Series 65 Formula Practice

Question 1

A $10 stock has a beta of 2.0. The expected return in the market, based on its recent performance is 7%, and the risk-free rate as measured by the Treasury bill rate is 2%. Using CAPM, we can calculate the expected return for the security

Answer 1

12%

2% + (2.0 × (7% – 2%)) = 12%.

Question 2

A $10 stock has a beta of 0.5. The expected return in the market is 7% and the risk-free rate 2%. What is the expected return for the security?

Answer 2

4.5%

2% + (0.5 × (7% – 2%)) = 4.5%

Question 3

ABC Company has a beta of -0.5, the market is expected to return 8% this coming year, and investors can earn 2% risk-free in short-term U.S. Treasury bills.

Answer 3

-1%

2% + (-0.5 × (8% – 2%)) = -1%

Question 4

At the beginning of the year, your client, Ms. Jones, had a portfolio with a beta of 1.0. The T-bill rate is 2%, and the market is expected to return 4%. At the end of the year, her actual return showed a positive alpha of 2%. What was her actual return on her portfolio?

Answer 4

6%

Alpha levels can be both positive and negative. Alpha = actual return – expected return (2% = actual return – 4%). Thus, her actual return was 6%.

Question 5

Suppose Ms. Jones owns shares of Technix, whose positive alpha is 2%. The market is expected to return 4%. The beta of her stock is 0.5, and the T-bill rate is 2%. What is the actual return on Technix?

Answer 5

5%

To answer this question, you first must know the expected return of the stock. We can then use CAPM to calculate the stock’s actual return. First, expected return = risk-free rate + (beta × (market return – risk-free rate)), or 2% + (0.5 × (4% – 2%)) = 3%. So if alpha = actual return – expected return, or 2% = actual return – 3%, then the stock’s actual return is 5%.

Question 6

A portfolio has a beta of 1.0. The S&P 500 experiences 8% growth, and the portfolio produces an actual return of 12%. The riskless rate is 2%. What is the alpha of the portfolio?

Answer 6

4%

expected return = 2% + (1 × (8% – 2%)) = 8%.
Next we must calculate alpha.
alpha = actual return – expected return
So, 12% – 8% = 4%.

Question 7

Given the following assumptions for Stock ABC, what is its expected return using the capital asset pricing model (CAPM)? Risk-free rate: 3%; return of broader stock market: 11%; beta: 1.2, standard deviation: 2.

Answer 7

Answer: C. The formula for the capital asset pricing model (CAPM) is given by the following: return on stock = risk-free rate + beta of stock × (return of broad market – risk-free rate). Plugging in for Stock ABC gives: return on Stock ABC = 3% + 1.2 × (11% – 3%) = 12.6%. Note: The standard deviation is not used in the CAPM formula.

Question 8

An investor paid $20 per share for 100 shares of XYZ and a $40 commission. What is the investor’s cost-basis per share?

Answer 8

Answer: $20.40. The $40 commission on a per share basis is $.40 so $2,040 / 100 shares = $20.40 per share. If the investor now sold all 100 shares at $25 for $2,500 with a $40 commission, the proceeds would be $2,500 – $40 commission = $2,460 net. Divided by 100 shares, the net proceeds per share would be $24.60. Therefore, the capital gain per share would be $24.60 – $20.40 = $4.20 per share, or $420 total for the 100 shares.

Question 9

Imagine an investor has a federal tax rate of 27% and a state tax rate of 3%. The investor would like to compare a corporate bond with a 10% yield and a municipal bond issued by the state in which he lives that has a yield of 7.5%.

Answer 9

7%

10% × (1 – 0.30), which equals 7%
after-tax yield on a corporate bond = coupon rate × (1 – tax rate)

Question 10

Susan, a resident of Mississippi, has purchased a Georgia municipal bond with a rate of 5.12%. If Susan’s federal tax bracket is 30% and the state income tax rate is 4%, what would she need to earn on a corporate bond to have a comparable rate?

Answer 10

7.31%

5.12% / (1-.30) = 7.31%
coupon rate / 1- tax rate
Corporate bonds are taxed at the federal and state level. Municipal bonds are not taxed at the federal level, but in this case, it will be taxed at the state level, because Susan is not a resident of Georgia. Thus, to get the comparable corporate rate, we need to divide by 1 minus Susan’s federal rate.

Question 11

Catie, a resident of Georgia, has purchased a Georgia municipal bond with a rate of 5.12%. If Catie is in the 30% federal tax bracket and the state income tax rate is 4%, what would she need to earn on a corporate bond to have a comparable rate?

Answer 11

7.76%

5.12% / (1-.34) = 7.76%
coupon rate / 1- tax rate
This municipal bond will not be taxed at either the federal or state level, because Catie is a Georgia resident. To get the comparable corporate rate, we need to divide by 1 minus the federal plus the state tax rate

Question 12

If you have $100 and you can get 4% annual return on this money, in one year, you will have how much will you have? How about in two years? How about in three years?

Answer 12

Y1: 100(1+.04) = 100 (1.04) = $104
Y2: 100 (1.041.04) = $108.16
Y3: 100 (1.041.04*1.04) = $112.49

FV = Principal*(1+r)t

Question 13

If someone promises you $100 in three years, assuming an interest rate of 3%, how much is that $100 worth today?

Answer 13

100/(1+r)t, 100/(1.031.031.03)
100/ 1.092727 =91.51

PV = FV/(1+r)t

Question 14

If a client invests $5,000 at 6% per year. What will it be worth after four years?

Answer 14

5,000(1.061.061.06*1.06)
5,000(1.26247696)= $6,312.38

FV= principle(1+r)t