Securities come in a bewildering variety of forms - there are more types of securities than there are breeds of cats and dogs, for instance. They range from relatively straightforward to incredibly complex. A straight bond promises to repay a loan over a fixed amount of interest over time and the principal at maturity. A share of stock, on the other hand, represents a fraction of ownership in a corporation, and a claim to future dividends. Today, much of the innovation in finance is in the development of sophisticated securities: structured notes, reverse floaters, IO's and PO's -- these are today's specialized breeds. Sources of information about securities are numerous on the world-wide web. For a start, begin with the Ohio State Financial Data Finder. All securities, from the simplest to the most complex, share some basic similarities that allow us to evaluate their usefulness from the investor's perspective. All of them are economic claims against future benefits. No one borrows money that they intend to repay immediately; the dimension of time is always present in financial instruments. Thus, a bond represents claims to a future stream of pre-specified coupon payments, while a stock represents claims to uncertain future dividends and division of the corporate assets. In addition, all financial securities can be characterized by two important features: risk and return. These two key measures will be the focus of this second module.
I. Finance from the Investor's Perspective
Most financial decisions you have addressed up to this point in the term have been from the perspective of the firm. Should the company undertake the construction of a new processing plant? Is it more profitable to replace an old boiler now, or wait? In this module, we will examine financial decisions from the perspective of the purchaser of corporate securities: shareholders and bondholders who are free to buy or sell financial assets. Investors, whether they are individuals or institutions such as pension funds, mutual funds, or college endowments, hold portfolios, that is, they hold a collection of different securities. Much of the innovation in investment research over the past 40 years has been the development of a theory of portfolio management, and this module is principally an introduction to these new methods. It will answer the basic question, What rate of return will investors demand to hold a risky security in their portfolio? To answer this question, we first must consider what investors want, how we define return, and what we mean by risk.
II. Why Investors Invest
What motivates a person or an organization to buy securities, rather than spending their money immediately? The most common answer is savings -- the desire to pass money from the present into the future. People and organizations anticipate future cash needs, and expect that their earnings in the future will not meet those needs. Another motivation is the desire to increase wealth, i.e. make money grow. Sometimes, the desire to become wealthy in the future can make you willing to take big risks. The purchase of a lottery ticket, for instance only increases the probability of becoming very wealthy, but sometimes a small chance at a big payoff, even if it costs a dollar or two, is better than none at all. There are other motives for investment, of course. Charity, for instance. You may be willing to invest to make something happen that might not, otherwise -- you could invest to build a museum, to finance low-income housing, or to re-claim urban neighborhoods. The dividends from these kinds of investments may not be economic, and thus they are difficult to compare and evaluate. For most investors, charitable goals aside, the key measure of benefit derived from a security is the rate of return.
III. Definition of Rates of Return
The investor return is a measure of the growth in wealth resulting from that investment. This growth measure is expressed in percentage terms to make it comparable across large and small investors. We often express the percent return over a specific time interval, say, one year. For instance, the purchase of a share of stock at time t, represented as Pt will yield P t+1 in one year's time, assuming no dividends are paid. This return is calculated as: R t = [ P t+1 - Pt]/ Pt. Notice that this is algebraically the same as: Rt= [P t+1/ Pt]-1. When dividends are paid, we adjust the calculation to include the intermediate dividend payment: Rt=[ P t+1 - Pt+Dt]/ Pt. While this takes care of all the explicit payments, there are other benefits that may derive from holding a stock, including the right to vote on corporate governance, tax treatment, rights offerings, and many other things. These are typically reflected in the price fluctuation of the shares.
IV. Arithmetic vs. Geometric Rates of Return
There are two commonly quoted measures of average return: the geometric and the arithmetic mean. These rarely agree with each other. Consider a two period example: P0 = $100, R1 = -50% and R2 = +100%. In this case, the arithmetic average is calculated as (100-50)/2 = 25%, while the geometric average is calculated as: [(1+R1)(1+R2)]1/2-1=0%. Well, did you make money over the two periods, or not? No, you didn't, so the geometric average is closer to investment experience. On the other hand, suppose R1 and R2 were statistically representative of future returns. Then next year, you have a 50% shot at getting $200 or a 50% shot at $50. Your expected one year return is (1/2)[(200/100)-1] + (1/2)[(50/100)-1] = 25%. Since most investors have a multiple year horizon, the geometric return is useful for evaluating how much their investment will grow over the long-term. However, in many statistical models, the arithmetic rate of return is employed. For mathematical tractability, we assume a single period investor horizon.
V. Capital Market History
The 1980's was one of the greatest decades for stock investors in the history of the U.S. capital markets.
(Courtesy Ibbotson Associates)
(Courtesy Ibbotson Associates)
(Courtesy Ibbotson Associates)
| Investment | geom. mean | arith.mean | std | high ret. | low ret. |
| S&P total return | 10.30 | 12.45 | 22.28 | 42.56 | -29.73 |
| U.S. Small Stock TR | 12.28 | 17.28 | 35.94 | 73.46 | -36.74 |
| U.S. LT Govt TR | 4.91 | 5.21 | 8.00 | 15.23 | -8.41 |
| U.S. LT Corp. TR | 5.49 | 5.73 | 7.16 | 13.76 | -8.90 |
| U.S. 30 day T-Bills | 3.70 | 3.70 | .96 | 1.35 | -0.06 |
VII. Standard Deviation as a Measure of Risk
Stock returns may be riskier or more volatile, but this concept is a difficult one to express simply. To do so, we borrow a concept from statistics, called standard deviation. standard deviation is a summary measure about the average spread of observations. It is the square root of the variance, which is calculated as:
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