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solution to the test for chp 2

第2章

Problem1: Dee Trader opens a brokerage account, and purchases 300 shares of Internet Dreams at $40 per share. She borrows $4,000 from her

8%.

a. What is the margin i n Dee’s account when she first purchases the stock?

b. If the price falls to $30 per share by the end of the year, what is the remaining margin in her account? If the maintenance margin requirement is 30%, will she receive a margin call?

c. What is the rate of return on her investment?:

answers:

a.The stock is purchased for: (300 ? $40) = $12,000

The amount borrowed is $4,000. Therefore, the investor put up equity, or margin,

of $8,000. 5 points

b.If the share price falls to $30, then the value of the stock falls to $9,000($30*300). By the end of the year, the amount of the loan owed to the broker grows to:

($4,000 ?1.08) = $4,320. // The interest rate on the loan is 8%.

Therefore, the remaining margin in the investor’s account is:

($9,000 - $4,320) = $4,680. 5 points

The percentage margin is now: ($4,680/$9,000) = 0.52 = 52%. >30%

Therefore, the investor will not receive a margin call. 5 points

c.The rate of return on the investment over the year is:

(Ending equity in the account - Initial equity)/Initial equity

= ($4,680 - $8,000)/$8,000 = -0.415 = -41.5% 5 points

Problem2: Old Economy Traders opened an account to short sell 1,000 shares of Internet Dreams from the problem 1.// at $40 per share// The initial margin requirement was 50%. (The margin account pays no interest.) A year later, the price of Internet Dreams has risen from $40 to $50, and the stock has paid a dividend of $2 per share. 15 points

a. What is the remaining margin in the account?

answers:

a. The initial margin was: (0.50 ? 1,000 ? $40) = $20,000 As a result of the increase in the stock

price, Old Economy Traders loses: ($10 ? 1,000) = $10,000. Therefore, margin

decreases by $10,000. Moreover, Old Economy Traders must pay the dividend of

$2 per share to the lender of the shares, so that the margin in the account decreases

by an additional $2,000. Therefore, the remaining margin is: ($20,000 - $10,000 -

$2,000) = $8,000 .or. (20000+40000)-50000-2000 5 points

b. If the maintenance margin requirement is 30%, will Old Economy receive a margin call?

b. The percentage margin is: ($8,000/$50,000) = 0.16 = 16%

Therefore, there will be a margin call. 5 points

c. What is the rate of return on the investment?

c. The rate of return on the investment is:

(Ending equity in the account - Initial equity)/Initial equity

= ($8,000 - $20,000)/$20,000 = -0.60 = -60.0%

Or. = (40000-50000-2000)-20000/$20000= -60.0% 5 points

Problem3: Consider the following limit-order book of a broker. The last trade in the stock took place at a price of $50. 10 points

a. If a market-buy order for 100 shares comes in, at what price will it be filled?

a.The buy order will be filled at the best limit-sell order price(the asked price of the

specialist): $50.25 5 points

b. At what price would the next market-buy order be filled?

b.The next market buy order will be filled at the next-best limit-sell order price: $51.50

5 points

Problem4: Suppose that Intel currently is selling at $40 per share. You buy 500 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%. 27points

answers:

a. What is the percentage increase in the net worth of your brokerage

account if the price of Intel immediately changes to (i) $44; (ii) $40; (iii) $36?

The total cost of the purchase is ($40 ? 500) = $20,000. You borrow $5,000 you’re your

broker, and invest $15,000 of your own funds. Your margin account starts out with net

worth of $15,000.

a. (i) Net worth increases to: ($44 ? 500) – $5,000 = $17,000

Percentage gain = $2,000/$15,000 = 0.1333 = 13.33%

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

Percentage gain = zero

(iii) Net worth falls to ($36 ? 500) – $5,000 = $13,000

Percentage gain = –$2,000/$15,000 = –0.1333 = –13.33%

6 points

b. If the maintenance margin is 25%, how low can Intel’s price fall before you get a margin

call?

b. The value of the 500 shares is: 500P

Equity is: (500P – $5,000)

