Equities: Positions and Portfolio Returns

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1 Foundaions of Finance: Equiies: osiions and orfolio Reurns rof. Alex Shapiro Lecure oes 4b Equiies: osiions and orfolio Reurns I. Readings and Suggesed racice roblems II. Sock Transacions Involving Credi III. orfolio Reurns IV. Appendix V. Addiional Readings Buzz Words: Going Long, Buying on Margin, Selling Shor, ercenage Margin, Mainenance Margin, orfolio Weighs

2 Foundaions of Finance: Equiies: osiions and orfolio Reurns I. Readings and Suggesed racice roblems BKM, Chaper 3: Secions Suggesed roblems, Chaper 3: -4, 3, 4. II. Sock Transacions involving Credi Use he sock of XYZ corporaion as an example. The following are he dividends and closing prices for XYZ: Dae Dividend: XYZ Closing rice:xyz end Jan 0 8 end Feb 0 0 end Mar 0 7 Suppose you have $8000 cash a he end of January. Your balance shee a he end of January looks like: Asses Liabiliies Cash 8000 e Worh 8000 Toal Asses 8000 Toal Liab & e W Assume your broker requires ineres of % per monh on any funds borrowed from her. Any funds placed wih your broker also earn %. We consider his rae EAR.68% as he riskless rae known in advance wih cerainy. oe ha XYZ s sock is a risky asse because is price over ime is no known in advance.

3 Foundaions of Finance: Equiies: osiions and orfolio Reurns A. Long he Sock Long he Sock: Means buying he sock wih your own funds. Example A he end of January, you wan o inves your $8000 in XYZ shares a he closing price; so buy 000 shares: Asses Liabiliies 000 XYZ $ e Worh 8000 Toal Asses 8000 Toal Liab & e W By he end of February, XYZ s price has gone up: Asses Liabiliies 000 XYZ $ e Worh 0000 Toal Asses 0000 Toal Liab & e W By he end of March, XYZ s price has plunged: Asses Liabiliies 000 XYZ $ e Worh 7000 Toal Asses 7000 Toal Liab & e W

4 Foundaions of Finance: Equiies: osiions and orfolio Reurns B. Buying Sock on Margin Leveraging Buying Sock on Margin: Means buying sock using funds borrowed from a broker. The clien is charged an ineres on he borrowed funds plus a fee. ercenage margin: refers o ne worh value of he sock less amoun borrowed as a percenage of he value of he sock: e Worh ercenage Margin 00% Value of Sock. The Board of Governors of he Federal Reserve Sysem ha has he auhoriy o se he margin-credi limi by he Securiies Exchange Ac of 934 has se he minimum iniial margin a 50%. Regulaion T, par 0 Credi by Brokers and Dealers. So he borrowed amoun mus be less han 50% of he value of he sock purchased. Usually, he invesor is no allowed o le he porion of deb rise higher han 75% of he value of he socks in he accoun ercenage Margin mus remain above 5%.. If he percenage margin falls below he mainenance margin se by he broker which may be above 5%, he cusomer has o pu up enough collaeral o saisfy he mainenance margin. 4

5 Foundaions of Finance: Equiies: osiions and orfolio Reurns A he end of January, you wan o buy 400 shares in XYZ. You hus need o borrow 400 $8 - $8000 $300 from your broker. ercen Margin 8000/ %>50%: Asses Liabiliies 400 XYZ $8 00 Loan 300 e Worh 8000 Toal Asses 00 Toal Liab & e W. 00 By he end of February, XYZ s price is up: ercen Margin 0768/ %. Asses Liabiliies 400 XYZ $ Loan 33 e Worh 0768 Toal Asses 4000 Toal Liab & e W By he end of March, XYZ s price has plunged: ercen Margin 6536/ %. Asses Liabiliies 400 XYZ $ Loan 364 e Worh 6536 Toal Asses 9800 Toal Liab & e W

