BKM Ch 03 Answers w CFA

CHAPTER 3: HOW SECURITIES ARE TRADED

2.

Who sets the bid and asked price for a stock traded over the counter (OTC)? Would you expect the

spread to be higher on actively or inactively traded stocks?

OTC stock markets are

dealer markets

(as opposed to “exchange markets” like the NYSE)

. In dealer markets,

the dealer buys the asset from the seller and then holds the assets until he or she is able find a buyer. The

dealer’s profit comes from buying at the bid and selling at the ask

. The difference between the bid and ask is

called the spread. Since all transactions are between sellers and dealers or buyers and dealers, the prices are set

by the dealers.

Active stocks will have more dealers. To compete for business, dealers will decrease the profit margin and

therefore quote smaller (tighter) spreads. Spreads will be larger for inactively traded stocks and smaller on

actively traded stocks.

3.

Suppose you short sell 100 shares of IBM, now selling at $$120 per share.

(a)

What is your maximum possible loss?

Potential losses from a short position are unbounded, since the price can go infinitely high.

(b)

What happens to the maximum loss if you simultaneously place a stop-buy order at $$128?

The stop-buy order (

also known as a “

stop-loss buy order to go flat

”

) becomes a market buy order if the

stock trades at or above $$128. If the order is filled at $$128, the maximum loss per share is $$8. If the price

of IBM shares goes above $$128 before it is filled, the loss would be greater.

4.

A market order has:

The answer is (a)

–

Price uncertainty but not execution uncertainty.

A market order is an order to execute the trade immediately at the best possible or current market price. An

advantage is immediate execution. The disadvantage is that the price at which it will be executed at is not

known ahead of time (price uncertainty).

5.

Where would an illiquid security in a developing country most likely trade?

Given these three choices, the answer is broker market. Brokers would mitigate search costs in illiquid markets

by finding or waiting for a counter party for the security. In the US, many illiquid bonds trade through broker

markets. A portfolio manager will contact their representative at a bank with the desire to sell an issue. The

broker will contact other portfolio manager clients to try to place the bond. The broker will either earn a

commission or a spread or both. The broker can also mitigate information asymmetry in illiquid markets by

only dealing in “reputable” securities.

It might be also the case that the bank representative acts a

dealer

and not a broker. In this case, the dealer

provides liquidity by buying the security from the first portfolio manager. The dealer is compensated for

providing liquidity by paying a lower price for the bond with the expectation of selling it later for a higher price

(earning a large spread). The spread compensates the dealer for risk incurred while holding the bond and for the

commitment of capital

–

having the money available to buy the bond and hold it in inventory. Like brokers,

d

ealers can also mitigate information asymmetry by only dealing in “reputable” securities.

Electronic Limit-Order Markets (ELOM), also known as continuous auction markets, such as the market for

most stocks in the US, collect and sort by price and time priority limit orders placed by market participants.

ELOM are useful in more liquid markets where many buyers and sellers are present and information asymmetry

is lower (both buyers and sellers are informed about the securities). Continuous auctions with many market

participants placing buy and sell limit orders creates tighter spreads than those typically found on broker or

dealer markets. The ELOM charges a fee to transact on the market instead of earning the spread.

The text uses the term “Electronic Crossing Networks” but the more common

names are Electronic

Communications Network (ECN) and Crossing Network. Both are more useful in liquid markets.

1

Electronic Communications Network (ECN) is a broad term encompassing pretty much any market system that

does not require placing an order with a person. So an ELOM is an ECN but some ECNs are not ELOM.

For example, some ECNs

(called “dark pools”)

allow market participants to anonymously place an order for a

stock. The order will be executed with a counter party on the ECN at a price (for example) equal to the average

price traded for the stock on all the other markets over a five minute period. This can be useful because the

market participant can execute a large order without changing the public quote. For example, if a mutual fund

wants to sell a large stock position and places a limit sell order on an ELOM book, the presence of that order

might cause buyers to reconsider and lower the price at which the shares can be sold. The terms Alternative

Trading System (ATS) is often used to describe ECNs that are not ELOMs.

True broker markets still exist for small stocks in the US which do not meet

NASDAQ or NYSE listing

requirements

. These stocks are traded on the

OTCBB

or Pink Sheet markets. They are illiquid and have high

information asymmetry.

6.

Dé

e Trader opens a brokerage account and purchases 300 shares of Internet Dreams at $$40 per share.

She borrows $$4,000 from her broker to help pay for the purchase. The interest rate on the loan is 8%

(a)

What is the margin in Dé

e's account when she first purchases the stock

The stock is purchased for 300

?

$$40 = $$12,000

The amount borrowed is $$4,000.

Therefore, the investor put up equity $$8,000

The margin rate is 8,000/12,000 = 66.67%

(b)

If the share 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?

