Understanding Exchange Rates, Spot & Forward Rates, Triangular Arbitrage, and Concepts - P, Study notes of International Economic Relations

Download Understanding Exchange Rates, Spot & Forward Rates, Triangular Arbitrage, and Concepts - P and more Study notes International Economic Relations in PDF only on Docsity! ECN 4861 INTERNATIONAL ECONOMIC PROBLEMS N. BRODSKY, INSTRUCTOR I. THE FOREIGN EXCHANGE MARKET -THE SPOT-OR CURRENT RATE DEFINITION OF EXCHANGE RATE: 1. e = F/D 2. e = D/F THE AMERICAN STANDARD IS 2. e = F/D IF e then the domestic currency "depreciates" IF e then the domestic currency "appreciates" SAY $1.90 = £1 AND 30 DAYS LATER $1.70 = £1 WE SAY THE U.S. DOLLAR appreciates. SAY ¥128 = $1 AND 30 DAYS LATER ¥135 = $1 WE SAY THE U.S. DOLLAR appreciates. THE FORWARD EXCHANGE RATE FN = FORWARD RATE TODAY FOR DELIVERY "N" DAYS INTO THE FUTURE FORWARD PREMIUM fN = e – FN (e=F/D) or FN – e (e=D/F) e e FORWARD RATES ARE AVAILABLE ON 30, 90, 180 DAYS (THIS CORRESPONDS TO TREASURY BILL MATURATIONS) THE RATE IS OFTEN REFERRED TO IN STANDARDIZED PERCENTAGE TERMS. THIS MEANS ANNUALIZED FORM: STANDARD FORWARD PREMIUM PN = e - FN • 360 • 100 (e=F/D) or FN - e • 360 • 100 (e=D/F) e N e N IF THE VALUE OF PN OR fN IS POSITIVE, THEN THE FOREIGN CURRENCY IS SAID TO BE SELLING AT A PREMIUM (YOU PAY MORE DOLLARS IN THE FUTURE (ON DELIVERY) THAN YOU WOULD AT THE SPOT RATE TODAY. IF THE VALUE OF PN OR fN IS NEGATIVE, THEN THE FOREIGN CURRENCY IS SAID TO BE SELLING AT A DISCOUNT (YOU PAY LESS DOLLARS IN THE FUTURE (ON DELIVERY) THAN YOU WOULD AT THE SPOT RATE TODAY. For Thursday January 9, 1992: British £ : P£30 = (0.55066 - .55374)/.55066*(360/30)*100 = - 6.6740 German DM : PDM180 = (1.56006 – 1.60051)/1.56006*(360/180)*100 = - 5.0546 Japanese ¥ : P¥90=(126.295 – 125.290)/126.295*(360/90)*100 = -1.258970 IS THIS ENOUGH INFORMATION? SINCE THE INVESTMENT MUST BE MADE IN D-MARKS, AND THE GERMAN D-MARK COULD APPRECIATE OVER THE INVESTMENT HORIZON, GERMAN YIELDS ARE NOT ENOUGH INFORMATION: YOU NEED TO KNOW THE FORWARD RATE. THE FORWARD EXCHANGE RATE WILL ALLOW YOU TO LOCK IN THE RATE OF RETURN OVER THE INVESTMENT HORIZON: INVESTMENT IN GERMANY IS NOW: RG = (F/e)(1 + i*) WHERE F AND e ARE $-DM FORWARD AND SPOT RATES THIS RESULTS IN THE COVERED INTEREST DIFFERENTIAL: CD = RG - RUS = (F/e)(1 + i*) - (1 + i) OR f + i* - i WHERE f = (F - e)/e SINCE f IS THE FORWARD PREMIUM WE CAN SEE THE CHOICE OF INVESTMENT AS A MATTER OF THE PERCENT FORWARD PREMIUM (DISCOUNT) + INTEREST RATE DIFFERENTIAL WHEN POSITIVE, CD FAVORS INVESTMENT ABROAD, NEGATIVE, INVESTMENT IN THE DOMESTIC MARKET USING FOREIGN PRIME RATES AND USA PRIME (NOT CORRECT - SHOULD USE TREASURY NOTE RATES) For Thursday January 9, 1992: British Prime : 10.50% FORWARD DISCOUNT (30 DAYS) = 6.6740 German Prime: 11.00% FORWARD DISCOUNT (180 DAYS) = 5.0546 Japanese Prime : 6.125% FORWARD DISCOUNT (90 DAYS) = 1.258970 United States Prime: 6.50% CD = British : -6.6740 + 10.50 - 6.50 = -2.6740 German : -5.0546 + 11.00 - 6.50 = -0.5546 Japan : -1.258970 + 6.125 - 6.50 = -1.633970 WE GENERALLY EXPECT CAPITAL TO FLOW INTO THE USA SIMPLE MANIPULATION OF THE CD EQUATION RESULTS IN THE DEFINITION OF COVERED INTEREST PARITY: f = i - i* OR (F - e)/e = i - i* DEVIATIONS FROM COVERED INTEREST PARITY MAY EXIST DUE TO: 1. Transactions costs 2. Information costs 3. Regulations and Central Bank Intervention 4. Capital market imperfections 5. Lack of equivalence in assets] MARKET IMPERFECTIONS RESULT IN A COVERED INTEREST PARITY "BAND" We can graph the relationship between forward premium and interest differential: UNCOVERED INTEREST PARITY Actually, this is a combined speculative and interest rate arbitrage position. An