Workshop 1 Answers

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Finance 261 Workshop 1
Answers
1. You have been given the following probability distribution for the return on ABC stock:
	State of Economy
	Probability
	Return
	Boom
	0.3
	20%
	Normal
	0.4
	10%
	Bust
	0.3
	-10%
What is the expected return on ABC stock? 
Expected return = 0.3×20% + 0.4×10% + 0.3×(-10%) = 7%
2. You have been given the following probability distribution for the return on XYZ stock:
	State of Economy
	Probability
	Return
	Boom
	0.35
	20%
	Normal
	0.3
	10%
	Bust
	0.35
	-10%
	
What is the return standard deviation of XYZ stock?
Expected return = 0.35×20% + 0.3×10% + 0.35×(-10%) = 6.5%
Variance = 0.35×(0.2-0.065)2+0.3×(0.1-0.065)2+0.35×(-0.1-0.065)2=0.016275
Standard deviation = (0.016275)1/2 = 12.76%
 
3. Suppose that the variance of a portfolio is a function of w: Var(RP) = 100(1-w)2+200w2. What is the value of w that minimizes the variance? 
(1-w)2 = 1-2w+w2
Var(RP) = 100(1-w)2+200w2 = 100(1-2w+w2)+ 200w2 =300w2 – 200w + 100
Vertex: w = -(-200)/(2×300) =1/3
Or 
Derivative = 600w – 200.
Setting equal to 0: w = 1/3
4. Consider the SML equation: . Stock 1 and Stock 2 have expected returns of 10% and 20% with betas of 0.5 and 1.5, respectively. What should the risk-free rate Rf be?
Stock 1: 10% = Rf + 0.5×(E[RM]- Rf)
Stock 2: 20% = Rf + 1.5×(E[RM]- Rf)
Subtracting equation 1 from equation 2: 10 = (E[RM]- Rf)
Rf = 5%
5. A $1 investment can be made for two years at 6% p.a. or for five years at 7% p.a. now. If you take the two-year investment option, what would be the break-even annual return for year three, four, and five?
(1.06)2×(1+x)3 = (1.07)5 → x = (1.075 / 1.062)1/3 -1 = 7.67%
6. Assuming an investor is in the 15% tax bracket, what taxable equivalent must be earned on a security to equal a tax exempt municipal bond yield of 5.5%?
7. The coupon rate on tax-exempt bond is 5.6%, and the rate on a taxable bond is 8%. Both bonds sell at par. At what tax bracket (marginal tax rate) would an investor be indifferent between the two bonds?
If the after-tax yields are equal, then: 
Solving for t, we find that t=0.30 or 30%
8. (2013SC Test) A 90-day $1000 par Treasury bill was just issued at $995. What is the discounted (quoted) yield based on the issuance price? 
A. 0.5%
B. 2%
C. 2.5%
D. 4%
	(1000 – 995) / 1000 × 360 / 90 = 2%
9. (2012SC Test) An investor buys a T-bill at a quoted yield of 4.80 with 150 days to maturity. The investor's actual (annualized) investment yield on this investment was _____. 
A. 4.80%
B. 4.97%
C. 4.67%
D. 5.13%
(Assuming $1,000 face value but any face value would work)
Price = 1,000 × (1 – 0.0480 × 150 / 360) = $980
Investment yield = (20 / 980) × (365 / 150) = 4.97%