## Stocks and Stock Markets

Stock represents ownership of a corporation. The stockholders, or shareholders, are the holders of the stock. There are different types of stock, but in this book we study common stock.1

A corporation in need of funds may issue stock to private investors. The investors purchase shares of stock in the company. These investors assume a large amount of risk in return for the possibility of growth of the company and a corresponding increase in the value of the shares. If the company is successful, then it may decide to "go public" and offer shares of stock to the general public. This is accomplished through an initial public offering. If in the future the company wants to raise additional funds, then it may have a secondary public offering. It is important to realize that the corporation receives its money when the shares are issued. Any trading after that point takes place between the shareholders and the persons wishing to purchase the stock, and does not directly represent a profit or loss to the company.

Investors who purchase stock may receive dividends periodically (usually quarterly). Thus, the investor may profit in two ways: through an increase in the value of the stock and through the receipt of dividends. There can be substantial risk for the shareholders, but historically stocks have been a very good investment for individuals who hold stocks for long periods of time.

Corporations sometimes use stock splits to create more shares of the stock at a lower price per share. For example, if a company declares a two-for-one stock split, then each shareholder receives two new shares for each old share of the stock. The price of each new share is initially one-half the price of an old share. Companies may do this to attract new buyers since the new price is less than the old price. Less frequently, a company may declare a reverse

1 Owners of common stock have voting rights and are entitled to the earnings of the company after all obligations are paid.

stock split. For example, it may declare a two-for-one reverse split. In this case one new share is issued for every two old shares. A company may do this to attract institutional investors, who may have a minimum price requirement per share.

The first stock market in the United States originated in Philadelphia in 1790. It eventually became known as the Philadelphia Stock Exchange. The New York Stock Exchange (NYSE), initiated in 1792, is the largest stock exchange in the world. As many as one billion shares are traded during a single day on the NYSE. Trading on this exchange occurs auction style. The buyers and sellers have the option of sending bids and offers to the exchange and accepting the bids and offers from others at the exchange. Stock is sold to the highest bidder and bought at the lowest offer. The NASDAQ (National Association of Securities Dealers Automatic Quotation System) is another major United States stock exchange. As with the NYSE, over one billion shares have been traded on this exchange during some trading days. This exchange differs in operation from the NYSE in that orders are placed and trades are made electronically.

There are several types of risk involved in the purchase and sale of stock. Among these are economic risk, interest rate sensitivity, the possibility of company failure, company management problems, competition from other companies, and governmental rulings that may negatively affect the company. In order to study some of these risks, we break companies into three different groups, depending on the CAPITALIZATION—the total value of issued shares2—of the company.3

Common Stock Issuer Corporation

Risks Default, Exchange Rate, Interest Rate, Market Price, Volatility, Political

The largest companies are called big caps or large caps. In general, these companies have a very high capitalization (over $10 billion). These are large companies with an established track record. There is usually little possibility of company failure. Stock prices are usually relatively high, and thus there may not be a high growth potential. Many of these companies pay regular dividends.

Mid-cap companies have a capitalization of around $1.5 billion to $10 billion. These companies usually have a higher growth potential than big cap companies.

Small-cap companies have a capitalization of less than $1.5 billion. These companies have the highest growth potential but also have a corresponding higher chance of company failure.

2 The total value of issued shares is the product of the share price and the number of shares issued. Shares that have been issued to investors are frequently called "outstanding shares".

3 The capitalization cut-off values between these groups are approximate.

### 9.1 Buying and Selling Stock

In order to buy or sell stock in the United States, the investor uses an investment firm registered with the appropriate governmental agencies—the Securities and Exchange Commission (SEC) and the National Association of Securities Dealers (NASD). The person actually making the transactions for the firm is called a broker.4

The fee or commission charged for the transaction is an important consideration. Fees are highest for a full-service broker, who can also provide investment advice. Investors placing trades through the Internet usually pay lower commissions. It is important to note that a commission is charged for both buying and selling stock.

