCY ARBITRAGE
In the presence of a bid-ask spread, arbitrageurs buy (from market makers) at the higher bid rate and sell (to market makers) at the lower bid rate (note that Sb< Sa). Let us now consider the no-arbitrage condition in the presence of a bid-offer spread.
THREE-CURRENCY ARBITRAGE
Therefore, if the no-arbitrage condition (1.29) is violated such that (1.31) is valid, three-currency arbitrage will be profitable by . Now let's see what happens if the arbitrageur follows the sequence x® ® ®x, starting with a unit of x.
MULTI-CURRENCY ARBITRAGE
Equations (1.38) and (1.41) are used to calculate the bid and ask exchange rates when currency is the numeraire. If the bid-ask spread is the same for all exchange rates, this is a situation.
EXAMPLES
- COVERED INTEREST ARBITRAGE WITHOUT DISTORTIONS
- THE NO-ARBITRAGE CONDITION WITH BID–OFFER SPREADS
- DEVIATIONS FROM THE CIP NO-ARBITRAGE CONDITION
- COMBINING COVERED ARBITRAGE WITH THREE
It can be shown that the profitability of an x to y arbitrage is lower in the presence of bid-offer spreads. To be more precise, recall that the equation of the no-arbitrage line in Figure 2.5 is ix – iy = f.
CURRENCY ARBITRAGE
UNCOVERED INTEREST ARBITRAGE
Another specification of the no-arbitrage condition can be obtained by manipulating equation (2.39). This is because if the arbitrager wants to go long on the high interest rate currency, any gains from the interest rate differential will be offset by the depreciation of the currency.
COMMODITY ARBITRAGE
The LOP can be generalized by assuming that the latter applies to every commodity. Moreover, equation (3.8) can be written in the following form, making it something like an exchange rate determination model.
ARBITRAGE UNDER THE GOLD STANDARD
Similarly, the gold import point, which is the lower bound of the exchange rate, is given by. The exchange rate can move between the gold import and export points, but not outside this range.
ARBITRAGE BETWEEN EUROCURRENCY AND DOMESTIC INTEREST RATES
In the absence of a bid-offer spread, a no-arbitrage condition would take the form. In the presence of a bid-offer spread, the no-arbitrage condition would take shape.
EUROCURRENCY–EUROBOND ARBITRAGE
The absence of regulatory requirements on the euro currency market, which makes borrowing and lending cheaper than on the domestic market. Borrowers are of higher quality and creditworthiness than in the domestic market, which makes the risk premium lower in the Eurocurrency market.
ARBITRAGE BETWEEN CURRENCY FUTURES AND FORWARD CONTRACTS
Buying a bond and holding it until maturity when it pays V(1 + iy) units of your or V(1 + iy)funit x at the current forward rate. If the bond sells at par such that P= V, equation (3.22) reduces to the no-arbitrage CIP condition, ix – iy = f.
REAL INTEREST ARBITRAGE
The left-hand side of equation (3.28) is the real return on currency x, while the right-hand side is the real return on y expressed in terms of currency x. The first type of arbitrage maintains uncovered interest parity, while the second type maintains purchasing power parity.
UNCOVERED ARBITRAGE WHEN THE CROSS RATES ARE STABLE
For example, –5.62 is the yen interest rate minus the Australian dollar interest rate. For example, by going short the Swiss franc and long the Norwegian krone, an arbitrageur can gain over four percentage points on the interest rate differential.
If i x < Sbj j, a short position on the base currency and a long position on the portfolio must be taken. By the end of the 1990s, the profitability of the operation would have been lower due to the convergence of the KWD interest rate on the weighted average interest rate of the basket component currencies.
MISCONCEPTIONS ABOUT ARBITRAGE
The no-risk condition is satisfied in the case of covered interest arbitrage, since all the decision variables (interest rates and exchange rates) are known in advance. This condition is the equality of the exchange rates across financial centers in the case of two-point arbitrage;.
DEFINITION AND MEASUREMENT OF FOREIGN EXCHANGE RISK
Variance or standard deviation is a measure of risk because it represents the dispersion of the rate of change around its mean value. In this case, the expected value of the rate of change of the exchange rate is calculated as
VALUE AT RISK
In this case, the VAR (with a probability of 1%) can be calculated by identifying the lowest 1% of the percentage change in the exchange rate and then applying that value to the size of the position. They suggest that investors consider risk and the possibility of loss throughout the investment horizon; otherwise, their wealth may not survive to the end of the investment horizon.
DEFINITION AND MEASUREMENT OF EXPOSURE TO FOREIGN EXCHANGE RISK
Case 4: Vy is positively and linearly related to the exchange rate If Vy is an increasing linear function of the exchange rate, then. The curve in the lower part of figure 4.6 has an increasing positive slope, which means that the exposure increases as the exchange rate increases.
TRANSACTION EXPOSURE
The exposure in this case is a measure of the sensitivity of the net position to changes in the exchange rate. Thus, any gain (loss) on the long position would be exactly offset by the loss (gain) on the short position, so that the change in the net base currency value of the position would be zero.
