Using the data in Example 10.13, compare the logarithmic return on an investment in the following securities over the period from 0 to 3: a) zero-coupon bonds maturing at time 3; b) single-period zero-coupon bonds; c) the money market account.

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a) For an investment of $100 in zero-coupon bonds, divide the initial cash by the price of the bond B(0, 3) to get the number of bonds held, 102.82, which gives final wealth of $102.82. The logarithmic return is 2.78%. b) For an investment of $100 in single-period zero-coupon bonds, compute the number of bonds maturing at time 1 as 100/B(0, 1) ≅ 100.99. Then, at time 1 find the number of bonds maturing at time 2 in a similar way, 100.99/B(1, 2) ≅ 101.54. Finally, we arrive at 101.54/B(2, 3) ≅ 102.51 bonds, each giving a dollar at time 3. The logarithmic return is 2.48%. c) An investment of $100 in the money market account, for which we receive 100A(3) ≅ 102.51 at time 3, produces the same logarithmic return of 2.48% as in b).

Question 10.22: Using the data in Example 10.13, compare the logarithmic ret...

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