Assume the current yield curve is 5% for all maturities. Now, consider two portfolios: The first portfolio is currently worth $0100, and is a combination of two zero-coupon bonds. In particular, this portfolio has $050 invested in a zero coupon bond that matures one year from now, and it has $050 invested in a zero coupon bond that matures 19 years from now. (Note: these are not face values, but rather present values, as indicated by the units $0.)

1A) Assuming annual compounding, determine the maturity value (or equivalent, face value) for each of these two zero-coupon bonds.

1B) Determine the duration (Macaulay or modified your choice) of this portfolio. The second portfolio is also currently worth $0100, and has all of its value invested in a zero-coupon bond that matures 10 years from now.

1C) Assuming annual compounding, determine the maturity value for this zero-coupon bond portfolio.

1D) Determine the duration (Macaulay or modified your choice) of this portfolio. Now, consider purchasing the first portfolio and shorting the second portfolio, and then holding this portfolio value for one year. 1E) What is the initial cost of this entire portfolio?

1F) Graph the final value of this portfolio for the range of y = 1% - 10%. What do you conclude about the profit-loss of this portfolio? Is this an arbitrage opportunity? If so, what does this tell you about your assumptions that the yield curve is required to move in parallel shifts?