Definition of Expected return

Expected return

The return expected on a risky asset based on a probability distribution for the possible rates
of return. expected return equals some risk free rate (generally the prevailing U.S. Treasury note or bond rate)
plus a risk premium (the difference between the historic market return, based upon a well diversified index
such as the S&P500 and historic U.S. Treasury bond) multiplied by the assets beta.

Expected Return

The total amount of money (return) an investor anticipates to receive from an investment.

Expected return on investment

The return one can expect to earn on an investment. See: capital asset
pricing model.

Expected return-beta relationship

Implication of the CAPM that security risk premiums will be
proportional to beta.

Expected future return

The return that is expected to be earned on an asset in the future. Also called the
expected return.

CARs (cumulative abnormal returns)

a measure used in academic finance articles to measure the excess returns an investor would have received over a particular time period if he or she were invested in a particular stock.
This is typically used in control and takeover studies, where stockholders are paid a premium for being taken over. Starting some time period before the takeover (often five days before the first announced bid, but sometimes a longer period), the researchers calculate the actual daily stock returns for the target firm and subtract out the expected market returns (usually calculated using the firm’s beta and applying it to overall market movements during the time period under observation).
The excess actual return over the capital asset pricing model-determined expected return market is called an ‘‘abnormal return.’’ The cumulation of the daily abnormal returns over the time period under observation is the CAR. The term CAR(-5, 0) means the CAR calculated from five days before the
announcement to the day of announcement. The CAR(-1, 0) is a control premium, although Mergerstat generally uses the stock price five days before announcement rather than one day before announcement as the denominator in its control premium calculation. However, the CAR for any period other than (-1, 0) is not mathematically equivalent to a control premium.

Base probability of loss

The probability of not achieving a portfolio expected return.

Capital asset pricing model (CAPM)

An economic theory that describes the relationship between risk and
expected return, and serves as a model for the pricing of risky securities. The CAPM asserts that the only risk
that is priced by rational investors is systematic risk, because that risk cannot be eliminated by diversification.
The CAPM says that the expected return of a security or a portfolio is equal to the rate on a risk-free security
plus a risk premium.

Cumulative abnormal return (CAR)

Sum of the differences between the expected return on a stock and the
actual return that comes from the release of news to the market.

Efficient diversification

The organizing principle of modern portfolio theory, which maintains that any riskaverse
investor will search for the highest expected return for any level of portfolio risk.

Efficient frontier

The combinations of securities portfolios that maximize expected return for any level of
expected risk, or that minimizes expected risk for any level of expected return.

Efficient portfolio

A portfolio that provides the greatest expected return for a given level of risk (i.e. standard
deviation), or equivalently, the lowest risk for a given expected return.
Efficient set Graph representing a set of portfolios that maximize expected return at each level of portfolio
risk.

Exante return

The expected return of a portfolio based on the expected returns of its component assets and
their weights.

Financial leverage

Use of debt to increase the expected return on equity. Financial leverage is measured by
the ratio of debt to debt plus equity.

Indifference curve

The graphical expression of a utility function, where the horizontal axis measures risk and
the vertical axis measures expected return. The curve connects all portfolios with the same utilities according
to g and s .

Magic of diversification

The effective reduction of risk (variance) of a portfolio, achieved without reduction
to expected returns through the combination of assets with low or negative correlations (covariances).
Related: Markowitz diversification

Market capitalization rate

expected return on a security. The market-consensus estimate of the appropriate
discount rate for a firm's cash flows.

Markowitz efficient portfolio

Also called a mean-variance efficient portfolio, a portfolio that has the highest
expected return at a given level of risk.

Mean-variance criterion

The selection of portfolios based on the means and variances of their returns. The
choice of the higher expected return portfolio for a given level of variance or the lower variance portfolio for
a given expected return.

Minimum-variance frontier

Graph of the lowest possible portfolio variance that is attainable for a given
portfolio expected return.

Naive diversification

A strategy whereby an investor simply invests in a number of different assets and
hopes that the variance of the expected return on the portfolio is lowered.
Related: Markowitz diversification.

One-factor APT

A special case of the arbitrage pricing theory that is derived from the one-factor model by
using diversification and arbitrage. It shows the expected return on any risky asset is a linear function of a
single factor.

Opportunity cost of capital

expected return that is foregone by investing in a project rather than in
comparable financial securities.

Opportunity set

The possible expected return and standard deviation pairs of all portfolios that can be
constructed from a given set of assets.

Portfolio opportunity set

The expected return/standard deviation pairs of all portfolios that can be
constructed from a given set of assets.

Required return

The minimum expected return you would require to be willing to purchase the asset, that is,
to make the investment.

Risk lover

A person willing to accept lower expected returns on prospects with higher amounts of risk.

Risk premium approach

The most common approach for tactical asset allocation to determine the relative
valuation of asset classes based on expected returns.

Security market line

Line representing the relationship between expected return and market risk.
Security market plane A plane that shows the equilibrium between expected return and the beta coefficient
of more than one factor.
Security selection
See: security selection decision.

Systematic risk principle

Only the systematic portion of risk matters in large, well-diversified portfolios.
The, expected returns must be related only to systematic risks.

Utility function

A mathematical expression that assigns a value to all possible choices. In portfolio theory the
utility function expresses the preferences of economic entities with respect to perceived risk and expected return.

Weighted average cost of capital

expected return on a portfolio of all the firm's securities. Used as a hurdle
rate for capital investment.