You will receive a margin call when:

P 500000 ,5$

500-

= 0.25 ? when P = $13.33 or lower

5 points

c. How would your answer to (b) change if you had financed the initial purchase with only $10,000 of your own money?

c.The value of the 500 shares is 500P. But now you have borrowed $10,000 instead of

$5,000. Therefore, equity is: (500P – $10,000)

You will receive a margin call when:

P 500000 ,

500-

= 0.25 ? when P = $26.67

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

5points

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) $44; (ii) $40;(iii) $36?

d. By the end of the year, the amount of the loan owed to the broker grows to:

($5,000 ? 1.08) = $5,400

The equity in your account is: (500P – $5,400)

Initial equity was $15,000. Therefore, your rate of return after one year is as

follows:

(i)

000

400

,5$

)

500

= 0.1067 = 10.67%

(ii)

000

400

,5$

)

500

= –0.0267 = –2.67%

(iii)

000

400

,5$

)

500

= –0.1600 = –16.00%

6 points

e. Continue to assume that a year has passed. How low can Intel’s price fall before you get a margin call?

e. The value of the 500 shares is: 500P

Equity is: (500P – $5,400)// ($5,000 ? 1.08) = $5,400

You will receive a margin call when:

P 500400 ,5$

500-

= 0.25 ? when P = $14.40 or lower 5 points

Problem6: Suppose that you sell short 500 shares of Intel, currently selling for $40 per share, and give your broker $15,000 to establish your margin account.

a.If you earn no interest on the funds in your margin account, what will be your rate

of return after one year if Intel stock is selling at (i) $44; (ii) $40; (iii) $36? Assume

that Intel pays no dividends.

answers:

a. The gain or loss on the short position is: (–500 ??P)

Invested funds are $15,000.

Therefore: rate of return = (–500 ??P)/15,000

The rate of return in each of the three scenarios is:

(i) rate of return = (–500 ? $4)/$15,000 = –0.1333 = –13.33%

(ii) rate of return = (–500 ? $0)/$15,000 = 0%

(iii)rate of return = [–500 ? (–$4)]/$15,000 = +0.1333 = +13.33%

b. If the maintenance margin is 25%, how high can Intel’s price rise before you get a

margin call?

b.Total assets in the margin account are:

$20,000 (from the sale of the stock) + $15,000 (the initial margin) = $35,000

Liabilities are: 500P

A margin call will be issued when:

P 500P

500

000

$-= 0.25 ? when P = $56 or higher

c. Redo parts (a) and (b), now assuming that Intel’s dividend (paid at year end) is $1 per share.( group 1)

c.With a $1 dividend, the short position must now pay on the borrowed shares:

($1/share ? 500 shares) = $500

Rate of return is now: [(–500 ??P) – 500]/15,000

(i) rate of return = [(–500 ?4)– 500]/15,000 = –0.1667 = –16.67%

(ii) rate of return = [(–500 ?0) – 500]/15,000 = –0.0333 = –3.33%

(iii) rate of return = [(–500) ? (–4) – 500]/15,000 = +0.1000 = +10.00% Total assets are $35,000, and liabilities are: (500P + 500)

A margin call will be issued when:

P 500

500 P

500

000

35-

= 0.25 ? when P = $55.20 or higher

Addition: An expiring put will be exercised and the stock will be sold if the stock price is

below the exercise price. A stop-loss order causes a stock sale when the stock price falls below some limit. Compare and contrast the two strategies of purchasing put options versus issuing a stop-loss order.

answers:

The stop-loss order will be executed once the stock price decreases to the limit price. If the

stock price later rebounds, the investor does not participate in the gains because the

investor no longer owns the stock.

In contrast, the put option need not be exercised when the stock price falls below the

exercise price. An investor who owns a share of stock and a put option can hold on to both securities. If the stock price never rebounds, the investor can eventually exercise the put by selling the stock for the exercise price. This provides the same downside protection as the stop-loss order. If the price does rebound, however, the investor benefits because the investor still owns the stock. This advantage of the put over the stop-loss order justifies the cost of the put.

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