CHAPTER 2
FINANCIAL MARKETS AND INSTRUMENTS
2. a.
b. One reason is that the discount yield is computed by dividing the dollar discount from par by the par value, $10,000, rather than by the bill’s price, $9,600. A second reason is that the discount yield is annualized by a 360day rather than a 365day year.
6. a. i. 1 + r = ($10,000/$9,764)^{4} = 1.1002
r = 10.02%
ii. 1 + r = ($10,000/$9,539)^{2} = 1.0990
r = 9.90%
The threemonth bill offers a higher effective annual yield.
b. i. r_{BD} = = 0.0934 = 9.34%
ii. r_{BD} = = 0.0912 = 9.12%
7. a. Price = $1,000 × [1 – 0.03 × ] = $992.5
b. 90day return = = 0.007557 = 0.7557%
c. r_{BEY} = 0.7557% × = 3.06%
d. Effective annual yield = (1.007557)^{365/90} – 1 = 0.0310 = 3.10%
10. a. The index at t = 0 is (60 + 80 + 20)/3 = 53.33. At t = 1, it is (70 + 70 + 25)/3 = 55, for a rate of return of 3.13%.
b.
Stock

Q

P_{0}

Market Value

P_{1}

Market Value

A

200

60

12,000

70

14,000

B

500

80

40,000

70

35,000

C

600

20

12,000

25

15,000

The index at t = 0 is (12,000 + 40,000 + 12,000)/100 = 640. At t = 1, it is also 640, so the rate of return is zero.
c.

Before Splits

After Splits


Stock

P_{0}

Q

P_{0}

Q

P_{1}

A

60

200

30

400

35

B

80

500

20

2,000

17.5

C

20

600

20

600

25

After the splits the index has to remain unchanged so the divisor (which initially was 3) has to be reset. The sum of the three prices after the split is 70, while the index value before splits was 53.33. Therefore 70/d = 53.33 and the new divisor must be 1.3125. The index at t = 1 is (35 + 17.5 + 25)/1.3125 = 59.05 for a return of 10.71%.
d. The total market value of A and B as well as that of the market remain unchanged after the two splits so that the return on the valueweighted index is not affected by the splits (and it is zero).
11. a. The index at t = 0 is (90 + 50 + 100)/3 = 80. At t = 1, it is 250/3 = 83.333, for a rate of return of 4.17%.
b. In the absence of a split, stock C would sell for 110, and the index would be 250/3 = 83.333. After the split, stock C sells at 55. Therefore, we need to set the divisor d such that 83.333 = (95 + 45 + 55)/d, meaning that d = 2.34.
c. The return is zero. The index remains unchanged, as it should, since the return on each stock separately equals zero.
2
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