Buying on Margin and Short Selling BKM 3

Buying on Margin and Short Selling BKM: 3. 6 – 3. 7 1

Buying on Margin o Buying on Margin n n 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. 2

Buying on Margin o Price of MSFT=50 o Suppose you have $10, 000 and you expect Microsoft to perform well in the near future. n You put $10, 000 in Microsoft (200 shares) o You borrow $5000 from broker at 10% n effective annual rate n Buy $15, 000 worth of MSFT stock (300 shares) n Assets=15000, Liabilities=5000, Equity=10000 o What are the returns of this trading strategy if Microsoft stock increases or falls by 25% during the next year? 3

Return of Buying on Margin MSFT increases 25% Assets Pay Back Loan (Liability) 15, 000*1. 25=18, 750 -5, 500 Equity 13, 250 Return 32. 5% MSFT decreases 25% 15, 000*. 75=11, 250 -5, 500 5750 -42. 5% 4

“Get” from Buying on Margin o “Get” = IE(1+rs) + L(1+rs) – L(1+rf) n n IE = Investment Equity L = Loan amount rs= return on asset rf = risk-free rate Use algebra to rearrange: n P = IE(1+rs) + L(rs – rf) 5

Return from Buying on Margin o return = get/pay – 1 n In this case, price = IE 6

Returns and Buying on Margin o Again, the return is a weighted sum of the returns of the assets in your portfolio. o Weights are a fraction of you investment equity in each asset. o The asset you have borrowed money to invest in will always have a weight that is greater than one. o The weight on the risk-free return (at which you are borrowing) will have a negative weight. o The weights still add to one. 7

Returns and Buying on Margin o o o Assets = 15000 Equity=10000 Liabilities=5000 Weight in MSFT = 15000/10000=1. 5 Weight in bonds = -5000/10000=-0. 5 If Microsoft returns 25% n Your return: 1. 5*. 25+(-. 5)*. 1=32. 5% o If Miscrosoft returns -25% n Your return: 1. 5*(-. 25)+(-. 5)*. 1=-42. 5% 8

Returns and Buying on Margin o What is the return on the portfolio If MSFT price increases immediately by 25%? n n Can ignore interest owed on margin account Return = 1. 5(. 25) = 37. 5% 9

Margin and Stat Rule #1 o Example: n E[rs]=16%, rf=10% n w=1. 5 n E[rp]=1. 5(. 16)-0. 5(. 10)=19% 10

Margin and Stat Rule #2 o Example: n ss=. 18 n w=1. 5 n sp=(1. 5). 18=. 27 o What is 5% VAR if I just buy MSFT? n. 16 -1. 64*. 18=-13. 52% o What is 5% VAR on margin position? n. 19 -1. 64*. 27=-25. 28% 11

Margin and Losses o Lower bound for any stock: 0 n Assets = Liabilities + Equity n Equity = Assets - Liabilities n Lower bound for assets = 0 n Lower bound for equity = - Liabilities 12

Margin Limits o SEC mandates limitations on borrowing. o Limit is defined in terms of “the margin”. n P=Price of security n S=Shares owned n L=Value of Loan 13

Margin Limits o Initial margin must exceed 50% o Maintenance margin set by broker o MSFT example: Initial margin = (300*50 -5000)/15000= 67% 14

Example of Margin Calls o Assume MSFT drops within a year by 40%. o Price of MSFT= o Your margin equals: [300*30 -5000(1. 10)]/[300(30)]=39% o Assume Broker has set maintenance margin at 40%. o Your current margin is lower than the maintenance margin and you will receive a margin call from your broker. n Broker mandates you close position, or increase margin back to 50% 15

Three Possible Options to Satisfy Margin Call o Close out position n Sell the MSFT stocks for $9, 000 n Pay back the loan of $5000+interest o Reduce your loan – how much? n 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 16

Three Possible Options to Satisfy Margin Call o Increase your position in MSFT n How much? n [S*30 -5500]/S*30=. 50 S=5000/(30 -. 5*30)=334 Buy 34 more shares 17

Example o 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 18

Short Selling o Securities are sold by someone who does not own them. 1. Borrow the securities from somebody. 2. Sell the securities at the current price. 3. Eventually, buy back the securities and return them to the owner. Profit=Initial Price – Ending Price 19

