173A Practice Problems PDF

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Practice Problems for Exam 1...

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Example 1 Suppose you bought a share of XYZ Co. one year ago at $45 per share. Over the last year, you received $0.27 in dividends. At the end of the year, the stock sells for $48. How did you do? Example 2 Compute the four-year holding period return for an investment that provides the following returns: Year

Return

1

10%

2

-5%

3

20%

4

15%

Example 3 Suppose the returns on common stock from 2010 to 2013 are 0.1370, 0.3580, 0.4514, and -0.0888. Whatis the average or mean return over these four years? Example 4 Calculate the geometric average return for S&P 500 large-cap stocks for a five-year period using the following numbers: Year

S&P 500 Returns

1

13.75%

2

35.70%

3

45.08%

4

-8.80%

5

-25.13%

Example 5 -Compute the annualized return for the weekly return of 0.2%. -If the return for 15 days is 0.4%, compute the annualized return.

Example 6 Suppose the returns on common stock from 2010 to 2013 are 0.1370, 0.3580, 0.4514, and -0.0888.Compute the variance and standard deviation for this sample. Example 7 Compute the expected return and risk for the following investment:

Problem 1 Suppose a stock had an initial price of $75 per share, paid a dividend of $1.20 per share during the year, and had an ending share price of $86. Compute the percentage total return, dividend yield, and capital gains yield. - Rework the problem assuming the ending share price is $67.

Problem 3 A stock had returns of 16.12%, 12.11%, 5.83%, 26.14%, and -13.19% over the past five years, respectively. What was the holding period return for the stock? Problem 4 What are the portfolio weights for a portfolio that has 135 shares of Stock A that sells for $47 per share and 105 shares of Stock B that sells for $41 per share?

Problem 6 Security F has an expected return of 10% and a standard deviation of 43% per year. Security G has an expected return of 15% and a standard deviation of 62% per year. a) What is the expected return on a portfolio composed of 30% of Security F and 70% of Security G? b) If the correlation between the returns of Security F and Security G is 0.25, what is the standard deviation of the portfolio described in part a?

Problem 8 Suppose the risk-free rate is 4.2% and the market portfolio has an expected return of 10.9%. The market portfolio has a variance of 0.0382. Portfolio Z has a correlation with a market of 0.28 and a variance of 0.3285. According to the CAPM, what is the expected return on portfolio Z?

PRACTICE PROBLEMS 1. You hold a portfolio consisting of a $5,000 investment in each of 20 different stocks. The portfolio beta is equal to 1.12. You have decided to sell a coal mining stock (β = 1.00) at $5,000 net and use the proceeds to buy a like amount of a mineral rights company stock (β = 2.00). What is the new beta of the portfolio? 2. Calculate the rate of return for the Wagner Assets Management Group, which holds 4 stocks. The market's rate of return is 15.0%, the risk-free rate is 7.0%, and the Fund's assets are as follows:

3. Explain variance and standard deviation. 4. Explain correlation. 5. Suppose an investor starts with a portfolio consisting of one randomly selected stock. As more and more randomly selected stocks are added to the portfolio, what happens to the portfolio’s risk? Explain the formula that relates total risk, market risk, and diversifiable risk. 6. Which is the best measure of risk for an asset held in isolation, and which is the best measure for an asset held in a diversified portfolio? 7. According to the Capital Asset Pricing Model, what measures the amount of risk that an individual stock contributes to a well-diversified portfolio? Define this measurement. 8. What is a characteristic line? How is this line used to estimate a stock’s beta coefficient? 9. What is the Security Market Line (SML)? How is beta related to a stock’s required rate of return? 10. Explain the efficient frontier. TRUE/FALSE (Questions 11 – 20)