investor must take a position in a foriegn currency to hold foriegn bonds. But without the forward contract, the investor is left "open" or "uncovered", which means he is subject to exchange rate risk. Tests of Uncovered Interest Parity rely on "ex-post" known rates of depreciation of the domestic currency, and assume them to be the "ex-ante" anticipated movement in the exchange rate. This requires perfect forsight. The equation becomes: i = i* + x where x is anticipated rate of depeciation of domestic currency, and i & i* are domestic and foriegn interest rates This implies that all differences in the interest rates are a result of anticipated movement in exchange: i - i* = x Now, consider 2 portfolios: 1: i* + x (uncovered) 2: i* + f (covered) If the uncovered portfolio increases risk (over the covered), then its rate of return should be higher to compensate risk-adverse investors. Call that [R], the risk premium (if < 0, discount). We can say: x = f + R Market equilibrium occurs where anticipated exchange movement = forward premuim + risk premium This also establishes the difference between covered and uncovered interest parity: i - i* = f = x - R Covered interst parity could hold, but uncovered interest parity fails unless we take into account R, the risk premium associated with exchange rate variations. BOP = Pd ex(Yf, Pf/Pd, e) - 1/e Pf im(Yd, Pf/Pd, e) - F(rd, rf) [Nominal Exports] - [Nominal Imports] - [Net Cap Outflow] BOP = Pd ex(Yf, Pf/Pd, e) - 1/e Pf im(Yd, Pf/Pd, e) - F(rd, rf) [---Demand for $---) (---- Supply of $ ----) (-Both-) [N] [real or Quantity] [Nominal] [Real or Quant] BOP = Pd ex(Yf, Pf/Pd, e) - 1/e Pf im(Yd, Pf/Pd, e) - F(rd, rf) (---Demand for $---) (---- Supply of $ ----) (-Both-) FLOW APPROACH TO EXCHANGE RATE DETERMINATION: Supply of $: S = s(Yd, Pf, Pd, rd, rf) + - + - + Demand for $: D = d(Yf, Pf, Pd, rd, rf) + + - + - NATIONAL INCOME ACCOUNTING IN AN OPEN ECONOMY DOMESTIC ABSORBTION: AN  CN + IN + GN DOMESTIC ABSORBTION SPENT EXCLUSIVELY ON DOMESTIC GOODS: ANd  AN - MN  CN + IN + GN - MN GNP IN AN OPEN ECONOMY: YN  CN + IN + GN - MN + XN YN  AN - MN + XN REARRANGE, AN FIND THE BALANCE ON GOODS AND SERVICES IS EQUAL TO THE GAP BETWEEN DOMESTIC INCOME AND ABSORBTION XN  MN + YN - AN GIVEN NO UNILATERAL TRANSFERS, THE CURRENT ACCOUNT BALANCE IS: CAB  YN -AN IF CAB > 0, THERE IS AN EXCESS OF INCOME OVER SPENDING, IF CAB < 0, THERE IS AN EXCESS OF SPENDING OVER INCOME - THIS LED TO ALEXANDER (1952) "ABSORPTION APPROACH" TO BOP SINCE FUNDS ALWAYS FLOW IN THE REVERSE DIRECTION OF GOODS, WE CAN INFER THE FOLLOWING: IF CAB > 0, (NET FLOW OF GOODS OUT) THEN FOREIGN ASSETS ARE BEING ACCUMULATED (FUNDS FLOW IN) OR FOREIGN LIABILITIES DEACCUMULATE IF CAB < 0, (NET FLOW OF GOODS IN) THEN FOREIGN ASSETS ARE BEING DEACCUMULATED (FUNDS FLOW OUT) OR FOREIGN LIABILITIES ACCUMULATE THIS DOES NOT MEAN THE DOMESTIC SYSTEM IS VARYING ITS WEALTH, AS DOMESTIC RESIDENTS MAY BE INVESTING IN DOMESTIC ASSETS - THIS TELLS ABOUT THE PORTFOLIO HELD BY DOMESTIC RESIDENTS (AND FOREIGNERS) CAB  YN - CN - IN - GN (INCOME - ABSOPTION) ADD TAXES (AND SUBTRACT TAXES): CAB  YN - TXN - CN - IN + TXN - GN ---SAVINGS---INVEST---BUDGET- CAB  (SN - IN) + (TXN - GN) PVT SAVINGS BUDGET SURPLUS LET THE GOVERNMENT BUDGET BE IN BALANCE, THEN IF PRIVATE SAVINGS IS IN SURPLUS, THE CAB IS ALSO IN SURPLUS - DOMESTIC RESIDENTS ARE SAVING MORE THAN THEY INVEST AND THEY MUST BE INVESTING ABROAD; IF PRIVATE SAVINGS IS IN DEFICIT, THEN THE CAB IS IN DEFICIT - INVESTMENT IS HIGHER THAN SAVINGS, DOMESTIC RESIDENTS MUST BE BORROWING FROM ABROAD. ASSUME AWAY BONDS: A = Ao + aYF + (M/Pw) Absorption Absorption exceeds income...Trade deficit ...Assets Deaccumulate (M/Pw) will fall back to (M/Pw)E _______________________________ (W/P) = (M/P) = (M/ Pw) Real Wealth, Small Country Case Rearrange the equation to find YF: YF = AE = Ao + aYF + (M/Pw)E And the Money Stock: (M/Pw)E = (1/)[(1-a)YF - Ao] Notice that the only variable is M - (money): thus adjustment is a purely monetary mechanism TO FIND THE TRADE BALANCE: Full Employment Equilibrium: YF = AE = Ao + aYF + (M/Pw)E T = YF - A T = YF -[Ao + aYF + (M/Pw)] T = YF - Ao - aYF - (M/Pw) T = YF - aYF - Ao - (M/Pw) T = (1-a)YF - Ao - (M/Pw) At equilibrium T=0 and (M/Pw)E 0 = (1-a)YF - Ao - (M/Pw)E (M/Pw)E = (1-a)YF - Ao To evaluate the trade balance compare equilibrium with trade equation determination: T = (1-a)YF - Ao - (M/Pw) [--------------] = (M/Pw)E T = (M/Pw)E - (M/Pw) T = [(M/Pw)E - (M/Pw)] [----------------] stock adjustment mechanism Trade Surplus/Deficit will automatically adjust to balance by changes in Money Stock - p represents the speed at which money balances are spent - so implies the adjustment speed. There are 2 speed of adjustment determinants: 1. Value of p - the fraction of the gap between desired and actual money holdings eliminated in a given time period. As p rises, the more of these holdings are eliminated in a given time, so the faster the speed of adjustment to long run equilibrium. (empirical evidence suggests p is small) 2. The size of the gap between exisisting money stock (m/p) and the desired (equilibrium) level (m/p)e - The larger this gap, the larger the changes in money stock - so the faster the adjustment. Can anything damage the automatic adjustment mechanism? If the Central Bank intervenes to counter-act the effects of Bop deficits by injection money into the ststem, then adjustment is THE MONETARY APPROACH TO EXCHANGE RATES (ALSO KNOWN AS THE ASSET MARKET APPROACH) EXCHANGE RATES WILL BE DETERMINED BY THE RELATIVE PRICE OF MONIES - SO WE NEED THE SUPPLY AND DEMAND FOR MONEY: DOMESTIC: M/P = L(i, Y) (-) (+) Real Money Supply = Real Money Demand Foreign: M*/P* = L*(i*, Y*) (-) (+) Apply Absolute Purchasing Power Parity: P = (1/e)P* which can be transformed into: e = P*/P So the exchange rate is reflective of the relative prices. Now solve for prices: M/P = L(i, Y) P/M = 1/L(i, Y) P = M/L(i, Y) symmetrically: P* = M*/L*(i*, Y*) e = (M*/M) L(i, Y)/L*(i*, Y*) Let Y rise (Hold all else constant!): results in an increase in domestic money demand, which results in e - appreciation (opposite of flow approach - which depends on relative prices) Let i rise (Hold all else constant!): results in an decrease in domestic money demand, which results in e  - depreciation Results are diametrically opposed to flow approach - where capital flow is emphasized by r  capital flow in D$  S$  e . Does this form of the monetary approach to the exchange rate do a good job of explaining variations in the exchange rate? consider Table 15-1 (p.476) - It clearly doesn't do all that well - but the approach assumes absolute PPP - If we relax the assumption to it's relative form, we may get better results: Let q be the ratio foriegn prices in domestic terms to domestic prices. q = (1/e)P*/P If q = 1 then Absolute Purchasing Power Parity (PPP) If q > 1 then Foriegn Prices (1/e)P* are higher than domestic If q < 1 then domestic Prices are higher than foreign Solve for e: qP/P* = 1/e e = P*/qP In the relative form of PPP, changes in the exchange rate are reflection of movements in prices in the two countries. We need to consider rates of change: e = P* - P - q where e = de/e If relative PPP holds, then q=0, so: e = P* - P which is the definition of the relative form of PPP Now we have: M/P = L(i, Y) and M*/P* = L*(i*, Y*) in rates of change: M - P = L(i, Y) and M* - P* = L*(i*, Y*) Solve for P: P = M - L(i, Y) and P* = M* - L*(i*, Y*) Now substitute into e = P* - P e =M*-L*(i*, Y*)-[M - L(i, Y)] OPEN ECONOMY MACROECONOMICS Domestic Absorption, Income and Hoarding Absorbtion is a function of income, consumption, investment, taxes and government expenditures: A = A(Y, C, I, T, G) + + + - + For simplicity, and to highlight fiscal policy, assume absorption as a function of income and government expenditure only: A = A(Y, G) = Ao + aY + Go where: Ao, Go are exogenous expenditures a = marginal propensity to spend Hoarding: Excess of income over spending (monetary assets acquired by the public) H = Y - A H = Y - (Ao + aY + Go) H = (1-a)Y - Ao - Go = -(Ao + Go) + sY where s = MPS note; negative hoarding is called "dishoarding" which translates to a deaccumulation of assets. NOMINAL VALUE OF TRADE: TN = XN + MN = PM* - (1/e)P*M (since XN = M*) REAL VALUE OF TRADE: T = TN/P = M* - (P*/eP)M DOMESTIC EXPORTS ARE A FUNCTION OF PRICES, EXCHANGE RATE AND FORIEGN INCOME: M* = M*(P , P*, e, Y*) - + - + DOMESTIC IMPORTS ARE A FUNCTION OF PRICES, EXCHANGE RATE AND DOMESTIC INCOME: M = M(P , P*, e, Y) + - + + so: T = M* - (P*/eP)M T = T(P*,P,e,Y,Y*) For simplicity, assume Trade to be a function of an exogenous component and an income related component: T = To - mY where m = marginal propensity to import Y-A-G, T To --------------------------------------------- Y1 YF -(Ao+Go) EQUILIBRIUM: Y = A + T (Output = Aggregate Demand) Y - A = T H = -(Ao+Go) + sY = To - mY = T solve for Y: sY = (Ao+Go) + To - mY sY + mY = (Ao+Go) + To (s + m)Y = (Ao+Go) + To Y = [(Ao+Go) + To]/(s + m) or let  = 1/(s+m), then: Y = [(Ao+Go) + To] where  = open economy multiplier Fiscal Policy Effects: Devaluation impacts domestic income through the shift in purchases by both domestic and foreign residents toward domestic goods. This means that the larger the elasticities of import demand and foreign import demand, the more powerful the effect of a devalution. How is the Trade Balance affected by domestic income? dT = dTo - mdY =M*(* +  - 1)(e/de) - mM*(* +  - 1)(e/de) =sM*(* +  - 1)(e/de) which is unambiguously positive. Why? Because the effect of a devalution on absorption is always weaker than income itself (a<1) so, income must rise faster than absorption. Since Y-A = T, T must improve. Y-A-G, T To T1 --------------------------------------------- Y2 Y1 YF -(A1+Go) -(Ao+Go) THE LAURSEN-METZLER EFFECT: So far we have assumed that domestic absorption is not affected by changes in relative price. However, a devalation does make imports more expensive than domestic goods. The terms-of-trade effect must reduce real income of domestic residents, and this is what we usually assume generates the reduction in domestic absorption. Reality creates a different scenario. Domestic residents try to maintain their standard of living, thus they increase their spending on foreign goods. Remember that foreign goods are more expensive, so domestic absorption rises as total spending rises to offset the adverse terms-of-trade effect. This is called the Laursen-Matzler Effect. Even though a devaluation improves an economy's competitiveness, it does damage to the residents through the terms-of-trade effect. DEAVALUATION IN THE SHORT AND LONG TERM: THE J-CURVE EFFECT: When a country devalues its currency, we usually turn to the Marshall-Lerner condition to establish a positive impact on trade balance. The reality of the case is that the sum of price elasticities of imports and exports are often quite small in the short run. This is primarily due to 2 slow reactions: 1. Consumer responce lag - the time it takes to recognize the shift in relative