2 - 1 FINS 5513 Investments and Portfolio Selection...

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1 FINS 5513 Investments and Portfolio Selection University of New South Wales Semester 1 2012 Week 2 Russell Jame

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Buying on Margin & Short Selling BKM 3.6-3.7 2
Buying on Margin 3 Buying on Margin Borrow cash to buy more of the asset Incur liability to pay back cash Increase expected return Increase standard deviation

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Buying on Margin 4 Price of MSFT=50 Suppose you have \$10,000 and you expect Microsoft to perform well in the near future. You borrow \$5000 from broker at 10% effective annual rate Buy \$15,000 worth of MSFT stock (300 shares) Assets=15000, Liabilities=5000, Equity=10000
Return of Buying on Margin MSFT increases 25% MSFT decreases 25% Assets Pay Back Loan (Liability) Equity Return 5 15,000*1.25=18,750 15,000*.75=11,250 5,000 * 1.10 =-5,500 18,750 – 5,500 =13,250 11,250 – 5,500 =5,750 13,250/10,000 -1 =32.5% 5,750/10,000-1=-42.5% 5,000 * 1.10 =-5,500

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Portfolio Weights 6 Portfolio weights allow us to find returns from buying on margin more quickly. Let’s see how this works. Payoff= IE(1+rs) + L(1+rs) – L(1+rf) IE = Investment Equity L = Loan amount rs= return on asset rf = risk-free rate
Portfolio Weights return = payoff/IE – 1 7 s s f s f IE(1+r ) + L(r - r ) IE return= IE IE Do some algebra to get . . . (IE+L) L return (r ) (r ) IE - = -

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Returns and Buying on Margin 8 Again, the return is a weighted sum of the returns of the assets in your portfolio. Weights are a fraction of your investment equity in each asset. The asset you have borrowed money to invest in will always have a weight that is greater than one. The weight on the risk-free return (at which you are borrowing) will have a negative weight. s f return r (1-w)r IE+L IE w w = + =
Returns and Buying on Margin 9 Assets = 15000 Equity=10000 Liabilities=5000 Weight in MSFT = 15000/10000=1.5 Weight in bonds = -5000/10000=-0.5 If Microsoft returns 25% Your return: 1.5*.25+(-.5)*.1=32.5% If Miscrosoft returns -25% Your return: 1.5*(-.25)+(-.5)*.1=-42.5%

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Margin and Losses 10 Lower bound for any stock: 0 Assets = Liabilities + Equity Equity = Assets - Liabilities Lower bound for assets = 0 Lower bound for equity = - Liabilities
Margin Limits SEC mandates limitations on borrowing. Limit is defined in terms of “the margin”. P=Price of security S=Shares owned L=Value of Loan 11 equity P(S)-L margin Value of Stock P(S) = =

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Margin Limits 12 Initial margin must exceed 50% Maintenance margin set by broker MSFT example: Buy 300 shares of MSFT at \$50 per share Use 10,000 of equity and 5,000 borrowed Initial margin = (300*50-5000)/15000= 67%
Margin Call 13 Assume MSFT drops within a year by 40% Price=.60*50=30 Margin=[300*30-5000*1.10]/ (3000*30)=39% Assume maintenance margin=40% You will get a margin call Broker will mandate either that you close

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Three Possible Options to Satisfy Margin Call 14 Close out position Sell the MSFT stocks for \$9,000 Pay back the loan of \$5000+interest Reduce your loan – how much?
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This note was uploaded on 03/19/2012 for the course FINS 5513 taught by Professor Wangjianxin during the Three '10 term at University of New South Wales.

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2 - 1 FINS 5513 Investments and Portfolio Selection...

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