There are different ways to buy and sell stock. The most common way is to pay the full price in cash. For example, if Helen Kendrick buys 500 shares of a stock when the price is $20 a share, then she pays $10,000 to her investment firm plus the commission for the purchase. If the stock increases in price to $30 per share, then she sells the stock through her investment firm, receiving $15,000 less commission for the sale. So Helen makes a profit of $5,000 less any commissions.

Suppose that Helen and Hugh Kendrick both buy the same stock on a regular monthly basis using different methods. Helen buys 10 shares every month, while Hugh buys $100 worth of the same shares, regardless of the number that can be purchased for that amount. The method of investing used by Hugh is called DOLLAR COST AVERAGING. We discuss these two methods in more detail.

Let S(t) be the stock price at time t. If we buy the same number of shares, N, at times t = 1 and t = 2, then we pay NS(1) + NS(2) for a total of 2N shares, so the average price per share is

If we buy the same number of shares at times t = 1,...,n, then the average price per share is

If we use dollar cost averaging and spend D dollars to buy shares at times t = 1 and t = 2, then we pay 2D for a total of D/S(1) + D/S(2) shares, so the average price per share is

4 We use the terms "the firm" and "the broker" interchangeably.

If we spend D dollars to buy shares at times t = 1,...,n, then the average price per share is

The question we want to answer is, "Which method gives the lower average price per share?"

First, we concentrate on n = 2. If we look at the difference between the average prices per share, then we see that

This difference is positive unless 5(1) = 5(2), in which case it is zero. Thus, unless 5(1) = 5(2), dollar cost averaging gives the lower average share price if n = 2. If 5(1) = 5(2), then both methods give the same average price per share.

This can be generalized to n time intervals by considering the sign of the quantity nt™-rnfnsk nsrwt(£5(t))(Sm)-

Now, the Cauchy-Schwarz inequality (see Appendix A.3 on p. 249) states that

\t=i j \t=i / \t=i with equality if and only if either at = Xbt (t = 1, 2,...,n) for some constant A, or bt = 0 (t = 1, 2,..., n). With at = v/5(t) and bt = 1/^fS{i), we see that n

t=i / \t=i sw with equality if and only if v/5(i) = A/v/5(t), that is, 5(1)) = 5(2) = ••• = 5(n) = A. Thus, unless 5(1) = 5(2) = ••• = 5(n), then dollar cost averaging gives the lower average price per share. If 5(1) = 5(2) = ••• = 5(n), then both methods give the same average price per share.

This leads to the following theorem.

### Theorem 9.1. The Dollar Cost Averaging Theorem.

If we are buying shares of stock, then dollar cost averaging gives a lower average price per share than buying a fixed number of shares on a regular basis. If we are selling shares, then selling a fixed number of shares on a regular basis gives a higher average price per share than dollar cost averaging.

Another way to buy stock is BUYING ON MARGIN, which allows investors to leverage their purchases. An investor who wishes to buy stock on margin must set up a margin account with a broker. The investor may then purchase stock in this account using money borrowed from the broker. However, the investor is required to deposit a down payment on the purchase of the stock. The required minimum down payment, the margin equity, is 50% of the purchase price of the stock.5 This is called the margin requirement. The equity in the margin account is the difference between the current market value of the shares and the money owed to the broker for the purchase of the stock, the debit balance. As the market value of the shares fluctuates then so will the equity in the margin account. Although the margin requirement applies only to the initial purchase of the stock, the investor is required to maintain sufficient equity in the margin account at all times. The required minimum equity, the required (maintenance) equity, is a specified proportion, the maintenance level, of the current market value of the shares. This is called the maintenance requirement.

We illustrate this with the following example. An investor opens a margin account with a deposit of $5,000 and borrows $5,000 from the broker, so the debit balance is $5,000. The investor uses the $10,000 to buy 500 shares of stock at $20 a share. At this point the investor has a total of $10,000 —$5,000 = $5,000 in equity. In this example, the maintenance requirement is 25% of the market value of the shares in the account. This means that the equity in the account must be at least 25% of the market value of the shares. The required equity is 0.25 x $10,000 = $2,500, which is smaller than the equity of $5,000, so the investor satisfies the maintenance requirement.