If the share price falls to $$30, then the value of the stock falls to $$9,000.

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

$$4,000

?

1.08 = $$4,320

Therefore, the remaining margin in the investor’s account is: $$9,000

?

$$4,320 = $$4,680

The percentage margin is now: $$4,680/$$9,000 = 0.52 = 52%

Therefore, the investor will not receive a margin call.

(c)

What is the rate of return on her investment?

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%

7.

Old Economy Traders opened an account to short sell 1,000 shares of Internet Dreams from the previous

problem. 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.

(a)

What is the remaining margin in the account?

(See the calculations below)

The trader put up $$20,000

The trader lost $$10,000 in the share price move ($$10 x 1000)

The trader paid $$2,000 in dividends ($$2 x 1000)

Ending Equity = $$20,000 - $$10,000 - $$2,000 = $$8,000

(b)

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

Margin Rate = Equity / Liability is: $$8,000/$$50,000 = 0.16 = 16%

So there will be a margin call.

(c)

What is the rate of return on her investment?

2

The equity in the account decreased from $$20,000 to $$8,000 in one year.

Return = -$$12,000/$$20,000 = -0.60 = -60%

Calculations:

Beginning of the Year:

Assets

Liabilities & Equity

Cash from Stock Sale = $$40 x 1000 = $$40,000

Value of Stocks Owed = 1000 x $$40 = $$40,000

Margin Cash = $$20,000

Equity = $$60,000 - $$40,000 = $$20,000

Total Assets = $$60,000

Margin Rate = Equity/Value of Stocks Owed = Equity/(Shares x P)

Margin Rate = $$20,000/(1000 x $$40) = 0.50

End of the Year:

Price = $$50

Dividend Payable = 1000 x $$2 = $$2,000

Assets

Cash from Stock Sale = $$40 x 1000 = $$40,000

Margin Cash = $$20,000

Total Assets = $$60,000

Once the Dividend is Paid

:

Assets

Cash from Stock Sale = $$40 x 1000 = $$40,000

Margin Cash = $$20,000 - $$2,000 = $$18,000

Total Assets = $$58,000

Liabilities & Equity

Value of Stocks Owed = 1000 x

$$50

= $$50,000

Div Payable = $$2,000

Equity = $$60,000 - $$50,000 - $$2,000 = $$8,000

Margin Rate = Equity/Value of Stocks Owed = Equity/(Shares x P)

Margin Rate = $$8,000/(1000 x $$50) = 0.16

Liabilities & Equity

Value of Stocks Owed = 1000 x

$$50

= $$50,000

Equity = $$58,000 - $$50,000 = $$8,000

8.

Consider the following limit-order book of a specialist. The last trade in the stock occurred at a price of

$$50.

Limit Buy Orders

Limit Sell Orders

Price

Shares

Price

Shares

$$49.75

500

$$50.25

100

$$49.50

800

$$51.50

100

$$49.25

500

$$54.75

300

$$49.00

200

$$58.25

100

$$48.50

600

(a)

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

At the best (lowest) limit-sell order price: $$50.25

(b)

At what price would the next market buy order (after the 100 shares in part (a)) be filled?

At the next-best limit-sell order price: $$51.50

(c)

If you were the specialist, would you want to increase or decrease your inventory of this stock?

You would want to increase your inventory. There is considerable buying demand at prices just below $$50,

indicating that downside risk is limited. In contrast, limit-sell orders are sparse. If the assumption is that

there is equal probability that the next order to arrive at the market will be either a buy or sell, then the price

is more likely to rise

“

a lot

”

since a moderate size buy order (501 shares) would result in a price increase to

$$58.25 while a moderate size sell order (501 shares) would cause the price to drop to only $$49.50.

3

The point of the question is to recognize that the sell-side of the limit-order book is very

thin

and the buy-

side is

deep

. HOWEVER, how can the market maker increase his or her position in the stock without

affecting the limit order book? That is not easily answered.

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 interest rate of 8% per year and

invest $$10,000 in the stock.

(a)

What will be your rate of return if the price of Telecom stock goes up by 10% during the next year?

The stock currently pays no dividends.

Increase in share value = 10% x $$10,000 = $$1,000

Interest Expense = 8%

?

$$5,000 = $$400

Return = ($$1,000 - $$400)/$$5,000 = 0.12 = 12.00%

(b)

How far does the price of Telecom stock have to fall for you to get a margin call if the maintenance

margin is 30%? Assume the price fall happens immediately.

The value of the Assets is the value of the 200 shares (200P).

