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BUS 431a: Investment and Portfolio Management

SPRING 2013, AUBG

Quiz 4(a)Solution GuideProblem 1 (8 points): Table 12.B contains data on market advances and declines. Calculate cumulative .breadth and decide whether this technical signal is bullish or bearish. If the trading volume in advancing shares on day 1 was 300 million shares, while the volume in declining issues was 200 million shares, what was the Trin statistics for that day? Was Trin bullish or bearish?Day AdvancesDeclinesDayAdvancesDeclines

19067046970702

265398671002609

37217898903722

45039689850748

5497109510766766

Solution:DayAdvancesDeclinesNet AdvancesCumulative Breadth

1906704202202

2653986-333-131

3721789- 68-199

4503968-465-664

54971,095-598-1,262

6970702268-994

71,002609393-601

8903722181-420

9850748102-318

107667660-318

The signal is bearish as cumulative breadth is negative; however, the negative number is declining in magnitude, indicative of improvement. Perhaps the worst of the bear market has passed.

Trin =

This is a slightly bullish indicator, with average volume in advancing issues a bit greater than average volume in declining issues.

Problem 2 (12 points): Assume you have a 1-year investment horizon and you are trying to choose among three bonds. All have the same degree of default risk and mature in 10 years. The first is a zero-coupon bond that pays $1000 at maturity. The second has an 8% coupon rate and pays the $80 coupon once per year. The third has a 10% coupon rate and pays the $100 coupon once per year.a. (3 points) If all these three bonds are now priced to yield 8% to maturity, what are their prices? b. (3 points) If you expect their yields to maturity to be 8% at the beginning of the next year, what will their prices be then? What is your before-tax holding-period return on each bond?c. (3 points) If your tax bracket is 30% on ordinary income and 20% on capital gains income, what will your after-tax rate of return be on each bond? d. (3 points) Recalculate your answers to part b) under the assumption that you expect the yield to maturity on each bond to be 7% at the beginning of next year.Solution:

Zero coupon8% coupon10% coupon

a. Current prices$463.19$1,000.00$1,134.20

b. Price 1 year from now$500.25$1,000.00$1,124.94

Price increase$ 37.06$ 0.00 $ 9.26

Coupon income$ 0.00$ 80.00$100.00

Pre-tax income$ 37.06$ 80.00$ 90.74

Pre-tax rate of return8.00%8.00%8.00%

Taxes*$ 11.12$ 24.00$ 28.15

After-tax income$ 25.94$ 56.00$ 62.59

After-tax rate of return5.60%5.60%5.52%

c. Price 1 year from now$543.93$1,065.15$1,195.46

Price increase$ 80.74$ 65.15$ 61.26

Coupon income$ 0.00$ 80.00$100.00

Pre-tax income$ 80.74$145.15$161.26

Pre-tax rate of return17.43%14.52%14.22%

Taxes**$ 19.86$ 37.03$ 42.25

After-tax income$ 60.88$108.12$119.01

After-tax rate of return13.14%10.81%10.49%

* In computing taxes, we assume that the 10% coupon bond was issued at par and that the decrease in price when the bond is sold at year end is treated as a capital loss (tax saving) and therefore is not treated as an offset to ordinary income.

** In computing taxes for the zero coupon bond, $37.06 is taxed as ordinary income (see part (b)); the remainder of the price increase is taxed as a capital gain.PAGE 2

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