This is expressed symbolically in Table 9.1, where m is the maintenance level (expressed as a decimal).

Price |
Number |
Market |
Debit Equity |
Required |
Margin |

Shares |
Value |
Balance |
Equity |
Equity | |

S |
N |
V = NS |
D E = V - D |
mV |
0.5V |

$20 |
500.00 |
$10,000.00 |
$5,000.00 $5,000.00 |
$2,500.00 |
$5,000.00 |

5 The rate of 50% is the rate in effect in the United States as of July, 2006.

We consider three scenarios.

1. The price of the stock rises to $30 per share.

(a) If the investor sells all of the shares, then the investor makes a profit of 500 x ($30 — $20) = $5,000 less any commissions and interest charged for the loan.

(b) If the investor sells no shares, then because the market value of the shares is now V = NS = 500 x $30 = $15,000, but the debit balance is still D = $5, 000, the equity is now E = V — D = $15,000 — 5,000 = $10,000. The required equity is mV = 0.25 x $15,000 = $3,750, so the maintenance requirement is satisfied. The margin equity is 0.5V = 0.5 x $15,000 = $7,500. Thus, there is excess equity in the margin account of $10,000 — $7,500 = $2,500.

This excess equity can be used to borrow an additional $2,500/0.5 = $5,000 to purchase $5,000/$30 = 166.67 additional shares. The market value of the shares is now V = 666.67 x $30 = $20,000, and the investor has a debit balance of D = $5,000 + $5,000 = $10,000.6 The equity is E = V — D = $20,000 — $10,000 = $10,000, the required equity is 0.25V = 0.25 x $20,000 = $5,000, and the margin equity is 0.5V = 0.5 x $20,000 = $10,000. As long as the stock price rises, the investor can buy additional shares by borrowing from the broker without investing more money. This is an example of leveraging money. Table 9.2 follows this example as the stock price increases from $20 to $50 a share assuming that the excess equity is always used to purchase additional shares on margin.

Price |
Number |
Market |
Debit |
Equity |
Required |
Margin |

Shares |
Value |
Balance |
Equity |
Equity | ||

$20 |
500.00 |
$10,000.00 |
$5,000.00 |
$5,000.00 |
$2,500.00 |
$5,000.00 |

$30 |
500.00 |
$15,000.00 |
$5,000.00 |
$10,000.00 |
$3,750.00 |
$7,500.00 |

$30 |
666.67 |
$20,000.00 |
$10,000.00 |
$10,000.00 |
$5,000.00 |
$10,000.00 |

$40 |
666.67 |
$26,666.67 |
$10,000.00 |
$16,666.67 |
$6,666.67 |
$13,333.33 |

$40 |
833.33 |
$33,333.33 |
$16,666.67 |
$16,666.67 |
$8,333.33 |
$16,666.67 |

$50 |
833.33 |
$41,666.67 |
$16,666.67 |
$25,000.00 |
$10,416.67 |
$20,833.33 |

$50 |
1000.00 |
$50,000.00 |
$25,000.00 |
$25,000.00 |
$12,500.00 |
$25,000.00 |

At this stage the investor owns 1,000 shares with a market value of $50,000, and the equity is $25,000. The value of the investor's position in the stock has quintupled! It is important to note that the investor pays commissions on each purchase and pays interest on the loans.

6 Note that at this point the broker loaned the investor another $5,000 for the purchase of additional shares, bringing the debit balance to $10,000.

2. The price of the stock falls to $15 per share. At this point the required equity is mV = mNS = 0.25 x 500 x $15 = $1,875, and the equity is E = V-D = 500 x $15-$5,000 = $2,500, so the maintenance requirement is satisfied. These calculations are summarized in Table 9.3.