6 Foundaions of Finance: Equiies: osiions and orfolio Reurns C. Shor Selling Sock Shor Selling Sock: Means borrowing he sock and selling i. roceeds from he sale mus remain wih he broker. The shor-seller will reurn he sock back when asked o do so by he broker, or when he/she chooses o do so, whichever occurs firs. If he sock pays dividends, he shor-seller mus pay hem o he original owner. ercenage margin: refers o ne worh as a percenage of he value of he sock borrowed: ercenage e Worh Margin 00% Value of Sock Borrowed If he percenage margin falls below he mainenance margin se by he broker, he cusomer has o pu up enough collaeral o saisfy he mainenance margin. 6

7 Foundaions of Finance: Equiies: osiions and orfolio Reurns Example. A he end of January, you have $8000 in cash wih your broker, and you wan o shor-sell 400 shares of XYZ. a. You borrow 400 shares of XYZ. The loan is denominaed in shares of XYZ no in dollars. Asses Liabiliies 400 XYZ $8 00 Loan 400 $8 00 Cash 8000 e Worh 8000 Toal Asses 900 Toal Liab & e W. 900 b. You sell he borrowed shares a he closing price a he end of January: ercen Margin 8000/ % Asses Liabiliies Cash 900 Loan 400 $8 00 e Worh 8000 Toal Asses 900 Toal Liab & e W By he end of February, XYZ s price has gone up: ercen Margin 539/ % Asses Liabiliies Cash 939 Loan e Worh 539 Toal Asses 939 Toal Liab & e W

8 Foundaions of Finance: Equiies: osiions and orfolio Reurns. By he end of March, XYZ s price has plummeed: ercen Margin 9786/ % Asses Liabiliies Cash 9586 Loan e Worh 9786 Toal Asses 9586 Toal Liab & e W To close ou he posiion a he end of March, ake he following seps: a. purchase 400 shares of sock: Asses Liabiliies Cash 9786 Loan sh 9800 e Worh 9786 Toal Asses 9586 Toal Liab & e W b. repay he sock loan: Asses Liabiliies Cash 9786 e Worh 9786 Toal Asses 9786 Toal Liab & e W

9 Foundaions of Finance: Equiies: osiions and orfolio Reurns D. Comparison of osiions Wha is he monhly reurn, each monh, for he above hree holding sraegies? Recall ha in he absence of any dividend paymen: So, Reurn [rice end / rice sar] -. orfolio Reurn [orfolio Valueend / orfolio Valuesar] - where in our example he orfolio Value is given by e Worh. Long 000 shares of XYZ Buy 400 shares of XYZ on Margin Shor Sell 400 shares of XYZ Dae e Worh Reurn e Worh Reurn e Worh Reurn Jan Feb % % % Mar % % %. Buying on Margin vs Going Long: Insead of using saring ne worh o buy a firm s sock, he invesor uses i o buy a larger number of he firm s shares on margin he porfolio is leveraged. a. A given price decline causes a larger reducion in ne worh. b. A given price increase causes a larger increase in ne worh. c. So he invesor s ne worh is more sensiive o changes in he sock price.. Shor-Selling vs Buying he Sock: Shor-selling causes ne worh o have a negaive sensiiviy o changes in he sock price. a. A price decline causes an increase in ne worh. b. A price increase causes a decrease in ne worh. 9

10 Foundaions of Finance: Equiies: osiions and orfolio Reurns III. orfolio Reurns A. orfolio Reurn Formula The following formula can be used o calculae he reurn on a porfolio, in period, given he reurns on he asses ha comprise he porfolio: r p w,p r + w,p r w,p r where is he number of asses in he porfolio; r i is he reurn on asse i in period ; w i,p is he weigh of asse i in porfolio p; r p is he reurn on porfolio p in period. Remarks:. orfolio weighs mus sum o.. The noaion r f or R f is usually reserved for he riskless rae also referred o as he risk-free rae Example Suppose you have $8000 o inves a he end of January. You decide o inves $6000 in XYZ and $000 in he Riskless Asse i.e., he Money-Marke accoun, which yields %. You have invesed: $6000/$ or 75% of your money in XYZ. You have a weigh w XYZ,p 0.75 in socks. $000/$ or 5% in he riskless asse. You have a weigh w f,p 0.5 in a riskless asse. 0

