FIN 435 (Faculty: SfR)

CHAPTER 3HOW SECURITIES ARE TRADED

Suggested Problems: 4, 5*, 6*,9,10,11,17 * Will be done in class

Problem 4: (a) In principle, potential losses are unbounded, growing directly with increases in

the price of IBM.

(b) If the stop-buy order can be filled at $ 128, the maximum possible loss per share is $8. If IBM’s shares go above $128, the stop-buy order is executed, limiting the losses from the short sale.

Problem 17: On January 1, you sold short 100 shares of Zenith stock at $14 per share. On March 1, a dividend of $2 per share was paid. On April 1, you covered the short sale by buying thestock at a price of $9 per share. You paid $0.50 per share in commissions for eachtransaction. What is the value of your account on April 1st?

The proceeds from the short sale (net of commission) were: ($14 x 100) – ($0.50 x 100) = $1,350

You must repay the dividend to the original owner of the borrowed shares. As a result,the dividend payment of $200 is withdrawn from your account.

Covering the short sale at $9 per share cost you (including commission): ($9 x 100) + ($0.50 x 100) = $950

Therefore, the value of your account is equal to the net profit on the transaction:$1350 – $200 – $950 = $200

Note that your profit ($200) equals (100 shares x profit per share of $2). Your netproceeds per share were:$14 selling price of stock–$ 9 repurchase price of stock–$ 2 dividend per share–$ 1 2 trades x $0.50 commission per share-------------------------------------------------- $ 2

Extra Problem (Similar to 9): You are bullish on Telecom stock. The current market price is $50 per share and you have $5,000 of your own to invest. You borrow an additional $5,000 from your broker at an annual interest rate of 8% and invest $10,000 in the stock.

(a) What will be the return on your margin position if the price of Telecom increases to

FIN 435 (Faculty: SfR)

$55 during the next year?(b) Suppose the price drops immediately after you take this position. At what price wouldyou receive a margin call from your broker?(c) Suppose instead that the large price drop occurs one year after you take the position.At what price would you receive a margin call from your broker?

a. You buy 200 shares of Telecom ($10,000/$50 per share). These shares increase invalue by 10%, or $1,000. You pay interest of: 0.08 x 5,000 = $400

The rate of return will be:($1,000 − $400)/5000 = 0.12 = 12%

b. The value of the 200 shares is 200P. The equity in the account is (200P – $5,000).You will receive a margin call when:

(200P − $5,000)/200P= 0.30 when P = $35.71 or lower

c. The value of the 200 shares is 200P. After one year, the equity in the account is(200P – $5,000(1.08)). You will receive a margin call when:

200P − $5,000(1.08)/200P= 0.30 when P = $38.57 or lower

Extra Problem (Similar to 11): Suppose that Intel currently is selling at $80 per share. You buy 250 shares, using $15,000 of your own money and borrowing the remainder of the purchase price from your broker. The rate on the margin loan is 8%.a. What is the percentage increase in the net worth of your brokerage account if the priceof Intel immediately changes to (i) $88; (ii) $80; (iii) $72? What is the relationship betweenyour percentage return and the percentage change in the price of Intel?b. If the maintenance margin is 30%, how low can Intel’s price fall before you get amargin call?c. How would your answer to (b) change if you had financed the initial purchase withonly $10,000 of your own money?d. What is the rate of return on your margined position (assuming again that you invest$15,000 of your own money) if Intel is selling after one year at (i) $88; (ii) $80; (iii) $72 What is the relationship between your percentage return and the percentagechange in the price of Intel? Assume that Intel pays no dividends.e. Continue to assume that a year has passed. How low can Intel’s price fall before youget a margin call?

Solution: Cost of purchase is $80 x 250 = $20,000. You borrow $5,000 from your broker, and invest $15,000 of your own funds. Your margin account starts out with a net worth of $15,000.

FIN 435 (Faculty: SfR)

a. (i) Net worth rises by $2,000 from $15,000 to $88 x 250 – $5,000 = $17,000.

Percentage gain = $2,000/$15,000 = .1333 = 13.33%

(ii) With unchanged price, net worth remains unchanged.

Percentage gain = zero

(iii) Net worth falls to $72 x 250 – $5,000 = $13,000.

Percentage gain =–$2,000$15,000 = –.1333 = –13.33%

The relationship between the percentage change in the price of the stock and the investor’s percentage gain is given by:

% gain = % change in price xTotal investment

investor's initial equity = % change in price x 1.333

For example, when the stock price rises from 80 to 88, the percentage change in price is 10%, while the percentage gain for the investor is 1.333 times as large, 13.33%:

% gain = 10% x$20,000$15,000 = 13.33%

b. The value of the 250 shares is 250P. Equity is 250P – 5000. You will receive a margin call

when: P250000,5P250

= .3 or when P = $28.57

c. The value of the 250 shares is 250P. But now you have borrowed $10,000 instead of $5,000. Therefore, equity is only 250P – $10,000. You will receive a margin call when

3.250

000,10250

P

Por when P = $57.14

With less equity in the account, you are far more vulnerable to a margin call.

d. The margin loan with accumulated interest after one year is $5,000 x 1.08 = $5,400. Therefore, equity in your account is 250P – $5,400. Initial equity was $15,000. Therefore, your rate of return after one year is as follows:

(i) 000,15$

000,15$)400,5$88$250( = .1067, or 10.67%.

(ii)000,15$

000,15$)400,5$80$250( = –.0267, or –2.67%.

FIN 435 (Faculty: SfR)

(iii) 000,15

000,15$)400,5$72$250( = –.160, or –16.0%.

The relationship between the percentage change in the price of Intel and investor’s percentage return is given by:

% gain = % changein price x

Total investmentinvestor's initial equity – 8% x

Funds borrowedinvestor's initial equity

For example, when the stock price rises from 80 to 884, the percentage change in price is 10%, while the percentage gain for the investor is

10% x 20,00015,000 – 8% x

500015,000 = 10.67%

e. The value of the 250 shares is 250P. Equity is 250P – 5,400. You will receive a margin call when

P250400,5P250

= .3 or when P = $30.86