Question

A simple optimal portfolio problem is the cash matching problem.

Answer 1

Answer:

The units of the 5-year zero coupon bond that should be purchased in the optimal portfolio is:

= 6 units

Explanation:

a) Data and Calculations:

Spot rates = 5% annually

Yield of a 1-year zero coupon bond = 5%

Yield of a 2-year zero coupon bond = 5%

Yield of a 3-year zero coupon bond = 5%

Yield of a 4-year zero coupon bond = 5%

Yield of a 5-year zero coupon bond = 5%

Yield of a 6-year up to a 10-year zero coupon bond = 5%

Future Monetary Obligations:

YEAR                  1         2         3         4          5         6        7      8      9     10

OBLIGATION 100    200    300     400     500    600    700 800 900 1000

PV factor      1.05 1.1025 1.1576 1.2155 1.2763 etc.

Present value of a 5-year zero coupon bond = $78.35 ($100/1.2763)

Number of units of the 5-year zero coupon bond that should be purchased in the optimal portfolio = 6.382 ($500/$78.35)

= 6 units