Portfolio Theory-Investment Managment And Portfolio-Lecture Notes, Study notes of Investment Management and Portfolio Theory

Download Portfolio Theory-Investment Managment And Portfolio-Lecture Notes and more Study notes Investment Management and Portfolio Theory in PDF only on Docsity! y g ( ) Lesson # 33 PORTFOLIO THEORY Measuring Risk: Risk is often associated with the dispersion in the likely outcomes. Dispersion refers to variability. Risk is assumed to arise out of variability', which is consistent with our definition of risk as the chance that the actual outcome of an investment will differ from the expected outcome. If an asset's return has no variability, in effect it has no risk. Thus, a one- year treasury bill purchased to yield 10 percent and held to maturity will, in fact, yield (a nominal) 10 percent No other outcome is possible, barring default by the U.S. government, which is not considered a reasonable possibility. Consider an investor analyzing a series of returns (TRs) for the major types of financial asset over some period of years. Knowing the mean of .this series is not enough; the investor also needs to know something about the variability in the returns. Relative to the other assets, common stocks show, the largest variability (dispersion) in returns, with small common stocks showing f ten greater variability. Corporate bonds have a much smaller variability and therefore a more compact distribution of returns. Of course, Treasury bills are the least risky. The "dispersion of annual returns for bills is compact. Standard Deviation: The risk of distributions' can be measured with an absolute measure of dispersion, or variability. The most commonly used measure of dispersion over some period of years is the standard deviation, which measures the deviation of each observation from the arithmetic mean of the observations and is a reliable measure of variability, because all the information in a sample is used. The standard deviation is a measure of the total risk of an asset or a portfolio. It captures the total variability in the assets or portfolios return whatever the source of that variability. The standard deviation can be calculated from the variance, which is calculated as: n 2 =  (X - X) i = 1 n - 1 Where; 2 = the variance of a set of values X = each value in the set X = the mean of the observations n = the number of returns in the sample 2 = (2) 1 / 2 = standard deviation Knowing the returns from the sample, we can calculate the standard deviation quite easily. Dealing with Uncertainty: Realized returns are important for several reasons. For example, investors need to know how their portfolios have performed. Realized returns, also can be particularly important in helping investors to form expectations about future returns, because investors must concern themselves with their best estimate of return over the next year, or six months, or whatever. docsity.com y g ( ) How do we go about estimating returns, which is what investors must actually do in managing their portfolios? The total return measure, TR, is applicable whether one is measuring realized returns; or estimating, future (expected) returns. Because it includes everything the investor can expect to receive over any specified future period, the TR is useful in conceptualizing the estimated returns from securities. Similarly, the variance, or its square root, the standard deviation, is an accepted measure of variability for both realized returns and expected returns. We will calculate both the variance and the standard deviation below and use them interchangeably as the situation dictates. Sometimes it is preferable to use one and sometimes the other. Using Probability Distributions: The return an investor will earn from investing is not known; it must be estimated. Future return is an expected return and may or may not actually be-realized. An investor may expect the TR on a particular security to be 0.10 for the coming year, but in truth this is only a "point estimate." Risk, or the chance that some unfavorable event will occur, is involved when investment decisions are made. Investors are often overly optimistic about expected returns. Probability Distributions: To deal with the uncertainty of returns, investors need to think explicitly about a: security's distribution of probable TRs. ln other words, investors need to keep in mind that, although they may expect a security to return 10 percent, for example, this is only a one-point estimate of the entire range of possibilities. Given that investors must deal with the uncertain future, a number of possible returns can, and will, occur. In the case of a Treasury bond paying fixed rate of interest, the interest payment will be made with l00-percent certainty barring a financial collapse of the economy. The probability of occurrence is 1.0; because no other outcome is possible. With the possibility of two or more outcomes, which is the norm for common stocks, each possible likely outcome must be considered and a probability of its occurrence assessed. The probability for a particular outcome is simply the chance that the specified outcome will occur. The result of considering these outcomes and their probabilities together is a probability distribution consisting of the specification of the likely outcomes that may occur and the probabilities associated with these likely outcomes. Probabilities represent the likelihood of various outcomes and are typically expressed as a decimal. The sum of the probabilities of all possible outcomes must be 1.0, because they must completely describe all the (perceived) likely occurrences. How are these probabilities and associated outcomes obtained? In the final analysis, investing for some future period involves uncertainty, and therefore subjective estimates. Although past occurrences (frequencies) may be relied on heavily to estimate the probabilities the past must be modified for any changes expected in the future. docsity.com