ECONOMIC AND OPERATING EXPOSURE
Consider Figure 4.9, which shows four different options for the effect of exchange rate changes on operating cash flows relative to the base currency, x. The selling price is set in currency x, so changes in the exchange rate do not affect Pxi.
A FORMAL TREATMENT OF OPERATING EXPOSURE
The effect on costs in terms of currency xis is also calculated by differentiating Cx with respect to S, which gives. The effect of a change in the exchange rate on the cost in terms of xis given by d d.
TRANSLATION EXPOSURE
The balance sheet contains the values of assets and liabilities at the end of the accounting period (which can be a year, a quarter or a month). All items are translated at the current exchange rate prevailing at the end of the accounting period (the closing rate).
WHY DO FIRMS HEDGE EXPOSURE TO FOREIGN EXCHANGE RISK?
According to this view, any loss made by the hedger on the hedged transaction represents an insurance premium paid on the risk-taking speculator. According to this view, hedging is a type of arbitrage that is engaged only when the hedger perceives a promising opportunity for profit.
TO HEDGE OR NOT TO HEDGE?
In the 1950s, Modigliani and Miller (1958) demonstrated by coming up with the Modigliani-Miller theorem that the mode of financing does not determine the value of the firm. However, Moosa cautions against the danger of interpreting this result to mean that exposure to currency risk should never be hedged.
THE BASIC PRINCIPLES OF HEDGING
This (relative) gain is equal to the difference between the base currency value of the asset under the no-hedge and hedge decisions. In this case, the base currency value of the combined position (the asset and the hedging instrument) is unaffected.
MONEY MARKET HEDGING OF SHORT-TERM TRANSACTION EXPOSURE
At time t 1, the base currency loan matures, so the principal and interest must be repaid. At time t + 1, the base currency loan matures, so the principal and interest must be repaid.
FORWARD AND FUTURES HEDGING OF SHORT-TERM TRANSACTION EXPOSURE
If the position is hedged, the value of the liability in the base currency KFt will remain unchanged. The upper part of the chart shows the profit/loss on the unhedged position relative to the exchange.
OPTIONS HEDGING OF SHORT-TERM TRANSACTION EXPOSURE
The contract is awarded and the actual exchange rate turns out to be less than the strike rate (St+1 < St). The contract is not awarded and the current rate turns out to be less than the exercise rate (St+1 < St).
FINANCIAL HEDGING OF LONG-TERM TRANSACTION EXPOSURE
Parallel loans (or sequential loans) can be used to hedge long-term payables and receivables in the same way as swaps.
OTHER FINANCIAL AND OPERATIONAL TECHNIQUES OF HEDGING TRANSACTION EXPOSURE
Within the neutral zone, liabilities are converted to S, which means that x is the value of the currency of the liability KS. If the exchange rate falls below the lower bound of the neutral zone such that St+1 The bottom line on firm value is that operational hedging benefits shareholders only when used in combination with financial hedging strategies. Operating exposure can be reduced by increasing the sensitivity of revenues and reducing the sensitivity of expenses to exchange rate movements. If the subsidiary's currency is expected to depreciate, direct fund adjustment methods include: (i) pricing exports in hard currency and imports in base currency, (ii) investing in hard currency securities and (iii) replacing hard currency loans with base currency loans. Even if the subsidiary's earnings in foreign currency are not actually converted to the parent company's base currency, depreciation in foreign currency results in a translation loss in the consolidated accounts. Indirect methods include (i) adjusting transfer prices; (ii) accelerating the payment of dividends, fees and royalties; and (iii) adjusting the leads and lags of the inter-subsidiary accounts. The industrial sector is a key determinant of the use of third-party derivatives, especially exchange-traded derivatives. The rate of return on the unhedged spot position and between t– 1 and tis is determined by. For now, let's define the rate of return on the futures position as St. Myers and Thompson (1989) argued that conventional hedge ratio estimation procedures are based on the unconditional rather than the more appropriate conditional variances and covariances. Myers (1991) and Baillie and Myers (1991) also suggested that estimating an optimal hedge ratio may require the necessary conditions. The state of the system H(t) is not directly observable, but can be observed through RU(t). Equation (6.52) shows the recursive nature of the calculation. 2001) suggest that the hedge ratio should be estimated from a nonlinear shape model. If the hedge ratio and test statistic are calculated on the basis of the full sample, it is a sample test. The sample's average domestic currency values of the debts or receivables are defined as respectively Therefore, the hedge ratio must be adjusted with changes in the delta of the option. The fourth reason is that it is possible for the structure of the underlying asset to change. Tables 6.3 and 6.4 report the corresponding results when the base currency is the Swedish krona rather than the US dollar. In Figure 6.8(a), the base currency is the US dollar, while the exposure currency is the pound sterling.
HEDGING OPERATING EXPOSURE
HEDGING TRANSLATION EXPOSURE
WHAT DO FIRMS DO IN PRACTICE?
THE CONCEPT OF THE HEDGE RATIO
MEASURING THE OPTIMAL HEDGE RATIO
EMPIRICAL MODELS OF THE HEDGE RATIO
EVALUATING THE EFFECTIVENESS OF HEDGING
STATIC AND DYNAMIC HEDGING
AN ILLUSTRATION USING CROSS CURRENCY HEDGING