11 Foundaions of Finance: Equiies: osiions and orfolio Reurns Your porfolio s reurn in February can be calculaed using he porfolio reurn formula. Insead of calculaing porfolio s dollar value using balance shees for he reurn calculaion, i is simpler o use he reurns and he weighs of individual asses wihin he porfolio. r p Feb w XYZ,p r XYZ Feb + w f,p r f Feb % % 9%. B. Inerpreaion of orfolio Weighs w. Buying a Sock on Margin: w Sock > When 400 shares of XYZ were bough on margin a he end of January, he weigh on XYZ in he porfolio was >. The value of he porfolio a he end of January was $8000, of which 400 $8 $00 was invesed in XYZ and -$300 was invesed in he riskless asse. So, w XYZ,p $00/$ w f,p -$300/$ noe he weighs sum o. Then can calculae he porfolio reurn for February 000: r p Feb w XYZ,p r XYZ Feb + w f,p r f Feb.4 5% % 34.6% which agrees wih he reurn calculaed on page 0.

12 Foundaions of Finance: Equiies: osiions and orfolio Reurns. Shor selling: w Sock <0 When 400 shares of XYZ were shor sold a he end of January 000, he weigh on XYZ in he porfolio was <0. The value of he porfolio a he end of January 000 was $8000, of which -400 $8 - $00 was invesed in XYZ and $8000+$00$900 was invesed in he riskless asse. So, w XYZ,p -$00/$ w f,p $900/$ noe he weighs sum o. Then can calculae he porfolio reurn for February 000: r p Feb w XYZ,p r XYZ Feb + w f,p r f Feb -.4 5% +.4 % -3.6% which agrees wih he reurn calculaed on page 0.

13 Foundaions of Finance: Equiies: osiions and orfolio Reurns IV. Appendix: More on he orfolio Reurn Formula This appendix is o assure he skepics among you, ha here is no magic in he porfolio reurn formula. Insead, i is jus a useful shorcu. You may skip his appendix. Since you are sill reading o illusrae he idea, consider a porfolio of wo asses: Sock and Sock. You are ineresed in he porfolio s reurn over he period from - o : A he ime - you have: shares of Sock, wih price per share - shares of Sock, wih price per share - orfolio value a - is A ime, he price of Sock is and he price of Sock is, and you sill have shares of Sock and shares of Sock, and he porfolio value is + You wan o verify ha he porfolio reurn r is given by he formula r W, r + W, r where he weighs are se a ime - as W, W, 3

14 Foundaions of Finance: Equiies: osiions and orfolio Reurns 4 and he reurns on each sock are, respecively, assuming here are no dividends paid during he sudied period. To verify he formula for he porfolio reurn r, jus use he formula and express he porfolio value a each ime, explicily: Clearly, he above wo-asse logic applies o asses as well, as in he general formula. r r r r [ ] + + / [ ] + / + / + r r,, r W r W +

15 Foundaions of Finance: Equiies: osiions and orfolio Reurns V. Addiional Readings The following aricles discuss: The ongoing debae abou Margin Deb To pu hings in hisoric perspecive: A he heigh of he Bull Marke, Margin deb in January 000 rose o.57% of marke value, equal o is peak in he fall of 987 ahead of he Ocober 987 sock-marke crash. Tha raio approached 30% in 99! The racice of Shor-Selling You can shor socks, bonds, and oher financial asses; he abiliy o shor and leverage is also one imporan disincion beween muual funds and hedge funds. 5

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