Finance

  RISK-FREE BORROWING AND LENDING: Assume that the efficient frontier, as shown by the arc AB in Figure 9-1, has been derived by an investor. The arc AB delineates the efficient set of portfolios of risky assets as explained in (For simplicity, assume these are portfolios of common stocks.) We now introduce a risk-free asset with return RF and σ = 0 . As shown in Figure 9-1, the return on the risk-free asset (RF) will plot on the vertical axis because the risk is zero. Investors can combine this riskless asset with the efficient set of portfolios on the efficient frontier. By drawing a line between RF and various risky portfolios on the efficient frontier, we can examine combinations of risk-return possibilities that did not exist previously. Lending Possibilities:  In Figure 9-1 a new line could be drawn between RF and the Markowitz efficient frontier above point X, for example, connecting RF to point V. Each successively higher line will dominate the preceding set of po...

 INTRODUCTION OF THE RISK-FREE ASSET: The first assumption of capital market theory listed above is that investors can borrow and lend at the risk-free rate. Although the introduction of a risk-free asset appears to be a simple step to take in the evolution of portfolio and capital market theory, it is a very significant step. In fact, it is the introduction of a risk-free asset that allows us to develop capital market theory from portfolio theory.  With the introduction of a risk-free asset, investors can now invest part of their wealth in this asset and the remainder in any of the risky portfolios in the Markowitz efficient set. This allows Markowitz portfolio theory to be extended in such a way that the efficient frontier is completely changed, which in turn leads to a general theory for pricing assets under uncertainty.  Defining a Risk-Free Asset: An asset which an indubitable return is a risk-free asset. This type of asset has a  definite future return, regardl...

 The Equation for the CML: We now know the intercept and slope of the CML. Since the CML is the tradeoff between expected return and risk for efficient portfolios, and risk is being measured by the standard deviation, the equation for the CML is shown as Equation 9-1: where:  E (Rp) = the expected return on any efficient portfolio on the CML   RF = the rate of return on the risk-free asset   E (RM) = the expected return on the market portfolio M   σM = the standard deviation of the returns on the market portfolio   σp = the standard deviation of the efficient portfolio being considered  In words, the expected return for any portfolio on the CML is equal to the risk-free rate plus a risk premium. The risk premium is the product of the market price of risk and the amount of risk for the portfolio under consideration. Important Points About the CML:   The following points should be noted about the CML:  1. Only efficient port...

 Capital Market Theory: Capital market theory is a positive theory in that it hypothesizes how investors do behave rather than how investors should behave, as in the case of modern portfolio theory (MPT).  It is reasonable to view capital market theory as an extension of portfolio theory, but it is important to understand that MPT is not based on the validity, or lack thereof, of capital market theory.  The specific equilibrium model of interest to many investors is known as the capital asset pricing model, typically referred to as the CAPM. It allows us to assess the relevant risk of an individual security as well as to assess the relationship between risk and the returns expected from investing.  The CAPM is attractive as an equilibrium model because of its simplicity and its implications. As a result of serious challenges to the model over time, however, alternatives have been developed. The primary alternative to the CAPM is arbitrage pricing theory, or APT, whic...

 GEOMETRIC MEAN: The arithmetic mean return is an appropriate measure of the central tendency of a distribution consisting of returns calculated for a particular time period, such as 10 years. However, when an ending value is the result of compounding over time, the geometric mean, is needed to describe accurately the “true” average rate of return over multiple periods.  The geometric mean is defined as the nth root of the product resulting from multiplying a series of return relatives together, as in : where TR is a series of total returns in decimal form. Note that adding 1.0 to each total return produces a return relative. Return relatives are used in calculating geometric mean returns, because TRs, which can be negative or zero, cannot be used in the calculation. The geometric mean return measures the compound rate of growth over time. It is important to note that the geometric mean assumes that all cash flows are reinvested in the asset and that those reinvested funds ear...

Statistics for Returns : Two such measures used with returns data are described below: ARITHMETIC MEAN: The arithmetic mean is the average of a sum of numbers, which reflects the central tendency of the position of the numbers. It is often used as a parameter in statistical distributions or as a result to summarize the observations of an experiment or a survey.  In finance, the arithmetic mean is appropriate to support future estimates. The best known statistic to most people is the arithmetic mean. Therefore, when someone refers to the mean return they usually are referring to the arithmetic mean unless otherwise specified. The arithmetic mean, customarily designated by the symbol X-bar, of a set of values is calculated as: or the sum of each of the values being considered divided by the total number of values n. For Example: Let us take an example of a batsman who scored the following runs in his last 10 innings during last one year: 45, 65, 7, 10, 43, 35, 25, 17, 78, 91. Calcula...