Security Trading

ObjectivesMargin Account

Short SaleSummary

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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?

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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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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

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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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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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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%

-50%

0%

50%

100%

40 60 80 100 120 140 160

Stock Price

Ret

urn

Return w/o margin

Return w/margin

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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)

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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

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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)

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Short Sale 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

Voting Dividend

Mr Owner is still entitled to Dividend

All deals are facilitated by brokers

IBM

Mr Short

Mr Owner

Ms Long

Morgan Stanley Dean Witter

facilitates all the deals

1

share

1 share

1 share

$100

$100

IOU

+ d

ivid

end

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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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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%

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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

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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