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 360-day rather than a 365-day 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

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. 90-day 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	P0	Market Value	P1	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	P0	Q	P0	Q	P1
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 value-weighted 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.