11. The tighter the probability distribution of its expected future returns, the greater the risk of a given investment as measured by its standard deviation. 12. When adding a randomly chosen new stock to an existing portfolio, the higher (or more positive) the degree of correlation between the new stock and stocks already in the portfolio, the less the additional stock will reduce the portfolio's risk. 13. Market risk refers to the tendency of a stock to move with the general stock market. A stock with above-average market risk will tend to be more volatile than an average stock, and its beta will be greater than 1.0. 14. An individual stock's diversifiable risk, which is measured by its beta, can be lowered by adding more stocks to the portfolio in which the stock is held. 15. If investors are risk averse and hold only one stock, we can conclude that the required rate of return on a stock whose standard deviation is 0.21 will be greater than the required return on a stock whose standard deviation is 0.10. However, if stocks are held in portfolios, it is possible that the required return could be higher on the stock with the low standard deviation. 16. A stock's beta measures its diversifiable risk relative to the diversifiable risks of other firms. 17. A stock's beta is more relevant as a measure of risk to an investor who holds only one stock than to an investor who holds a well-diversified portfolio. 18. A stock with a beta equal to −1.0 has zero systematic (or market) risk.

19. Bad managerial judgments or unforeseen negative events that happen to a firm are defined as "company-specific," or "unsystematic," events, and their effects on investment risk can in theory be diversified away. 20. The Y-axis intercept of the SML represents the required return of a portfolio with a beta of zero, which is the risk-free rate.

Problem 1 Company ABC recently completed its IPO. The stock was offered at a price of $14 per share. On the first day of trading, the stock closed at $19 per share. What was the initial return on ABC? Who benefited from this underpricing? Who lost, and why? 18

Problem 2 • A company sold 4 million shares in its IPO, at a price of $18.50 per share. Management negotiated a fee (the underwriting spread) of 7% on this transaction. What was the dollar cost of this fee?

INITIAL PUBLIC OFFERINGS (IPO) 1. A group of investment bankers who pool their efforts to underwrite a security are known as a(n)____________________________________________

2. Empirical evidence suggests that new equity issues are generally underpriced by _______% on average. 3. A_____ ____________________ IPO occurs when the investment banker buys the securities for less than the offering price and accepts the risk of not being able to sell them. 4. Under the _______________________ IPO, the underwriter does not purchase the shares but merely acts as an agent trying to sell the shares for the best possible price.

5. The preliminary prospectus is also called a(n) ____________________________

6. Aaron Inc went public at $10 per share. Aaron's investment banker charged them $0.70 per share for the IPO. This fee is called a(n):______________________________ 7. At the end of the road show, customers inform the underwriters of their interest by telling the underwriters how many shares they may want to purchase. Although these commitments are nonbinding, the underwriters' customers value their long-term relationships with the underwriters, so they rarely go back on their word. The underwriters then add up the total demand and adjust the price until it is unlikely that the issue will fail. This process for coming up with the offer price based on customers’ expressions of interest is called___________________.

8. _________ allows the underwriter to issue more stock amounting to 15% of the original offer size, at the IPO offer price. It is used to cover both oversubscription and excess demand.

9. What are the major advantages and disadvantages of going public?

10. What is the difference between best efforts and firm commitment IPOs? Define auction IPO.

11. What are the two ways of selecting underwriters and what are the characteristics of each?

12. Describe the mechanics of an IPO. a. What are some SEC regulations regarding sales of new securities? b. What is a road show? What is book building? c. What is underpricing? What is greenshoe provision?

13. Describe the four characteristics of IPOs that puzzle financial economists.

15. Your firm has 10 million shares outstanding, and you are about to issue 5 million new shares in an IPO. The IPO price has been set at $20 per share, and the underwriting spread is 7%. The IPO is a big success with investors, and the share price rises to $50 on the first day of trading. a) How much did your firm raise from the IPO?

b) What is the market value of the firm after the IPO? c) Assume that the post-IPO value of your firm is its fair market value. Suppose your firm could have issued shares directly to investors at their fair market value, in a perfect market with no underwriting spread and no underpricing. What would the share price have been in this case, if you raise the same amount as in part (a)?

d) Comparing part (b) and part (c), what is the total cost to the firm’s original investors due to market imperfections from the IPO?...