Finance

 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...

  Measuring Returns: TOTAL RETURN  We now know that a correct returns measure must incorporate the two components of return, yield and price change, keeping in mind that either component could be zero. The total return (TR) for a given holding period is a decimal or percentage number relating all the cash flows received by an investor during any designated time period to the purchase price of the asset calculated as The periodic cash flows from a bond consists of the interest payments received, and for a stock, the dividends received. For some assets, such as a warrant or a stock that pays no dividends, there is only a price change. Part A of Exhibit 1 illustrates the calculation of TR for a bond, a common stock, and a warrant. Although one year is often used for convenience, the TR calculation can be applied to periods of any length. Conclusions About Total Return:   In summary, the total return concept is valuable as a measure of return because it is all-inclusive,...

Return: A return, also known as a financial return, in its simplest terms, is the money made or lost on an investment over some period of time. A return can be expressed nominally as the change in dollar value of an investment over time. A return can also be expressed as a percentage derived from the ratio of profit to investment. Returns can also be presented as net results (after fees, taxes, and  inflation ) or gross returns that do not account for anything but the price change.  Key Points: A return is the change in price of an asset, investment, or project over time, which may be represented in terms of price change or percentage change. A positive return represents a profit while a negative return marks a loss. Returns are often annualized for comparison purposes, while a holding period return calculates the gain or loss during the entire period an investment was held. The real return accounts for the effects of inflation and other external factors, while the nominal ret...

Risk Measurement:   In addition to considering profit margins, the risk that an investment can create can be measured quantitatively through statistics.  The most common statistical measure used to describe investment risk is its standard deviation. Standard Deviation: From a statistics standpoint, the standard deviation of a dataset is a measure of the magnitude of deviations between the values of the observations contained in the data set.  From a financial standpoint, the standard deviation can help investors quantify how risky an investment is and determine their minimum required return on the investment. The most common statistical indicator of an asset’s risk is the standard deviation,  σ , which measures the dispersion around the expected value. The expected value of a return, k , is the most likely return on an asset. It is calculated as follows:                   Standard Deviation = n − 1 ∑ i = 1 n ​ ( x i ...