Security Trading
Objectives
Margin Account
Short Sale
Summary
Objectives

Margin Account Trading



Why do investors use margin account?
How does margin borrowing affect return
and risk?
Short Sale



What purpose does short sale serve?
How does short sale work?
How does short sale constraint affect stock
return?
Investments 5
2
Margin Account Trading

Definition

Account Values:


Asset: total holding of securities including cash
Liability: the amount of money owed to others




Either cash (margin borrowing) or stock (short sale)
Equity: the investors net worth = Asset - Liability
Stock Value: the market value of stock holding
Margin: equity as a percentage of stock value

Initial Margin Requirement: initial margin >= 50%




Investments 5
Set by Board of Governors of the Federal Reserve System
Maintenance margin: minimum amount of equity before
additional funds to be put into the account
Margin call: notice from broker for additional funds
Margin Interest: interest charge on capital borrowed
3
Margin Account Trading

Holding Period Return

E.g., you invest $10,000 and receive $1,000 of
dividends at the end of the year. The market value of
your stocks at the end of the year is $11,000.
Q: what’s your return for the year?
A: the holding period return is


Investments 5
4
Margin Account Trading

Un-leveraged Investment


Q: You open an account with $6,000. IBM stock price is $100.
If you invest all your money in IBM



Invest no more than the capital you have
What is your HPR if IBM appreciates to $130 in a year?
What is your HPR if IBM depreciates to $80 in a year?
A: Since this is a unleveraged position, your return is the same
as the stock price appreciation/depreciation

Appreciation

Depreciation
Investments 5
5
Margin Account Trading

Q: Same condition as previous case, but you buy 100 shares



What is your HPR if IBM appreciates to $130 in a year?
What is your HPR if IBM depreciates to $80 in a year?
A: 100 shares cost $10,000, you have to borrow $4,000 (at 9%)

Initial Position




Final Position when P =$130



Asset = stock value = $10,000
Liability = $4,000, Equity = Asset – Liability = $6,000
Initial Margin = Equity/Stock Value = 60%
Asset = stock value = 100×130 = $13,000
Liability = 4,000×(1+9%) = $4,360, Equity = $8,640
Final Position when P = $80

Asset = $8,000, Liability = $4,360, Equity = $3,640

Investments 5
6
Margin Account Trading

Effects of Margin on Return and Risk

Higher risk



Makes more in good times
Loses more in bad times
Higher return

Margin amplifies the expected return
100%
Ret urn w/ o margin
Return
50%
Ret urn w/ margin
0%
-50%
40
60
80
100
120
140
160
-100%
Stock Price
Investments 5
7
Margin Call

Margin Call (for Margin Account)


If equity falls below maintenance margin (25%-30% typical),
a margin call for more fund or for liquidation is issued
Assuming 30% maintenance margin

What is the margin call price one year later?


What is the margin call price today?



Solve the above equation: Pc = $62.29
Liability = $4,000 (instead of $4,360), so Pc = $57.14
What is the margin call price if the maintenance margin = 40%?
What happens to the investor receiving a margin call?


Investments 5
either deposit more fund (increase the equity), or
sell some stock (lowers the stock value)
8
Margin Call - Risks

Margin calls happen when your bets go
wrong (at least short-term)


Need to come up with cash (liquidity) - fast


The higher the leverage, the higher the chance
of getting margin calls
Can not profit from your position if you sell
stock
May trigger liquidity crisis



Try to use Rev/repos if you can
Tough luck, if you can’t come up with cash
This is where LTCM failed
Investments 5
9
Short Sale

What purpose does short sale serve?

Gives speculators a tool to profit from bear market



Allows arbitrageurs to enforce price convergence of similar
securities



Q: Jane believes IBM is going to drop from $100 to $90, what
should she do?
A: Jane borrows IBM shares and sells them at $100. She waits
to buy back the shares at $90 to make $10 profit per share.
Q: On Shenzhen Stock Exchange (China), one observes that A
share has P/E ratio = 55, and B share P/E ratio = 39. What
profitable opportunity does this price divergence provide?
A: If possible: short A share/buy B share to make $16 dollar
profit on $1 earning.
Provides investors with a vehicle to hedge its portfolio


Investments 5
Q: An investor holds a diversified portfolio with huge capital
gains, but is afraid of a market drop. What should she do?
A: sell short a market index portfolio like Spider (SPY)
10
Short Sale

$100
How Does Short Sale Work?

Mr Owner buys 1 share of IBM




Short borrows share from Owner
Short owes Owner a share (IOU)
Short sells the share to Ms Long
Ms Long has the rights of



Voting
Dividend
$100
Mr Owner is still entitled to

Dividend
All deals are facilitated by
brokers
Investments 5
Morgan Stanley
Dean Witter
facilitates all the
deals
1 share
Short Creation


Voting
Dividend
IOU + dividend

Mr Owner
1 share
Mr owner has the rights of


IBM
Ms Long
Mr Short
1 share
11
Short Sale

How does Short Sale Work?

Profit/Loss (so called P/L in industry)

Long position on one share of stock






P1 is the ending price
P0 is the beginning price
D1 dividend during the period paid in the end
Short position on one share of stock short
Q: What’s your profit if you short 200 share of a stock at $34,
and cover it at $30, while it pays a $1 dividend?
A:



Investments 5
You receive 200×34 = $6,800 at time 0
You pay 200×1= $200 dividends to the one you owed share to
You pay 200×30 = $6,000 to buy the share and pay it back.
12
Short Sale

Return and Margin Call

Q: You deposit $50,000 in the brokerage acct, and
sell short 1000 share of IBM at $100




What is your initial margin?
What is your investment return if IBM falls to $70?
What is the margin call price if $2 dividends are paid?
A: Both the margin and return depend on equity
Investments 5

Initial margin:

Return:

Assuming maintenance margin of 30%
13
Short Sale - Constraints

Cost of Borrowing



Scarcity of shares to borrow (stock “on
special”)



Broker fees
Low rebate rates on your collateral cash
After IPOs
Prior to rumored mergers/acquisitions (acquirer’s
stock is hard to borrow)
Risk of involuntary closing a short position

Borrowed stock can be recalled, and the broker
may not find a substitution
Investments 5
14
Wrap-up

Margin account to profit in the up
market


Margin trading increases both the expected
return and the level of risk
Short sale to profit in the down market


Short sale provides a mechanism for
hedging and downward market speculation
Short sale constrained stocks typically
exhibit underperformance
Investments 5
15