448_09CapMktsIntro - Lecture Notes 9 Introduction to...

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71 Lecture Notes 9 Introduction to Capital Markets Returns on stock • There are two components to the return on stocks. First, most, but not all stocks, pay a cash div- idend usually once a quarter. Second, the price of a stock can change from one year to the next. The change in the stock price is also part of the return whether or not the capital gain or loss is actually realized . Someone who does not realize their gain can be considered to have re-invested their income in the stock. • For a dividend D t +1 paid at the end of the current period, and using P t for the price of the stock, the total percentage return on a stock can be written (1) • When one examines the longer term return on a range of different stocks or portfolios of stocks one finds that, in general, those assets or portfolios with the highest variation in returns from one year to the next also tend to have the highest average return. Here the average return is calculated as follows. Suppose the percentage returns over T years were R 1 , R 2 , R 3 , …, R T . The average per- centage return R would then be 1 (2) Returns on bonds • Government bonds are usually regarded as the least risky type of bond. Since the government has 1. Note that this arithmetic average differs from the geometric average which can be defined as the constant rate of return that would have produced the same total return over the T years as the actual holding return obtained over that period. Specifically, the geometric average return R is given by R t 1 + D t 1 + P t ----------- P t 1 + P t () P t ------------------------ + = 1 R + T 1 R 1 + 1 R 2 + & 1 R T + 1 R t + t 1 = T == R R 1 R 2 & R T +++ T -------------------------------------- 1 T -- R t t 1 = T =
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72 the legal right to take resources (through taxes) to pay off its obligations, it is commonly believed that there is no default risk for government debt. 2 • The lack of default risk does not, however, make government debt riskless. Longer term govern- ment bonds are issued with a coupon payment that will guarantee, at the time the bond is sold, that an investor can earn a fixed nominal return by holding the bond to maturity. Shorter term Treasury Bills (or T-Bills) are auctioned once a week and are typically pure discount bonds. Giv- en the auction price, an investor can also guarantee the return on T-Bills by holding them to ma- turity, at which point they are redeemed by the Treasury for their face value. The return on both T-Bills and longer term government bonds is not fixed in advance, however, if neither type of bond is held to maturity. If interest rates change before the bond matures the market price of the bond will change so that the effective return matches the new market interest rate. An increase in interest rates will lead to a fall in the price of the bond and vice versa. • Furthermore, even if a bond is held to maturity, its ex-post real return will vary if the inflation rate varies. Variability in the inflation rate therefore raises the risk associated with investing in government bonds and makes them less attractive to risk averse investors.
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This note was uploaded on 12/20/2011 for the course ECON 448 taught by Professor Bejan during the Spring '06 term at Rice.

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448_09CapMktsIntro - Lecture Notes 9 Introduction to...

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