Price |
Number Shares |
Market Value |
Debit Balance |
Equity |
Required Equity |
Margin Equity |

$20 $15 |
500.00 500.00 |
$10,000.00 $7,500.00 |
$5,000.00 $5,000.00 |
$5,000.00 $2,500.00 |
$2,500.00 $1,875.00 |
$5,000.00 $3,750.00 |

3. The price of the stock falls to $10 per share. At this point the required equity is mV = 0.25 x 500 x $10 = $1,250, and the equity is E = V - D = 500 x $10 - $5,000 = $0. The value of the shares equals the amount owed for the purchase of the stock! Thus, the maintenance requirement is not met, and the investor receives a maintenance call from the broker because the investor owes $1,250. To meet the maintenance requirement the investor is required to deposit $1,250 into the margin account, increasing the equity in the account so that the maintenance requirement is met.7 If the price continues to fall, then the investor is required to deposit additional money to meet the maintenance requirement. It should be noted that the investor's potential loss is limited to the original price of the shares plus commissions plus interest on the loan. Table 9.4 follows this example as the stock price decreases from $20 to $5 a share.

Price |
Number |
Market |
Debit |
Equity |
Required |
Margin |

Shares |
Value |
Balance |
Equity |
Equity | ||

$20 |
500.00 |
$10,000.00 |
$5,000.00 |
$5,000.00 |
$2,500.00 |
$5,000.00 |

$15 |
500.00 |
$7,500.00 |
$5,000.00 |
$2,500.00 |
$1,875.00 |
$3,750.00 |

$10 |
500.00 |
$5,000.00 |
$5,000.00 |
$0.00 |
$1,250.00 |
$2,500.00 |

$10 |
500.00 |
$5,000.00 |
$3,750.00 |
$1,250.00 |
$1,250.00 |
$2,500.00 |

$5 |
500.00 |
$2,500.00 |
$3,750.00 |
-$1,250.00 |
$625.00 |
$1,250.00 |

$5 |
500.00 |
$2,500.00 |
$1,875.00 |
$625.00 |
$625.00 |
$1,250.00 |

At this point the investor has paid a total of $3,125 in maintenance fees8 to meet the maintenance requirement. This is in addition to the initial

### 7 The investor could also sell some shares.

8 When the price falls to $10 a share, the investor pays $1,250. When it falls to $5 a share the equity is —$1,250, and the required equity is $625, so the investor pays $625 + $1,250 = $1,875, for a total of $1,250 + $1,875 = $3,125.

deposit of $5,000. If the stock price continues to fall, then the investor is required to deposit more money, but the total amount of the maintenance fees can never exceed $5,000, the original debit balance.

Notice from Table 9.4 that somewhere between a share price of $15 and a share price of $10, there must be a price, S, at which the required equity equals the equity, below which a maintenance call is issued. In this case that will occur when

A natural question to ask is, "To what level can the stock price fall before a maintenance call is issued?" This is answered in the following theorem.

Theorem 9.2. The Long Sale Maintenance Level Theorem.

If a stock is purchased on margin, if the original market value of the shares purchased is Vo, if the original equity is Eo, and if the maintenance level is m, then the minimum market value, V*, for which the equity, E, is equal to or greater than the required equity (and so does not generate a maintenance call) is

Proof. We notice that D = Vo — Eo is the debit balance, the money owed to the broker for the purchase of the stock. However, if V is the current market value of the shares and E is the current equity, then V — E is also the money owed to the broker for the purchase of the stock (why?), so

At the minimum market value V* we have E* = mV*, so

We now show that (Vo — Eo)/(1 — m) is the minimum market value.

If V < (Vo — Eo)/(1 — m), then the current market value is less than 1/(1 — m) times the money owed to the broker for the purchase of the stock. This means that V < (V — E)/(1 — m), which gives E < mV, a maintenance call. □

Example 9.1. To avoid a maintenance call, what is the minimum level to which the market value of the stock can fall in a margin account containing 500 shares if the original market value is $10,000, if the original equity is $5,000, and if the maintenance level is 0.25? At what price per share does this occur?

