Forward rate. Using the spot rates and three months interest rates above, calcul

Question

Forward rate. Using the spot rates and three months interest rates above, calculate the 90-day forward rates for the following: SHOW ALL WORK a. Japanese yen/U.S. dollar exchange rate b. Japanese yen/Australian dollar exchange rate c. Australian dollar/U.S. dollar exchange rate Gross Domestic Product Industrial Unemploy Forecast Forecast Production Rate Country Latest Qtr Qtr* 2007e 2008e Recent Qtr Latest Australia 4.3% 3.8% 4.1% 3.5% 4.6% 4.2% Japan 1.6% -1.2% 2.0% 1.9% 4.3% 3.8% US 1.9% 3.8% 2.0% 2.2% 1.9% 4.7% Consumer Prices Interest Rates Forecast 3-month 1-yr Govt Bond Country Year Ago Latest 2007e Latest Latest Australia 4.0% 2.1% 2.4% 6.90% 6.23% Japan 0.9% -0.2% 0.0% 0.73% 1.65% US 2.1% 2.8% 2.8% 4.72% 4.54% Trade Balance Current Account Current Units (per US$) Last 12 mos Last 12 mos Forecast 07 Country (billion $) (billion $) (% of GDP) Oct 17th Year Ago Australia -13.0 -$47.0 -5.7% 1.12 1.33 Japan 98.1 $197.5 4.6% 117 119 US -810.7 -$793.2 -5.6% 1.00 1.00 Source: Data abstracted from The Economist, October 20, 2007, print edition. Unless otherwise noted, percentages are percentage changes over one year. Rec Qtr = recent quarter. Values for 2007e are estimates or forecasts.

Explanation / Answer

Forward rates can be defined as the way the market is feeling about the future movements of interest rates. They do this by extrapolating from the risk-free theoretical spot rate. For example, it is possible to calculate the one-year forward rate one year from now. Forward rates are also known as implied forward rates. To compute a bond's value using forward rates, you must first calculate this rate. After you have calculated this value, you just plug it into the formula for the prices of a bond where the interest rate or yield would be inserted. Example: An investor can purchase a one-year Treasury bill or buy a six-month bill and roll it into another six-month bill once it matures. The investor will be indifferent if they both produce the same result. An investor will know the spot rate for the six-month bill and the one-year bond, but he or she will not know the value of a six-month bill that is purchased six months from now. Given these two rates though, the forward rate on a six-month bill will be the rate that equalizes the dollar return between the two types of investments mentioned earlier. Answer: An investor buys a six-month bill for $x. At the end of six months, the value would equal: x(1 + z1) where z1 = one half of the bond equivalent yield on the six month spot rate. F= one half the forward rate (expressed as a BEY) of a six-month rate six months from now. If he bought the six-month bill and reinvested the proceeds for another six months the dollar return would be calculated like this: X(1 +z1) (1 + F) For the one year investment the future dollars would be x(1 +z)2 So F = (1 + z2)2/ (1 + z1) - 1 Then double F to get the BEY. Here are some numbers to try in this formula: Six-month spot rate is 0.05 = 0.025 = z1 1-year spot rate is 0.055 = 0.0275= z2 F = ( 1.0275)2/ (1.025) -1 F = .030 or .06 or 6% BEY To confirm this: X(1.025)(1.03) = 1.05575 X(1.02575)2 = 1.05575

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