Buying on Margin and Short Selling BKM: 3.6 – 3.7 Today we want to talk about what everyone does when they buy their house – buy on margin. If you don’t own it, you can buy it

Buying on Margin Buying on Margin Borrow cash to buy more of the asset Incur liability to pay back cash Increase expected return Increase standard deviation and probability of large losses.

Buying on Margin You put $10,000 in Microsoft (200 shares) Price of MSFT=50 Suppose you have $10,000 and you expect Microsoft to perform well in the near future. You put $10,000 in Microsoft (200 shares) 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 What are the returns of this trading strategy if Microsoft stock increases or falls by 25% during the next year?

Return of Buying on Margin MSFT increases 25% MSFT decreases 25% Assets Pay Back Loan (Liability) Equity Return 32.5% -42.5% 15,000*1.25=18,750 15,000*.75=11,250 -5,500 -5,500 5750 13,250

“Get” from Buying on Margin “Get” = IE(1+rs) + L(1+rs) – L(1+rf) IE = Investment Equity L = Loan amount rs= return on asset rf = risk-free rate Use algebra to rearrange: P = IE(1+rs) + L(rs – rf)

Return from Buying on Margin return = get/pay – 1 In this case, price = IE

Returns and Buying on Margin Again, the return is a weighted sum of the returns of the assets in your portfolio. Weights are a fraction of you 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. The weights still add to one.

Returns and Buying on Margin 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%

Returns and Buying on Margin What is the return on the portfolio If MSFT price increases immediately by 25%? Can ignore interest owed on margin account Return = 1.5(.25) = 37.5%

Margin and Stat Rule #1 Example: E[rs]=16%, rf=10% w=1.5 E[rp]=1.5(.16)-0.5(.10)=19%

Margin and Stat Rule #2 Example: What is 5% VAR if I just buy MSFT? ss=.18 w=1.5 sp=(1.5).18=.27 What is 5% VAR if I just buy MSFT? .16-1.64*.18=-13.52% What is 5% VAR on margin position? .19-1.64*.27=-25.28%

Margin and Losses 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

Margin Limits Initial margin must exceed 50% Maintenance margin set by broker MSFT example: Initial margin = (300*50-5000)/15000= 67%

Example of Margin Calls Assume MSFT drops within a year by 40%. Price of MSFT= Your margin equals: [300*30-5000(1.10)]/[300(30)]=39% Assume Broker has set maintenance margin at 40%. Your current margin is lower than the maintenance margin and you will receive a margin call from your broker. Broker mandates you close position, or increase margin back to 50%

Three Possible Options to Satisfy Margin Call Close out position Sell the MSFT stocks for $9,000 Pay back the loan of $5000+interest Reduce your loan – how much? The margin increases to [300(30)-X]/[300(30)] = 50% X=300*30-.5*300*30=4500 Must pay off 5000*1.1-4500=1000

Three Possible Options to Satisfy Margin Call Increase your position in MSFT How much? [S*30-5500]/S*30=.50 S=5000/(30-.5*30)=334 Buy 34 more shares

Example How far can price fall immediately before getting a margin call? (Ignore interest on loan.) (P*300-5000)/(P*300)=.40 P*300-5000=.40*P*300 P*(300-.4*300)=5000 P=5000/(300-.4*300)=27.78

Short Selling Securities are sold by someone who does not own them. Borrow the securities from somebody. Sell the securities at the current price. Eventually, buy back the securities and return them to the owner. Profit=Initial Price – Ending Price

Short Selling Example Suppose you short MSFT. Two months later the price is $40. What is your profit? Profit = $50 - 40 = 10 On a “per-share” basis

Short Selling Example Assets=Liabilities + Equity Initially: Assets = 50 (cash) Liabilities = 50 (value of stock owed) Equity = 0 Two Months Later Assets = 50 (cash) Liabilities = 40 Equity = 10

Short Selling Steps 1. Borrow the shares This is done via your broker. The term of the short-sell is almost always one day, but loans are typically renewed many times. The lender can require you to return the shares whenever he/she wants (short-squeeze)

Short Selling Steps 2. Shares are sold in the stock market Proceeds are put in a collateral account Do not have access to these funds until you return the borrowed shares. Money earns interest (risk-free rate) Assets = collateral account (cash) Liability=value of stock owed Equity=Assets-Liability

Step 2: Sell the Borrowed Shares You must contribute your own investment equity to the collateral account. is the “margin” on the short position. Your total assets include The proceeds from the short-sell Any extra equity you have provided Can be in the form of other security.

Short Selling Steps 3. Close out position Buy the amount of shares you borrowed and return them to broker. Collect all money in collateral account.

MSFT Example MSFT: $50/share You short sell 2000 shares Initial Margin is 50% What are Liabilities? L=100,000=P*S How much equity do you need to provide? E/100,000=0.50 E=50,000 What are assets? A=100,000+50,000=150,000

MSFT Example Assume you post equity in the form of cash. You could provide equity in the form of other stocks or bonds. Assume all cash in collateral account earns 5% interest annually. How much total cash do you have in your collateral account? Cash in account=Proceeds of short sell + equity 100,000+50,000 = 150,000

MSFT Example Suppose price of MSFT is 60 at the end of the year. What are total assets? A=150000*(1.05)=157,500 What are liabilities? L=2000*60=120,000 What is equity? E=157,500-120,000=37500 What is return? 37500/50000-1=-25% What is new margin? 37500/120000=0.3125

Margin Example Margin call [150000-P(2000)]/P(2000) = 0.35 Maintenance margin is 35% How far can price increase immediately before getting a margin call? Ignore interest earned on collateral account. Margin call [150000-P(2000)]/P(2000) = 0.35 P=150000/ (.35*2000+2000)=55.56

Three Possible Options to Satisfy Margin Call Close out position Buy the MSFT stocks for $55.56 Equity left: 150000-2000*55.56=38800 Reduce your liability – how much? Assume the margin must increase to 50% [150000-55.56*S]/[55.6*S] = 50% S=150000/(.5*55.56+55.56)=1800 Buy back 2000 shares with new equity and return to broker

Three Possible Options to Satisfy Margin Call Increase your collateral How much? [X-2000*55.56]/(2000*55.56)=.50 X=.5*2000*55.56+2000*55.56=166,680 Give broker an additional 16,680 in cash

Short Selling and Portfolio Weights Again, we can use portfolio weights: Equity:50,000 Position earning risk-free: 150,000 Weight=150/50=3.0 Position in MSFT: liability of 100,000 Weight=-100/50=-2 MSFT return: 60/50-1=20% Portfolio return: 3*.05+(-2)*(.20)=-25%

Short Selling and Portfolio Weights Suppose when you took the short MSFT position you expected MSFT to return -10% with a standard deviation of 0.25 What is expected return and standard deviation of your portfolio?

Short Selling and Stat Rules E[rp]=3*.05+(-2)*(-.10)=35% Stat Rule #2 = (-2)2*.252=0.25 = 2*(0.25)=0.50

Short Selling and Portfolio Weights At the beginning of the year, what is your 5% VAR? 5% VAR=0.35-1.64*.50=-47% If you get a -47% return, what happened to MSFT? -.47=-2*rH+3*.05 rH=(-.47-3*.05)/(-2)=0.31 Note: given that MSFT does have en expected return of -10% and a stdev of .25, the probability rH is 0.31 or greater is 5%

Borrowing as Short-Selling You can think of borrowing as short-selling a risk-free bond. Borrow $909.09 at 10% Short-sell 1 bond FV = 1000, Price = 909.09 Get $909.09 now Get $909.09 now Pay $1000 in future Pay $1000 in future