All bonds in the market have a $1,000 face value. You are faced with the following spot rates: Maturity (years) 1 2 3 Spot rate 2.0% 4.5% 6.0% Suppose you want to create a synthetic forward arrangement from zero-coupon bonds, where you lend $1,000 in 1 year and collect the proceeds at the end of year 2 at an appropriate interest rate derived from this pure yield curve. What would be your position and size of investment in shorter term zero-coupon bonds; and what would be your position and size of investment in longer term zero-coupon bonds?