I. Basic Concepts (Ch. 1-4)

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1 (Ch. 1-4) A. Real vs. Financial Asses (Ch 1.2) Real asses (buildings, machinery, ec.) appear on he asse side of he balance shee. Financial asses (bonds, socks) appear on boh sides of he balance shee. Creaing a financial asse creaes an offseing liabiliy. Secor ne worh is defined as he difference beween secor asses and liabiliies: Secor Ne Worh = Secor Asses asses Secor Liabiliies. liabiliie s Balance Shee for a Single Secor Secor Real Asses Secor Ne Worh Secor Financial Asses Secor Financial Liabiliies Since creaing a financial asse creaes an offseing liabiliy, he sum across he secors of he (closed, privae) economy yields: secors Secor Financial Asses = secors Secor Financial Liabiliies. Therefore, for he whole (closed, privae secor) economy: Real Asses = Ne Worh Δ Real Asses = Δ Ne Worh Invesmen = Savings. Financial asses do no direcly creae wealh (ne worh) bu indirecly conribue o producive capaciy by faciliaing he ransfer of funds. 1

2 B. Overview of Financial Asses Bonds, Equiies, Derivaives (Ch. 2) Bonds are fixed paymen securiies. - Failure o make paymen resuls in bankrupcy for he bond issuer. Equiy is an ownership claim o he residual value of he firm afer paymens of bonds and oher liabiliies. - Paymens o equiy holders are called dividends. - Mos ypes of equiy confer voing righs in corporae decisions. Varians on bonds and equiy are numerous. - e.g. preferred shares, like bonds, pay a fixed income and have no voing righs bu, like equiy, do no rigger bankrupcy if paymens are no made. Primary vs. derivaive asses: - Bonds and equiies are primary asses. - Opions, fuures and forwards are derivaive asses because heir payoffs depend on he value of underlying primary asses. C. Taxaion (Ref. Ch. 4.1 & 23A) Ineres income is axed like ordinary income. Dividend income is given preferenial reamen for risk aking. Capial gains income is given preferenial reamen for risk aking. 2

3 D. Calculaing Periodic Compound Ineres (Ch. 4.2) Suppose ineres is compounded n 1 imes per year so ha he year is broken up ino n periods of (equal) lengh 1/n years. Le r denoe he effecive period ne ineres rae. The effecive period gross ineres rae is 1+r. The effecive annual gross ineres rae is (1+r) n. Le r e denoe he effecive annual ne ineres rae (EAR), r e = (1+ r) n 1. Invesors are ulimaely ineresed in effecive raes. Unforunaely, raes r e are no quoed in he financial pages. The raes ha are usually quoed correspond o nr. Following he ex, we refer o his as he Annual Percenage Rae (APR). Le r a denoe he APR: r a = nr. If n = 1, hen r e = r a = r. If n > 1, hen r e > r a > r. e.g. r a = 0.1 and n = 12 r e = ( /12) 12 1 = > 0.1. r a = 5 and n = 365 r e = (1 + 5/365) = >> 5. For r and n small, r e r a. Noe: Ch 4.2 generalizes he effecive period rae o r f (T), where T is he number of years. For T 1, hen n =1/T. Wha is he error in (4.8)? 3

4 E. Coninuous Compounding (Ch. 4.2) The coninuously compounded annual gross rae of ineres is he limi of he periodic ineres relaionship as n : 1r lim(1 r / n) n. e n a To simplify he analysis, ake he naural logarihm ln(1 r ) lim ln(1 ra / n). e n n 1 The limi is ill defined, as he numeraor and denominaor go o 0. Applying l'hôpial's rule (he limi is given by he limi of he raio of he derivaive of he numeraor o he derivaive of he denominaor): r ln(1 r ) lim (1 / ) e lim r n (1 / n ) a r 2 a n n ra n 2 n ra r Take he anilog o solve for r e = e a 1. Coninuous compounding yields a finie r e. e.g. r a = 0.1 and n. Then r e = r a = 5 and n. Then r e = Noe: For coninuous compounding Ch 4.2 denoes r a = r cc. The Black-Scholes formula uses he coninuously compounded gross rae for T years, (1 + r e ) T r T = e a. However, i is denoed e rt. a. 4

5 F. Nominal vs. Real Ineres Raes (Ch. 4.1) Real ineres raes are usually no direcly observed. However, we can infer real ineres raes using nominal ineres raes and inflaion raes. i) Periodic Compounding The ex pos period real ineres rae can be consruced as follows: Gross Real Rae Gross Nominal Rae / Gross Inflaion Rae 1 + r = (1 + R)/(1 + i) r = (R i)/(1 + i) R i, where R is he period nominal ne ineres rae, and i is he period ne inflaion rae. Noe. The approximaion r R - i overesimaes he (discree period) real rae for i > 0. I is reasonably accurae only when i is small. ii) Coninuous Compounding When ineres is compounded coninuously, R and i becomes infiniesimally small. The ex pos gross rae is derived (his analysis uses APRs, R a and i a ): ra Ra a ( Ra a) e e / e e r a = R a - i a. i Noe. Ch. 4.2 uses he noaion r cc = R cc i cc. i * We ignore he disincion beween real and nominal raes in he res of he course (for he mos par). 5

