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Chapter 1

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Administrative Studies
ADMS 3531
Dale Domian

Chapter 1: A Brief History of Risk and Return Who wants to be a millionaire? - suppose at the age of 25, you begin saving $3,000/year. 40 years later, you retire at age 65. If you earn 10%, you will have about $1.3 million - based on the history of financial markets, the answer appears to be yes. (between 1950 and 2010, the Toronto Stock Index has yielded about 10.10% per year) - history of risk and return is made day by day in global financial markets - two key observations emerge from a study of financial market history (#1: there is a reward for bearing risk, and, at least on average, that reward has been substantial (that’s the good news), #2: the bad news is that greater rewards are accomplished by greater risks - the fact that risk and return go together is probably the single most important fact to understand about investments - the only way to earn a higher return is to take on greater risk 1.1 - Returns Dollar Returns - if you buy an asset of any type, your gain (or loss) from that investment is called the return on your investment - the return will usually have two components 1. You may receive some cash directly while you own the investment 2. The value of the asset you purchase may change (in this case, you have a capital gain or capital loss on your investment) Example of Dollar Returns: Suppose you purchase 100 shares of stock in Toronto Dominion (TD) Bank on January 1 . At that time, TD Bank was selling for $75 per share, so your 100 shares cost you $7,500. At the end of the year, you want to see how you did with your investment. • The first thing to consider is the over the year, a company may pay cash dividends to its shareholders • As a shareholder of TD, you are a part owner of the company and you are entitled to a portion of any money distributed • If TD chooses to pay a dividend, you will receive some cash for every share you own • In addition to every dividend, the other part of your return is the capital gain or loss on the stock – this part arises from changes in the value of your investment At the beginning of the year, on January 1 , the stock is selling for $75 per share, and as we calculated above, your total outlay for 100 shares is $7,500. Over the year, Toronto-Dominion pays dividends of $2.45 per share. By the end of the year, you receive dividend income of: Dividend income = $2.45 x 100 = $245 st In addition, suppose that as of December 31 , Toronto-Dominion was selling for $80, meaning that the value of your stock increased by $5 per share. Your 100 shares are now worth $8,000, so you have a capital gain of: Capital gain ($80.00 - $75.00) x 100 = $500 On the other hand, if the price had dropped to, say, $71.00. You would have a capital loss of: Capital loss ($71.00 - $75.00) x 100 = -$400 - capital loss = negative capital gain - total dollar return: the return on an investment measured in dollars that accounts for all cash flows and capital gains or losses Total Dollar Return = Dividend Income + Capital Gain (or Loss) Percentage Returns - more convenient to summarize information about returns in percentage terms than in dollar terms Example of Percentage Returns: Suppose at the beginning of the year, the shares are $75 per share and the dividend paid during the year on each share was $2.45. If we express this dividend as percentage of the beginning stock price, the result is the dividend yield. Dividend yield = D t+1 / P t = $2.45 / $75 = 0.0327 = 3.27% (for each dollar we invested, we received 3.27 cents in dividends) The second component of our percentage return is capital gains yield, the change in stock price as a percentage of the initial stock price. This yield is calculated as the change in price during the year (the capital gain) dividend by the beginning price. With $80 being the ending price, we get: Capital gains yield = (P t+1– P) /tP t = ($80 - $75) / $75 = 0.0667 = 6.67% (this 6.67 percent yield means that for each dollar invested we got 6.67 cents in capital gains) Putting it all together, per dollar invested, we get 3.27 cents in dividends and 6.67 cents in capital gains for a total of 9.94 cents. The total percent return is the return on an investment measured as a percentage that accounts for all cash flows and capital gains or losses. When a return is expressed on a percentage basis, we often refer to it as the rate of return OR “return” on the investment. If we combine the formulas for dividend yield and capital gains yield, we get a single formula for the total percentage return: Percentage return = Dividend Yield + Capital Gains Yield = (D t+1+ P t+1 – P)t/ P t A Note on Annualizing Returns - so far, we’ve only considered annual returns - the actual length of time you own an investment will almost never be exactly a year Example of Annualizing Returns: Suppose you bought 200 shares of Scotiabank at a price of $50 per share. In three months, you sell your stock for $54. You didn’t receive any dividends. What is your return for the three months? What is your annualized return? Your holding period, the length of the time you own the stock, is three months. Percentage return = (Pt+1 Pt / t = ($54 - $50) / $50 = 0.0800 = 8.00% The above 8.00% is the return for the three-month holding period. The return amounts differently on a per-year basis. To find out, we need to convert this to an annualized return, meaning a return expressed on a per-year basis. Such a return is called an effective annual return (EAR). 1 + EAR = (1 + holding period percentage return) m where m is the number of holding periods in a year In our example, the holding period percentage return is 8.00 percent. The holding period is three months, so there are four periods (12 months / 3 months) in a year. The annualized return, EAR, is: 1 + EAR = (1 + holding period percentage return) = (1 + 0.0800) = 1.3605 Therefore, the annualized return is 36.05% 1.3 Average Returns: The First Lesson Calculating Average Returns - if you add up the returns for a large-company common stocks for the 84 years, you will get about 986 percent. The average annual return is thus
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