Solution. Here Vo = 10000, Eo = 5000, and m = 0.25, so the minimum market value of the stock is 1/0.75 x ($10,000 - $5,000) = $6,666.67. The required equity is 0.25 x $6,666.67 = $1,666.67, and the equity is $6,666.67 - $5,000 = $1,666.67. At this level the price per share of the stock is $6,666.67/500 = $13.33, in agreement with our previous result. A

If an investor believes that a stock is going to decrease in value, then the investor may borrow shares from the broker, and then sell the stock. This is called Short Selling. If the stock decreases in value, then the investor may purchase an equivalent number of shares at the lower price, and use those shares to repay the loan.

The following example illustrates this. An investor wishes to short sell 100 shares of stock, which is currently selling at $50 per share. The market value of the stock is 100 x $50 = $5,000. The margin requirement is 50% of the market value of the stock, so the investor deposits 0.50 x $5,000 = $2,500 in a margin account, and the broker loans the investor 100 shares. The investor then sells the stock for $50 per share, and receives 100 x $50 = $5,000 (less commissions). So the investor has a credit balance of $2,500 + $5,000 = $7, 500 (the sum of the proceeds from the sale plus the initial deposit).

Because the investor must return the loaned shares to the broker, if there is an increase in price, then the investor loses money on the stock, and the investment firm incurs a risk. Therefore, there is a maintenance requirement for short sales. We assume that the maintenance requirement is 30%, which in this example is 0.3 x $5,000 = $1,500. This means that the equity in the account must be at least 30% of the value of the shares at all times. The equity is the difference between the credit balance and the current market value of the stock, so in this example the equity is $7,500 — $5,000 = $2,500, and the maintenance requirement is satisfied.

This is shown symbolically in Table 9.5, where m is the maintenance level (expressed as a decimal).

Credit |
Price |
Number of |
Market |
Equity |
Required |

Balance |
Per Share |
Shares |
Value |
Equity | |

C |
S |
N |
V = NS |
E = C - V |
mV |

$7,500 |
$50 |
100 |
$5,000 |
$2,500 |
$1,500 |

We consider two cases.

1. The price of the stock falls to $40 per share.

(a) If the investor buys the stock at $40 per share, and returns the shares to the firm, then the investor makes a profit of 100 x ($50 — $40) = $1,000, less commissions on the sale and purchase of the shares and any interest due to the broker on the loan of the shares.

(b) If the investor does not buy the stock at this time, then because the market value of the stock is $40 x 100 = $4,000, the required equity is 30% of $4,000, that is, 0.3 x $4,000 = $1,200. The equity is $7,500 -$4,000 = $3, 500. So if the price falls, then the equity is greater than the required equity, and the maintenance requirement is satisfied. This is summarized in Table 9.6. In fact any equity in excess of 50% of the current price can be used for further short selling. In this case 0.50 x $4,000 = $2,000, so there is $1,500 in excess equity. The investor could use this to borrow and sell $1,500/0.50 = $3,000 worth of stock.

Credit |
Price |
Number of |
Market |
Equity |
Required |

Balance |
Per Share |
Shares |
Value |
Equity | |

$7,500 |
$50 |
100 |
$5,000 |
$2,500 |
$1,500 |

$7,500 |
$40 |
100 |
$4,000 |
$3,500 |
$1,200 |

2. The price of stock rises to $60 per share. In this case, the required equity is 0.30 x $6,000 = $1,800, and the equity is $7,500 - $6,000 = $1,500, so the investor pays an extra $300 ($1, 800 — $1, 500) to satisfy the maintenance requirement. If the stock price rises rapidly, then the investor can lose an unlimited amount of money, whereas the investor's profit is limited to the proceeds of the sale less any costs (commissions and interest on the loan of the shares). This makes short selling extremely risky. Table 9.7 illustrates this. Notice that the maintenance fee paid when the price of the stock rises is the difference between the required equity and the equity before the fee is deposited.

