Question

1. What is the expected standard deviation of the returns of a portfolio that is invested 25 percent in Stock A, 40 percent in Stock B, and the remainder invested in Stock C? (Hint: create a column showing the distribution of returns for the portfolio. Then, find the portfolio's expected return and variance as normally done for a single asset.)

State of Economy			Probability		Return of A	Return of B	Return of C
Boom			0.20		29%	15%	6%
Normal			0.50		11%	12%	13%
Slow Down			0.20		0%	8%	25%
Recession					-10%	5%	30%
	A.	3.21 percent
	B.	1.55 percent
	C.	7.69 percent
	D.	11.71 percent

2.

The returns on the common stock of New Image Products are quite cyclical. In a boom economy, the stock is expected to return 46 percent in comparison to 16 percent in a normal economy and a negative 28 percent in a recessionary period. The probability of a recession is 25 percent while the probability of a boom is 30 percent. What is the standard deviation of the returns on this stock?

	A.	21.42 percent
	B.	27.39 percent
	C.	38.11 percent
	D.	32.48 percent
		3.

The outstanding bonds of Tech Express are priced at $1,092 and mature in 10 years. These bonds have a face value of $1,000, a coupon rate of 7.68 percent, and pay interest annually. The firm's tax rate is 21 percent. What is the firm's after tax cost of debt?

	A.	5.06 percent
	B.	7.68 percent
	C.	4.81 percent
	D.	6.40 percent
		4.

The Timken Company has announced a rights offer to raise $18 million for a new journal. The stock currently sells for $51 per share and there are 2.4 million shares outstanding. The subscription price is set at $45 per share. What is the ex-rights price per share?

	A.	$50.14
	B.	$58.12
	C.	$53.72
	D.	$48.17

Answer 1

1.

25% of portfolio is invested in stock A, 40% of portfolio in stock B and remainder 35% of portfolio in stock C. Probability of boom scenario is 20%, Probability of Normal scenario is 50%, Probability of slowdown scenario is 20% and Probability of recession scenario is 10%.

Boom Scenario

Expected return in boom case = (25% × 29%) + (40% × 15%) + (35% × 6%)

= 7.25% + 6.00% + 2.10%

= 15.35%

Expected return in boom case is 15.35%.

Normal Scenario

Expected return in Normal case = (25% × 11%) + (40% × 12%) + (35% × 13%)

= 2.75% + 4.80% + 4.55%

= 12.10%

Expected return in Narmal case is 12.10%.

Slow Down Scenario

Expected return in Slow down case = (25% × 0%) + (40% × 8%) + (35% × 25%)

= 0% + 3.20% + 8.75%

= 11.95%

Expected return in slow Down case is 11.95%.

Recession Scenario

Expected return in recession case = (25% × -10%) + (40% × 5%) + (35% × 30%)

= -2.50% + 2.00% + 10.50%

= 10%

Expected return in recession case is 10%.

Now, Expected return and standard deviation of portfolio is calculated in excel and screen shot provided below:

Expected return of portfolio is 12.51% and standard deviation is 1.59%.

Option (B) is correct answer.