Liabilities = Loan amount = $$5,000

Margin Rate = Equity/Assets = (Assets

–

Liabilities)/Assets = (200P

–

$$5,000)/200P

You will receive a margin call if Margin Rate < 0.30

Margin Call if (200P

–

$$5,000)/200P < 0.30

Solve for P:

Margin call if P < $$35.71

10.

You are bearish on Telecom and decide to sell short 100 shares at the current market price of $$50 per

share.

(a)

How much in cash or securities must you put into your brokerage account if the broker's initial

margin requirement is 50% of the value of the short position?

Initial Margin = 50% x 100 x $$50 = $$2,500.

(b)

How high can the price of the stock go before you get a margin call if the maintenance margin is 30%

of the value of the short position?

Total assets are $$7,500 ($$5,000 from the sale of the stock and $$2,500 put up for margin).

Liabilities are 100P.

Equity is ($$7,500

–

100P).

A margin call if ($$7,500

–

100P)/100P < 0.30

P > $$57.69

11.

Suppose that Intel currently is selling at $$20 per share. You buy 1,000 shares using $$15,000 of your own

money, 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 price of Intel

immediately changes to: (i) $$22; (ii) $$20; (iii) $$18? What is the relationship between your percentage

return and the percentage change in the price of Intel?

Assets = $$20

?

1,000 = $$20,000

Liability = $$5,000

Equity = $$15,000.

(i)

Price to $$22

Equity = Assets

–

Liabilities = ($$22

?

1,000)

–

$$5,000 = $$17,000

Return = $$17,000/$$15,000

–

1 = 0.1333 = 13.33%

(ii)

Price at $$20

Equity = Assets

–

Liabilities = ($$20

?

1,000)

–

$$5,000 = $$15,000

Return = $$15,000/$$15,000

–

1 = 0%

4

(iii)

Price at $$18

Equity = Assets

–

Liabilities = ($$18

?

500)

–

$$5,000 = $$4,000

Return = $$4,000/$$15,000

–

1 = -0.7333 = -73.33%

The relationship between the

Margin Return

and the

Stock Return

is given by:

Margin Return = Stock Return

?

Assets/Equity

Assets/Equity is a

leverage measure

so the stock’s return (the asset’s return) is increased by the leverage

ratio.

For example, when the stock price rises from $$40 to $$44, the stock return is 10%

The Equity Return = 10%

?

($$20,000/$$15,000) = 10%

?

1.333 = 13.33%

1.333 is the leverage measure.

(b)

If the maintenance margin is 25%, how low can Intel's price fall before you get a margin call?

The value of the Assets is the value of the 1,000 shares (1,000P).

Liabilities = Loan amount = $$5,000

Margin Rate = Equity/Assets = (Assets

–

Liabilities)/Assets = (1,000P

–

$$5,000)/1,000P

You will receive a margin call if Margin Rate < 0.25

Margin Call if (1,000P

–

$$5,000)/1,000P < 0.25

Solve for P:

Margin call if P < $$6.67

(c)

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

your own money?

The value of the Assets is the value of the 1,000 shares (1,000P).

Liabilities = Loan amount = $$10,000

Margin Rate = Equity/Assets = (Assets

–

Liabilities)/Assets = (1,000P

–

$$10,000)/1,000P

Margin Call if (1,000P

–

$$10,000)/1,000P < 0.25

Margin call if P < $$13.33

With less equity (and more debt), then more levered, more vulnerable to a margin call.

(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 1 year at: (i) $$22; (ii) $$20; (iii) $$18? What is the relationship

between your percentage return and the percentage change in the price of Intel? Assume that Intel

pays no dividends.

At the end of 1 year, the loan amount (liability) = $$5,000(1 + 0.08) = $$5,400

(i)

Price to $$22

Equity = Assets

–

Liabilities = ($$22

?

1,000)

–

$$5,400 = $$16,600

Return = $$16,600/$$15,000

–

1 = 0.1067 = 10.67%

(ii)

Price at $$20

Equity = Assets

–

Liabilities = ($$20

?

1,000)

–

$$5,400 = $$14,600

Return = $$14,600/$$15,000

–

1 = -0.0267 = -2.67%%

(iii)

Price at $$18

Equity = Assets

–

Liabilities = ($$18

?

1,000)

–

$$5,400 = $$12,600

Return = $$12,600/$$15,000

–

1 = -0.1600 = -16.00%

The relationship between the

Margin Return

and the

Stock Return

is given by:

Margin Return = (Stock Return

?

Assets/Equity)

–

(Loan Rate x Liabilities/Equity)

For example, when the stock price rises from $$20 to $$22, the stock return is 10%

Equity Return = (10%

?

($$20,000/$$15,000))

–

(8%

?

($$5,000/$$15,000))

= (10%

?

1.333)

–

(8%

?

0.333) = 13.33%

–

2.67% = 10.67%

5