Ch.6 Risk and Return

The expected rate of return

( r-hat) is the expected value of a probability distribution of expected returns. Written another way, the same formula is as follows: E(R) = w1R1 + w2Rq + ...+ wnRn ◉ The expected rate of return uses probabilities to weigh the various return outcomes that an investment may produce. The probability distribution varies according to the investor. ◉ In order to make investment decisions, investors often estimate the expected return of a potential investment. ◉ Expected value is a concept that the helps investors assess the value of a potential investment based on different future outcomes and a probability for each outcome. ◉ Once you have categories for different scenario 's, along with probabilities and returns in each scenario, you then calculate your expected return by multiplying each probability by it's respective outcome and adding these all together.

continuous probability distribution

A continuous probability distribution contains an infinite number of outcomes and is graphed from negative infinity to positive infinity, zero to infinity, or an interval like [0, 10], which represents all real numbers from 0 to 10, including 0 and 10.

variance:

In finance, variance is a term used to measure the degree of risk in an investment. ❖ It is calculated by finding the average of the squared deviations from the mean rate of return. Variance is a statistical concept describing the range around expected return within which an investment return can be reasonably expected to fall.

define three forms of market efficiency (2)

Semistrong-form efficiency states that current market prices reflect all publicly available information. Therefore, the only way to gain abnormal returns on a stock is to possess inside information about the company's stock.

define three forms of market efficiency (3)

Strong-form efficiency assumes that all information pertaining to a stock, whether public or inside information, is reflected in current market prices. Thus, no investors would be able to earn abnormal returns in the stock market.

SML equation

The slope of the SML equation is (rM - rRF), the market risk premium. The slope of the SML reflects the degree of risk aversion in the economy. The greater the average investors aversion to risk, then the steeper the slope, the higher the risk premium for all stocks, and the higher the required return.

probability distribution

is a listing, chart or graph of all possible outcomes, such as expected rates of return, with a probability assigned to each outcome. When in graph form, the tighter the probability distribution, the less uncertain the outcome.

CAPM

is a model based upon the proposition that any stock's required rate of return is equal to the risk free rate of return plus a risk premium reflecting only the risk remaining after diversification.

The market portfolio

is a portfolio consisting of all stocks.

Diversifiable risk

is also known as company specific risk, that part of a security's total risk associated with random events not affecting the market as a whole. This risk can be eliminated by proper diversification.

Stand-alone risk

is only a part of total risk and pertains to the risk an investor takes by holding only one asset.

The expected return on a portfolio

is simply the weighted-average expected return of the individual stocks in the portfolio, with the weights being the fraction of total portfolio value invested in each stock.

Market risk

is that part of a security's total risk that cannot be eliminated by diversification. It is measured by the beta coefficient.

A realized return

is the actual return an investor receives on their investment. It can be quite different than their expected return. The return that is actually earned over a given time period. ◉ This figure takes into consideration any earnings generated by each of the assets contained in the portfolio, as well as any losses that were incurred as a result of a shift in the value of the individual assets. ◉ When calculating the realized return on a portfolio that includes bond issues, it is important to focus on the actual interest payments that are received on bond coupon for the period cited. ◉ Employing the calculation of a realized return can go a long way toward helping an investor make decisions about what assets to hold for a little longer, which ones to sell immediately, and when acquiring additional shares or units of a given investment would be a wise choice. ◉By measuring the rate of return over time, it is possible to determine if the goals set for the investment effort are being met, and the potential impact of buying and selling assets on reaching those goals. ◉ As a management tool, knowing the realized return for successive periods can help an investor arrange his or her assets to best effect, and position the portfolio to move onward to the next level of profitability. ------------ --------- ------------------ There are several reasons why an investor would want to periodically confirm the actual return generated on his or her investments. (1)The first has to do with the stability of the portfolio itself. If the rate of return for the portfolio overall is low or should decrease, this is a sign that some diversification in the types of investments would be a good idea. (2) In the event that the portfolio is already diverse, a loss in return could indicate that one or more of the investment types compose a higher percentage of the overall worth of the collected assets than they should. (3) With both scenarios, noting that the realized return is not what it should be can prompt the investor to make changes before further losses are incurred.

Equilibrium

is the condition under which the expected return on a security is just equal to its required return,: r-hat= r and the market price is equal to the intrinsic value.

The market risk premium

is the difference between the expected return on the market and the risk-free rate.

A risk premium

is the difference between the rate of return on a risk-free asset and the expected return on Stock i which has higher risk.

Correlation

is the tendency of two variables to move together. A correlation coefficient (ρ) of +1.0 means that the two variables move up and down in perfect synchronization, while a coefficient of -1.0 means the variables always move in opposite directions. A correlation coefficient of zero suggests that the two variables are not related to one another; that is, they are independent.

The relevant risk

of a stock is its contribution to the riskiness of a well-diversified portfolio.

The security market line (SML)

represents in a graphical form, the relationship between the risk of an asset as measured by its beta and the required rates of return for individual securities. The SML equation is essentially the CAPM, ri = rRF + bi(RPM). It can also be written in terms of the required market return: ri = rRF + bi(rM - rRF).

The Efficient Markets Hypothesis (EMH)

states (1) that stocks are always in equilibrium and (2) that it is impossible for an investor to consistently "beat the market." In essence, the theory holds that the price of a stock will adjust almost immediately in response to any new developments. In other words, the EMH assumes that all important information regarding a stock is reflected in the price of that stock

define three forms of market efficiency (1)

weak-form, semistrong-form, and strong-form. Weak-form efficiency assumes that all information contained in past price movements is fully reflected in current market prices. Thus, information about recent trends in a stock's price is of no use in selecting a stock.

standard deviation

◉ The standard deviation of an investment is obtained by taking the square root of the variance. It has a more straightforward meaning than variance. It tells you that in a given year, you can expect an investment's return to be one standard deviation above or below the average rate of return. ◉ Standard deviation is a statistical measurement that sheds light on historical volatility.