Short Selling Example o Suppose you short MSFT. Two months later the price is $40. What is your profit? o Profit = $50 - 40 = 10 n On a “per-share” basis 20

Short Selling Example o Assets=Liabilities + Equity o Initially: n Assets = 50 (cash) n Liabilities = 50 (value of stock owed) n Equity = 0 o Two Months Later n Assets = 50 (cash) n Liabilities = 40 n Equity = 10 21

Short Selling Steps 1. Borrow the shares n This is done via your broker. n The term of the short-sell is almost always one day, but loans are typically renewed many times. n The lender can require you to return the shares whenever he/she wants (short-squeeze) 22

Short Selling Steps 2. Shares are sold in the stock market n Proceeds are put in a collateral account n Do not have access to these funds until you return the borrowed shares. n Money earns interest (risk-free rate) n Assets = collateral account (cash) n Liability=value of stock owed n Equity=Assets-Liability 23

Step 2: Sell the Borrowed Shares o You must contribute your own investment equity to the collateral account. is the “margin” on the short position. o Your total assets include n The proceeds from the short-sell n Any extra equity you have provided o Can be in the form of other security. 24

Short Selling Steps 3. Close out position n Buy the amount of shares you borrowed and return them to broker. n Collect all money in collateral account. 25

MSFT Example o o MSFT: $50/share You short sell 2000 shares Initial Margin is 50% What are Liabilities? n L=100, 000=P*S o How much equity do you need to provide? n E/100, 000=0. 50 n E=50, 000 o What are assets? n A=100, 000+50, 000=150, 000 26

MSFT Example o Assume you post equity in the form of cash. n You could provide equity in the form of other stocks or bonds. o Assume all cash in collateral account earns 5% interest annually. o How much total cash do you have in your collateral account? n Cash in account=Proceeds of short sell + equity n 100, 000+50, 000 = 150, 000 27

MSFT Example o Suppose price of MSFT is 60 at the end of the year. o What are total assets? n A=150000*(1. 05)=157, 500 o What are liabilities? n L=2000*60=120, 000 o What is equity? n E=157, 500 -120, 000=37500 o What is return? 37500/50000 -1=-25% o What is new margin? 37500/120000=0. 3125 28

Margin Example o Maintenance margin is 35% o How far can price increase immediately before getting a margin call? n Ignore interest earned on collateral account. o Margin call [150000 -P(2000)]/P(2000) = 0. 35 P=150000/ (. 35*2000+2000)=55. 56 29

Three Possible Options to Satisfy Margin Call o Close out position n Buy the MSFT stocks for $55. 56 n Equity left: 150000 -2000*55. 56=38800 o Reduce your liability – how much? n 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 30

Three Possible Options to Satisfy Margin Call o Increase your collateral n How much? n [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 31

Short Selling and Portfolio Weights o Again, we can use portfolio weights: o Equity: 50, 000 o Position earning risk-free: 150, 000 n Weight=150/50=3. 0 o Position in MSFT: liability of 100, 000 n Weight=-100/50=-2 o MSFT return: 60/50 -1=20% o Portfolio return: 3*. 05+(-2)*(. 20)=-25% 32

Short Selling and Portfolio Weights o Suppose when you took the short MSFT position you expected MSFT to return -10% with a standard deviation of 0. 25 o What is expected return and standard deviation of your portfolio? 33

Short Selling and Stat Rules o Stat Rule #1 n E[rp]=3*. 05+(-2)*(-. 10)=35% o Stat Rule #2 n n = (-2)2*. 252=0. 25 = 2*(0. 25)=0. 50 34

Short Selling and Portfolio Weights o At the beginning of the year, what is your 5% VAR? o 5% VAR=0. 35 -1. 64*. 50=-47% o If you get a -47% return, what happened to MSFT? -. 47=-2*r. H+3*. 05 r. H=(-. 47 -3*. 05)/(-2)=0. 31 o Note: given that MSFT does have en expected return of -10% and a stdev of. 25, the probability r. H is 0. 31 or greater is 5% 35

Borrowing as Short-Selling o You can think of borrowing as shortselling a risk-free bond. Borrow $909. 09 at 10% Short-sell 1 bond FV = 1000, Price = 909. 09 • Get $909. 09 now • Pay $1000 in future 36