1. Objectives Margin Account Short Sale Summary
Investments 5
Security Trading
Objectives
Margin Account
Short Sale
Summary

2. Objectives Margin Account Trading Short Sale
Investments 5
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

3. 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%
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
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4. 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

5. Margin Account Trading
Un-leveraged Investment
Invest no more than the capital you have
Q: You open an account with $6,000. IBM stock price is $100.
If you invest all your money in IBM
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
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6. 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
Asset = stock value = $10,000
Liability = $4,000, Equity = Asset – Liability = $6,000
Initial Margin = Equity/Stock Value = 60%
Final Position when P =$130
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
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7. Margin Account Trading
Investments 5
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
Is it good to have margin?
No recovery from ruin risk. The dreaded margin call
Investments 5

8. 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?
Solve the above equation: Pc = $62.29
What is the margin call price today?
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?
either deposit more fund (increase the equity), or
sell some stock (lowers the stock value)
Investments 5

9. Margin Call - Risks
Margin calls happen when your bets go wrong (at least short-term)
The higher the leverage, the higher the chance of getting margin calls
Need to come up with cash (liquidity) - fast
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

10. Short Sale What purpose does short sale serve?
Gives speculators a tool to profit from bear market
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.
Allows arbitrageurs to enforce price convergence of similar securities
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
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)
Investments 5

11. Morgan Stanley Dean Witter facilitates all the deals
Investments 5
Short Sale
$100
How Does Short Sale Work?
Mr Owner buys 1 share of IBM
Mr owner has the rights of
Voting
Dividend
Short Creation
Short borrows share from Owner
Short owes Owner a share (IOU)
Short sells the share to Ms Long
Ms Long has the rights of
Mr Owner is still entitled to
All deals are facilitated by brokers
IBM
Mr Owner
1 share
IOU + dividend
Morgan Stanley Dean Witter facilitates all the deals
1 share
$100
Ms Long
Mr Short
1 share
Investments 5

12. 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:
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.
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13. Short Sale Return and Margin Call
Investments 5
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
Initial margin:
Return:
Assuming maintenance margin of 30%
Two interpretation of equity:
New equity of old equity + profit
New equity = Asset - Liability
Question:
How does interest paid on cash affect the return and the margin call price?
What happens if one needs to pay money to borrow shares?
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14. Short Sale - Constraints
Investments 5
Short Sale - Constraints
Cost of Borrowing
Broker fees
Low rebate rates on your collateral cash
Scarcity of shares to borrow (stock “on special”)
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

15. Wrap-up Margin account to profit in the up market
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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