prices, and to deal with contracts made under the old exchange rate. 2. Production responce lag - the time it takes to find new customers, and to build new capacities (increasing inputs, possibly increasing plant size). Because of these lags, what we actually see is an intial worsening of the trade balance, as import prices are higher and export prices are lower, and then an improvement over time in the trade balance. Change in the trade balance 0 --------------------------------------------- time (2’’) –BYdY – SfYfdYf – BYfdYf + Irfdr = 0 (3’’) LYdY + Lrdr – dR = dD0 (4’’) LfYdYf + Lfrdr +dR = 0 -SY + BY BYf Ir 0 dY -dI0 -BY -(SYf+BYf) Irf 0 dYf = 0 LY 0 Lr -1 dr dD0 0 LYf Lfr 1 dR 0 = 1 Why 0dI dy > 0 but   0 f dI dy 0? Capital Mobility & Income Specie flow international adjustment. Expansion at home (via G increasing or I increasing) means domestic income increases, imports increase and tighter money (thus capital inflow), thus investment is pulled from the foreign countries – for the foreigners, an increased export demand is also occurring with decreased investment; thus sign indeterminate. Why 0dD dy > 0 & 0 f dD dy > 0? An increase in Domestic Money also increases World Money: Investment rises at home & abroad – thus income rises at both: This cannot occur indefinitely – Domestics will run out of reserves Flexible Exchange Rates Now we drop M & Mf, and hold Df0, R, Rf, constant (but now allow d  0) Why 0dI dy > & 0 f dI dy > 0? If G increases (or I increases), imports rise, and interest rates rise thus drawing capital in & tending to push the exchange rate up, thus pushing imports up further – the foreign country experiences decreased investment but this is offset by increased exports. Fixed Exchange Rates Why 0dI dy > 0 but   0 f dI dy 0? An increase in spending at home results in higher income, increased imports, tighter money-market conditions (and thus capital inflow). Foreign countries get the expansionary effect of increased exports, but also experience capital outflow (possibly due to higher world interest rates – note that f 0 RRW  ) this results in reduced investment spending – so the final results depend on which effect is greater. Why 0dD dy > 0 and 0 f dD dy > 0? An increase in Domestic money results in lower interest rates (thus higher investment and therefore higher domestic income). This also will result in capital outflow and higher imports. Plus, foreign countries experience lower interest rates and higher exports demand – the effects work together to increase foreign income. Flexible Exchange Rates Why 0dI dy > 0 and 0 f dI dy >0? A rise in government spending (or any spending) results in higher income and higher interest rates (via the transactions demand for money). This results in capital inflow, thus any depreciation due to the rise in domestic income is met with a tendency for appreciation due to the capital inflow. For foreign income, the increase in domestic income drives up domestic imports (thus foreign exports): the capital flow effect is diminished by the movements of the exchange rate – thus we generally expect the income expansion effect to dominate. 0dD dy > 0 and 0 f dD dy < 0? A rise in domestic money pushed down interest rates, and decreases the exchange rate, both effects reinforces each other (via higher investment and higher exports). This results in lower imports (we expect price (exchange) to dominate), thus foreign income tends to suffer. Capital Mobility with Fixed Exchange Rates – Fiscal Policy As G increases, r increases, funds flow in, R increases, LM increases Cap Mobility/Fixed Exchange Rates – Monetary Policy As D increases, r decreases, funds flow out, R decreases, LM decreases