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MT 217: Seminar 6

Chapter 7 and 8

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Return Measurement for a Single Asset: Expected Return

• The most common statistical indicator of an asset’s risk is the standard deviation, k, which measures the dispersion around the expected value.

• The expected value of a return, r-bar, is the most likely return of an asset.

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Return Measurement for a Single Asset: Expected Return (cont.)

Table 5.4 Expected Values of Returns for Assets A and B

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Risk Measurement for a Single Asset: Standard Deviation

• The expression for the standard deviation of returns, k, is given in Equation 5.3 below.

5-5

Risk Measurement for a Single Asset: Coefficient of Variation

• The coefficient of variation, CV, is a measure of relative dispersion that is useful in comparing risks of assets with differing expected returns.

• Equation 5.4 gives the expression of the coefficient of variation.

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Portfolio Return

• The return of a portfolio is a weighted average of the returns on the individual assets from which it is formed and can be calculated as shown in Equation 5.5.

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Risk of a Portfolio: Adding Assets to a Portfolio

0 # of Stocks

Systematic (non-diversifiable) Risk

Unsystematic (diversifiable) Risk

Portfolio Risk (SD)

σM

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Risk and Return: The Capital Asset Pricing Model (CAPM) (cont.)

• To measure the amount of systematic risk an asset has, they simply regressed the returns for the “market portfolio”—the portfolio of ALL assets—against the returns for an individual asset.

• The slope of the regression line—beta—measures an assets systematic (non-diversifiable) risk.

• In general, cyclical companies like auto companies have high betas while relatively stable companies, like public utilities, have low betas.

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The risk-free rate (RF) is usually estimated from the return on US T-bills

The risk premium is a function of both market conditions and the asset

itself.

Risk and Return: The Capital Asset Pricing Model (CAPM) (cont.)

• The required return for all assets is composed of two parts: the risk-free rate and a risk premium.

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Risk and Return: The Capital Asset Pricing Model (CAPM) (cont.)

• The risk premium for a stock is composed of two parts:

• The Market Risk Premium which is the return required for investing in any risky asset rather than the risk-free rate

• Beta, a risk coefficient which measures the sensitivity of the particular stock’s return to changes in market conditions.

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Risk and Return: The Capital Asset Pricing Model (CAPM) (cont.)

• After estimating beta, which measures a specific asset or portfolio’s systematic risk, estimates of the other variables in the model may be obtained to calculate an asset or portfolio’s required return.

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The Nature of Equity Capital: Voice in Management

• Unlike bondholders and other credit holders, holders of equity capital are owners of the firm.

• Common equity holders have voting rights that permit them to elect the firm’s board of directors and to vote on special issues.

• Bondholders and preferred stockholders receive no such privileges.

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Common Stock: Ownership

• The common stock of a firm can be privately owned by an individual, closely owned by a small group of investors, or publicly owned by a broad group of investors.

• Typically, small corporations are privately or closely owned and if their shares are traded, this occurs infrequently and in small amounts.

• Large corporations are typically publicly owned and have shares that are actively traded on major securities exchanges.

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Common Stock: Preemptive Rights

• A preemptive right allows common stockholders to maintain their proportionate ownership in a corporation when new shares are issued.

• This allows existing shareholders to maintain voting control and protect against the dilution of their ownership.

• In a rights offering, the firm grants rights to its existing shareholders, which permits them to purchase additional shares at a price below the current price.

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Stock Returns are derived from both dividends and capital gains, where the capital gain results from the appreciation of the stock’s market price.due to the growth in the firm’s earnings. Mathematically, the expected return may be expressed as follows:

E(r) = D/P + g

For example, if the firm’s $1 dividend on a $25 stock is expected to grow at 7%, the expected return is:

E(r) = 1/25 + .07 = 11%

Common Stock Valuation

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Stock Valuation Models: The Basic Stock Valuation Equation

5-177-17

Stock Valuation Models: The Zero Growth Model

• The zero dividend growth model assumes that the stock will pay the same dividend each year, year after year.

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The dividend of Denham Company, an established textile manufacturer, is expected to remain constant at $3 per share indefinitely. What is the value of Denham’s stock if the required return demanded by investors is 15%?

P0 = $3/0.15 = $20

Stock Valuation Models: The Zero Growth Model (cont.)

• Note that the zero growth model is also the appropriate valuation technique for valuing preferred stock.

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Stock Valuation Models: Constant Growth Model

• The constant dividend growth model assumes that the stock will pay dividends that grow at a constant rate each year—year after year forever.

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Stock Valuation Models: Variable-Growth Model

• The non-constant dividend growth or variable-growth model assumes that the stock will pay dividends that grow at one rate during one period, and at another rate in another year or thereafter.

• We will use a four-step procedure to estimate the value of a share of stock assuming that a single shift in growth rates occurs at the end of year N.

• We will use g1 to represent the initial growth rate and g2

to represent the growth rate after the shift.