Credit |
Price |
Number of |
Market |
Equity |
Required |

Balance |
Per Share |
Shares |
Value |
Equity | |

$7,500 |
$50 |
100 |
$5,000 |
$2,500 |
$1,500 |

$7,500 |
$60 |
100 |
$6,000 |
$1,500 |
$1,800 |

$7,800 |
$60 |
100 |
$6,000 |
$1,800 |
$1,800 |

$7,800 |
$70 |
100 |
$7,000 |
$800 |
$2,100 |

$9,100 |
$70 |
100 |
$7,000 |
$2,100 |
$2,100 |

$9,100 |
$80 |
100 |
$8,000 |
$1,100 |
$2,400 |

$10,400 |
$80 |
100 |
$8,000 |
$2,400 |
$2,400 |

$10,400 |
$90 |
100 |
$9,000 |
$1,400 |
$2,700 |

$11,700 |
$90 |
100 |
$9,000 |
$2,700 |
$2,700 |

$11,700 |
$100 |
100 |
$10,000 |
$1,700 |
$3,000 |

$13,000 |
$100 |
100 |
$10,000 |
$3,000 |
$3,000 |

In this example, the investor originally deposits $2,500 in the margin account to short sell the stock. When the price reaches $100 per share, the investor has paid an additional $5,500 in maintenance fees.9 With short selling there is no upper limit to the amount of money one can lose! In this example, once the price of the stock reaches $60 per share, for every $1,000 increase in the market value of the stock the investor must deposit an additional $1,300 to satisfy the maintenance requirement.

Notice from Table 9.7 that somewhere between a share price of $50 and a share price of $60, there must be a price, S, at which the required equity equals the equity, above which a maintenance call is issued. In this case that will occur when

A natural question to ask is, "To what level can the stock price rise before a maintenance call is generated?" This question is answered in the following theorem.

Theorem 9.3. The Short Sale Maintenance Level Theorem.

If an investor short sells a stock and has an initial credit balance of Co, and if the maintenance level is m, then the maximum level, V*, to which the market value of the stock can rise and not generate a maintenance call, is

Proof. If a stock is purchased on margin, if the original market value of the shares purchased is Vo, and if the original equity is Eo, then Co = Vo + Eo. If V is the current market value of the shares, and if E is the current equity, then we have

Co = V + E, as long as the equity has remained at least as large as the required equity. (Why?) At the maximum level V* we have E* = mV* and Co = V* + E*, which must be solved for V *, giving

9 When the price of this stock reaches $100 per share there have been five increases in price, each one generating a maintenance fee. The total of these additional maintenance fees is ($1,800 - $1,500) + ($2,100 - $800) + ($2,400 - $1,100) + ($2,700 - $1,400) + ($3,000 - $1,700) = $5,500.

To show that (Vo ± Eo)/(1 ± m) is the maximum level, suppose that v>VI±E.

Then the equity is

1 + m so E = C0 — V < mV, a maintenance call. □

Example 9.2. To avoid a maintenance call, what is the maximum level to which the market value of a stock can rise in a margin account containing 100 shares and an initial credit balance of $7,500 if the maintenance level is 0.3? At what price per share does this occur?

The required equity is 0.3 x $5,769.23 = $1,730.77, and the equity is $7,500 — $5,769.23 = $1,730.77. At this level the price per share is $5,769.23/100 = $57.69, in agreement with our previous result. A

Solution. Here C0 = 7500 and m = 0.3, so the maximum market value

### 9.2 Reading The Wall Street Journal Stock Tables

Section C (Money and Investing) of The Wall Street Journal (WSJ) contains tables for the New York Stock Exchange and the NASDAQ. There are explanatory notes for both.

The following stock table is taken from The Wall Street Journal of Wednesday, October 11, 2000. The latest trading day, mentioned below, is Tuesday, October 10, and the previous trading day is Monday, October 9.

52 Weeks Yld Vol Net

Hi Lo Stock Sym Div % P/E 100s Hi Lo Close Chg

We now explain each of these entries, one by one.

• 52 Weeks Hi: $49.58 is the highest price of the stock during the preceding 52 weeks including the current week, excluding the latest trading day.

• 52 Weeks Lo: $26.38 is the lowest price of the stock during the preceding 52 weeks including the current week, excluding the latest trading day.

• Stock: McDonalds is the company name.

• Sym: MCD is the company ticker symbol. Usually, companies with ticker symbols of three or fewer letters are traded on the NYSE, and those with four or more on the NASDAQ.