6 G. Sock, Indexes, and Lisings (Ch , ) i) Primary vs. Secondary Markes New securiies are issued in primary markes (e.g. IPOs), whereas rade of already-issued securiies akes place in secondary markes. Secondary markes include: - formal sock exchanges; e.g. TSX, NYSE, Nikkei. - less formal over-he-couner markes; e.g. NASDAQ. ii) Marke Indexes Marke-valued indexes are direcly relaed o he oal value of sock on he exchange, e.g. S&P/TSX Composie, S&P/TSX 60. The Dow Jones is an archaic price-weighed index. iii) Sock Lisings e.g. from he Globe and Mail websie: Canadian Tire Corporaion CTC.A-T Updaed: Dec 31, :00PM EST Close: C$ Ne Change: C$.67 % Change:.55% Open Bea 0.53 High Trailing P/E Low P/E 1-year forward Bid/Ask / Forward PEG 1.99 Volume 89,934 Indicaed Annual Div Week Range o Dividend Yield 1.71 Over he las five days, shares have gained 0.30% and ouperformed he S&P TSX index over he las 52 weeks wih a 23.37% increase in price. Exercise. The full lising also gives he Previous Close and Trailing EPS. Calculae hese values from he above. Exercise. Canadian Tire Co. also liss CTC-T. I closed a $250. Why are hey priced so differenly? 6

7 H. Buying Sock and Holding Period Rae of Reurn Time Acion Cash Flow 0 Buy share - P 0 1 Receive dividend, sell share P 1 + Dividend Buying sock a ime 0 and selling i a ime 1 yields: Accouning Profi = (P 1 + Dividend) - P 0. The one-period holding period rae of reurn (HPR 1 ) is he accouning profi over he iniial invesmen. For socks: HPR 1 ( P Dividend) P 1 0 P. 0 The -period HPR depends on how he dividends are reinvesed. If hey are reinvesed a he going ineres rae hen HPR ( P CD ) P 0 P, 0 where CD is he fuure value of he cumulaive dividends. Exercise. How would you calculae he HPR on CTC.A-T from he close a he end of 2013 o he close a he end of 2014? Wha informaion would you need? Esimae HPR. Wha is he reurn expressed as an annual rae? Ignore axes assuming invesmen in RRSP. For he dividend hisory (and share reinvesmen plan) see: hp://corp.canadianire.ca/en/investors/shareholderinfo/ Pages/DividenInformaion.aspx 7

8 I. Trading wih Margin (Ch. 3.5) Trading wih margin involves some form of borrowing from a broker. This pracice provides he invesor wih leverage. i) Buying Sock on Margin Buying sock on margin involves borrowing par of a sock purchase from a broker. The margin raio is: M MarkeValueofAsses LoanDeb. MarkeValueofAsses The mainenance margin is denoed by M. If M < M, he broker issues a margin call. When a margin call is issued, he invesor mus add cash o heir accoun or else he broker will sell some of he sock o saisfy M > M. Exercise. You re bullish on ABC sock and wan o use margin o maximize your leverage. You have $10,000, he sock price is currenly P 0 = 10 per share, he iniial margin requiremen is 50% of he marke value of asses (i.e. M I =.5), M = 0.3, and he effecive borrowing rae is r e = ABC does no pay dividends. a) How much sock can you iniially buy? b) Wha is HPR 1 if P 1 = 12.5 a he end of he year? c) Wha is HPR 1 if P 1 = 7.5? d) Wha is HPR 1 if P 1 = 10? e) Wha is he P a which you receive a margin call a an arbirary ime in he fuure? 8

9 Proposiion. In he long run, o avoid a margin call on a long posiion in a sock ha pays no dividends, he sock price mus rise a leas a he rae of ineres. Demonsraion. The margin raio a is: M P NLoan(1 re ). PN Le P = P 0 (1+p) and Loan = θ(p 0 N), where p is he geomeric average rae of reurn on he sock and θ is he proporion of he original marke value ha was borrowed. Subsiuing yields: P N [(1 ) (1 ) M p re ] PN (1 p ) 0 0 M 1 1 r 1 p e. If r e < p, hen M increases over ime and converges o 1. If r e = p, hen M is consan. If r e > p, hen M decreases and evenually his zero. To avoid a margin call in he long run, r e p. Exercise. In each case (r e < p, r e = p, r e > p), deermine wheher he average HPR on he sock is above or below r e and p; i.e. compare average one-period ne raes of reurn, HPR 1 1, o r e and p. 9

10 ii) Shor Sale of Sock Shor-selling involves borrowing he sock and immediaely selling i in he hope ha he sock can be repurchased cheaply in he fuure o repay he loan and earn a profi. Time Acion Cash Flow 0 Borrow share; sell i. P 0 1 Buy share and repay he dividend o replace he share originally borrowed. - (P 1 + Dividend) Proceeds from shor sale are kep wih a broker and earn ineres r b. Ofen on small accouns, brokers do no pay ineres, so r b = 0. Accouning Profi = P 0 (1+ r b ) - (P 1 + Dividend). The borrower mus pu up oher asses as collaeral (e.g. cash, bonds, sock) in a margin accoun and saisfy M s M s. Unlike equaion (3.2) in he ex which omis he 1 erm, we calculae margin as follows: M S MarkeValueofAsses 1. ValueofSockOwed Exercise. You re bearish on ABC sock and wan o shor sell he sock using maximum leverage. You have $10,000 cash in a margin accoun, he sock price is P 0 = 10, he iniial margin requiremen is 50% of he value of he shor posiion, M s =.3, he lending rae is r e =.1052, and r b = 0. f) How much sock can you shor iniially? g) Wha is HPR 1 if P 1 = 12.5 a he end of he year? h) Wha is HPR 1 if P 1 = 7.5? i) Wha is he P a which you receive a margin call for an arbirary ime in he fuure? 10

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