A stock’s rate of return for a past or future year is calculated by:
r = D/P 0 + (P 1 – P 0 )/P 0
The expected rate of return (“expected return”) to be realized from an investment is the mean value of the probability distribution of possible returns.
Probability Distribution – A list of all the possible outcomes of a future event together with the probability (chance of occurrence) for each outcome.
You can calculate the mean (expected value), the standard deviation, and the variance of a probability distribution.
The “expected value of returns” or “expected return” for a stock is the weighted average of the possible outcomes (possible returns) where the weights are the probabilities associated with the outcomes.
If there are n possible outcomes for a given stock:
7.
Measuring the Risk of Stocks: The Variance of Returns
The standard deviation, denoted by “sigma”( σ), is a measure of the variability, tightness , or spread of a set of outcomes expressed in a probability distribution.
Variance ( σ 2 ) is the standard deviation squared.
Variance is the expected value of the squared deviations.
The “risk-return tradeoff” - Risk averse investors require higher rates of return to induce them to invest in higher risk securities.
The higher a security’s risk, the higher the return investors demand. Thus, the less they are willing to pay for the investment, i.e. as risk increase, P 0 decreases .
Risk averse investors will diversify their investments in order to reduce risk.
Definition - An investment strategy designed to reduce risk by spreading the funds invested across many securities.
It is holding a broad portfolio of securities so as “not to have all your eggs in one basket.”
Since people hold diversified portfolios of securities, they are not very concerned about the risk and return of a single security . They are more concerned about the risk and return of their entire portfolio .
13.
The Two Components of a Security’s Variance (Risk)
1. Unique Risk - Also called “ diversifiable risk ” and “ unsystematic risk.” The part of a security’s risk associated with random outcomes generated by events specific to the firm. This risk can be eliminated by proper diversification.
2. Market Risk – Also called “ systematic risk .” The part of a security’s risk that cannot be eliminated by diversification because it is associated with economic or market factors that systematically affect most firms.
Market risk reflects economy-wide sources of risk that affect most firms and, hence, the overall stock market .
Combining stocks into a portfolio reduces the variability of possible returns as long as the returns on the individual stocks are not perfectly correlated, i.e. as long as their correlation coefficients are less than +1.0.
Diversification eliminates unique risk and leaves market risk .
Therefore, the relevant measure of risk for a portfolio is the portfolio’s “beta”: a measure of the sensitivity of the portfolio’s returns to changes in the return on the “market portfolio” which is closely approximated by a portfolio consisting of the S&P 500 stocks.
25.
How Do Investors View the Risk of a Single Security Held in a Portfolio?
26.
Answer: “Beta” Measures a Stock’s Market Risk Covariance with the market Variance of the market
Investors seem to be concerned with both market risk and total risk. Therefore, the SML may not produce a correct estimate of k i .
k i = k RF + (k M – k RF ) β i + ???
CAPM/SML concepts are based upon expectations, but betas are calculated using historical data. A company’s historical data may not reflect investors’ expectations about future riskiness.
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