• Div: $0.22 is the latest annual cash dividend.

• Yld %: 0.7% is the dividend expressed as a percentage of the closing price (Close), namely (0.22/29.94) x 100 = 0.7348, which is 0.7 rounded to one decimal place.

• P/E: 21 is the price to earnings ratio, which is obtained by dividing the closing price (Close) by the total earnings per share over the previous four quarters. Thus, the earnings per share is $29.94/21 = $1.4257. There are various ways of interpreting a P/E ratio of 21. One way is: If the price per share stays constant, then it takes 21 years for the total earnings per share to equal the current price per share. A second way is: It costs the stockholder $21 for every $1 the company earns.

• Vol 100s: Approximately 1,944,800 McDonalds' shares were traded (daily and unofficial).

• Hi: $30.38 is the stock's highest price on the latest trading day.

• Lo: $29.94 is the stock's lowest price on the latest trading day.

• Close: $29.94 is the stock's closing (that is, last) price on the latest trading day.

• Net Chg: —$0.13 is the change in the closing price of the stock on the latest trading day from the closing price on the previous trading day. Thus, the closing price on the previous trading day is $30.07.

### 9.3 Problems Walking

9.1. Use the Internet to find the ticker symbols and closing prices on April 10, 2006 for the following stocks: AT&T, International Paper, and Verizon.

9.2. Use the Internet to find the following information for Microsoft.

(a) What was the first day that Microsoft's stock was traded publicly?

(b) What is the highest price for Microsoft from the date in (a) to the present? (Note that there were several stock splits during this time. What does "highest price" mean in this context?)

9.3. Helen Kendrick buys 10 shares of stock once a month for 4 months. Hugh Kendrick buys $100 worth of the same stock each month at the same time as Helen. Who should have the lower cost per share if the price per share changes over the 4 month period? Verify this if the stock prices are $20, $21, $22, and $23 over the 4 months.

9.4. When is it better to sell a fixed number of shares on a regular basis rather than using dollar cost averaging if one is selling stock?

9.5. Helen Kendrick buys 100 shares on margin. If the margin requirement is 50%, if the maintenance requirement is 25%, and if the stock is selling for $30 a share, then at what price would she receive a maintenance call? Create a table similar to Table 9.4 on p. 155 with stock prices of $30, $25, $20, $15, and $10.

9.6. Referring to Problem 9.5, Hugh Kendrick, believing that the stock price will fall, short sells 100 shares. If the maintenance requirement for short sales is 30%, then at what price would Hugh receive a maintenance call? Create a table similar to Table 9.7 on p. 158 with share prices of $30, $35, $40, $45, and $50.

9.7. Turn to Section C in the latest edition of The Wall Street Journal, and find the listing for AT&T. What is the closing price? What is the closing price on the previous trading day? Estimate the earnings per share. How is the earnings calculated? How many shares were traded?

9.8. On which exchange (the NYSE or the NASDAQ) is the stock with ticker symbol CSCO listed? Find the listing in the latest edition of The Wall Street Journal. Explain each of the symbols and numbers listed for this stock.

9.9. Let S(t) be the price of XYZ at time t in months. Assume that S(1) = 10, S(2) = 15, S(3) = 18, S(4) = 20, and S(5) = 24. Wendy and Tom Kendrick each purchase 100 shares of the same stock at time t = 1. Show that Tom has a greater profit at time t = 5 if he purchases 100 shares at each time, t = 1, 2,..., 5, than Wendy, who uses dollar cost averaging each month. Does this contradict what was discussed concerning dollar cost averaging? Explain.

9.10. Hugh Kendrick short sells 100 shares of stock on margin. If the margin requirement is 50%, if the maintenance requirement for short sales is 30%, and if the stock is sold for $60 a share, then how many additional shares can Hugh short sell if the price falls to $55 a share? Create an appropriate table with share prices of $60, $55, $50, $45, and $40.

Questions for Review

• What is dollar cost averaging?

• What is short selling? What are the risks?

• What is the Long Sale Maintenance Level Theorem?

• What is the Short Sale Maintenance Level Theorem?

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