Objectives
Margin Account
Short Sale
Summary

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Why do investors use margin account?
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How does margin borrowing affect return and risk?
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What purpose does short sale serve?
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How does short sale work?
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How does short sale constraint affect stock return?
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Definition
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Account Values:
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Asset: total holding of securities including cash
Liability: the amount of money owed to others
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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
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Initial Margin Requirement: initial margin >= 50%
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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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Holding Period Return
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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
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Un-leveraged Investment
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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
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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
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Appreciation
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Depreciation
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Q : Same condition as previous case, but you buy 100 shares
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What is your HPR if IBM appreciates to $130 in a year?
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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%)
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Initial Position
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Asset = stock value = $10,000
Liability = $4,000, Equity = Asset
– Liability = $6,000
Initial Margin = Equity/Stock Value = 60%
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Final Position when P =$130
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Asset = stock value = 100
×130 = $13,000
Liability = 4,000 ×(1+9%) = $4,360, Equity = $8,640
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Final Position when P = $80
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Asset = $8,000, Liability = $4,360, Equity = $3,640
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Effects of Margin on Return and Risk
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Higher risk
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Makes more in good times
Loses more in bad times
Higher return
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Margin amplifies the expected return
100%
50%
Ret urn w/ o margin
Ret urn w/ margin
0%
-50%
40 60 80 100 120 140 160
-100%
Stock Price
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Margin Call (for Margin Account)
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If equity falls below maintenance margin (25%-30% typical), a margin call for more fund or for liquidation is issued
Assuming 30% maintenance margin
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What is the margin call price one year later?
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Solve the above equation: P c
= $62.29
What is the margin call price today?
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Liability = $4,000 (instead of $4,360), so P c
= $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)
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Margin calls happen when your bets go wrong (at least short-term)
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The higher the leverage, the higher the chance of getting margin calls
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Need to come up with cash (liquidity) - fast
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Can not profit from your position if you sell stock
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May trigger liquidity crisis
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Tough luck, if you can’t come up with cash
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This is where LTCM failed
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What purpose does short sale serve?
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Gives speculators a tool to profit from bear market
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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
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Q : On Shenzhen Stock Exchange (China), one observes that A share has P/E ratio = 55, and a similar company B share P/E ratio = 39. What profitable opportunity does this price divergence provide?
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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
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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 )
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How Does Short Sale Work?
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Mr Owner buys 1 share of IBM
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Mr owner has the rights of
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Voting
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Dividend
Short Creation
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Short borrows share from Owner
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Short owes Owner a share (IOU)
Short sells the share to Ms Long
Ms Long has the rights of
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Voting
Dividend
Mr Owner is still entitled to
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Dividend
All deals are facilitated by brokers
IBM
$100
1 share
Mr Owner
Morgan Stanley
Dean Witter facilitates all the deals
$100
Ms Long
1 share
Mr Short
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How does Short Sale Work?
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Profit/Loss (so called P/L in industry)
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Long position on one share of stock
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P
1 is the ending price
P
0 is the beginning price
D
1 dividend during the period paid in the end
Short position on one share of stock short
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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 :
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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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Return and Margin Call
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Q : You deposit $50,000 in the brokerage acct, and sell short 1000 share of IBM at $100
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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
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Initial margin:
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Return:
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Assuming maintenance margin of 30%
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Cost of Borrowing
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Broker fees
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Low rebate rates on your collateral cash
Scarcity of shares to borrow (stock “on special”)
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After IPOs
Prior to rumored mergers/acquisitions (acquirer’s stock is hard to borrow)
Risk of involuntary closing a short position
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Borrowed stock can be recalled, and the broker may not find a substitution
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up
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Margin trading increases both the expected return and the level of risk
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down
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Short sale provides a mechanism for hedging and downward market speculation
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Short sale constrained stocks typically exhibit underperformance
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