Efficient frontier

A graph representing a set of portfolios that maximizes
expected return at each level of portfolio risk. See Markowitz model.

Cost of capital

The blended cost of a company’s currently outstanding debt instruments
and equity, weighted by the comparative proportions of each one. During a capital
budgeting review, the expected return from a capital purchase must exceed this cost
of capital, or else a company will experience a net loss on the transaction.

risk premium

expected return in excess of risk-free return as compensation for risk.

security market line

Relationship between expected return and beta.

Abnormal returns

Part of the return that is not due to systematic influences (market wide influences). In
other words, abnormal returns are above those predicted by the market movement alone. Related: excess
returns.

After-tax real rate of return

Money after-tax rate of return minus the inflation rate.

Annualized holding period return

The annual rate of return that when compounded t times, would have
given the same t-period holding return as actually occurred from period 1 to period t.

Arithmetic average (mean) rate of return

Arithmetic mean return.

Arithmetic mean return

An average of the subperiod returns, calculated by summing the subperiod returns
and dividing by he number of subperiods.

Average accounting return

The average project earnings after taxes and depreciation divided by the average
book value of the investment during its life.

Average rate of return (ARR)

The ratio of the average cash inflow to the amount invested.

Dollar return

The return realized on a portfolio for any evaluation period, including (1) the change in market
value of the portfolio and (2) any distributions made from the portfolio during that period.

Dollar-weighted rate of return

Also called the internal rate of return, the interest rate that will make the
present value of the cash flows from all the subperiods in the evaluation period plus the terminal market value
of the portfolio equal to the initial market value of the portfolio.

Ex post return

Related: Holding period return

Excess return on the market portfolio

The difference between the return on the market portfolio and the
riskless rate.

Excess returns

Also called abnormal returns, returns in excess of those required by some asset pricing model.

Expected future cash flows

Projected future cash flows associated with an asset of decision.

Expected value

The weighted average of a probability distribution.

Expected value of perfect information

The expected value if the future uncertain outcomes could be known
minus the expected value with no additional information.

Geometric mean return

Also called the time weighted rate of return, a measure of the compounded rate of
growth of the initial portfolio market value during the evaluation period, assuming that all cash distributions
are reinvested in the portfolio. It is computed by taking the geometric average of the portfolio subperiod
returns.

Holding period return

The rate of return over a given period.

Horizon return

Total return over a given horizon.

Incremental internal rate of return

IRR on the incremental investment from choosing a large project
instead of a smaller project.

Internal rate of return

Dollar-weighted rate of return. Discount rate at which net present value (NPV)
investment is zero. The rate at which a bond's future cash flows, discounted back to today, equals its price.

Leveraged required return

The required return on an investment when the investment is financed partially by debt.

Market return

The return on the market portfolio.

Money rate of return

Annual money return as a percentage of asset value.

Multiple rates of return

More than one rate of return from the same project that make the net present value
of the project equal to zero. This situation arises when the IRR method is used for a project in which negative
cash flows follow positive cash flows. For each sign change in the cash flows, there is a rate of return.

Portfolio internal rate of return

The rate of return computed by first determining the cash flows for all the
bonds in the portfolio and then finding the interest rate that will make the present value of the cash flows
equal to the market value of the portfolio.

Rate of return ratios

Ratios that are designed to measure the profitability of the firm in relation to various
measures of the funds invested in the firm.

Realized return

The return that is actually earned over a given time period.

Return

The change in the value of a portfolio over an evaluation period, including any distributions made
from the portfolio during that period.

Return on assets (ROA)

Indicator of profitability. Determined by dividing net income for the past 12 months
by total average assets. Result is shown as a percentage. ROA can be decomposed into return on sales (net
income/sales) multiplied by asset utilization (sales/assets).

Return on equity (ROE)

Indicator of profitability. Determined by dividing net income for the past 12
months by common stockholder equity (adjusted for stock splits). Result is shown as a percentage. Investors
use ROE as a measure of how a company is using its money. ROE may be decomposed into return on assets
(ROA) multiplied by financial leverage (total assets/total equity).

Return on investment (ROI)

Generally, book income as a proportion of net book value.

Return on total assets

The ratio of earnings available to common stockholders to total assets.

Return-to-maturity expectations

A variant of pure expectations theory which suggests that the return that an
investor will realize by rolling over short-term bonds to some investment horizon will be the same as holding
a zero-coupon bond with a maturity that is the same as that investment horizon.

Riskless rate of return

The rate earned on a riskless asset.

Safety-net return

The minimum available return that will trigger an immunization strategy in a contingent
immunization strategy.

Subperiod return

The return of a portfolio over a shorter period of time than the evaluation period.

T-period holding-period return

The percentage return over the T-year period an investment lasts.

Time-weighted rate of return

Related: Geometric mean return.

Total dollar return

The dollar return on a nondollar investment, which includes the sum of any
dividend/interest income, capital gains or losses, and currency gains or losses on the investment.
See also: total return.

Total return

In performance measurement, the actual rate of return realized over some evaluation period. In
fixed income analysis, the potential return that considers all three sources of return (coupon interest, interest
on interest, and any capital gain/loss) over some i nvestment horizon.

Unleveraged required return

The required return on an investment when the investment is financed entirely
by equity (i.e. no debt).

RATE OF RETURN ON STOCKHOLDERS’ EQUITY

The percentage return or profit that management made on each dollar stockholders invested in a company. Here’s how you figure it:
(Net income) / (Stockholders’ equity)

RATE OF RETURN ON TOTAL ASSETS

The percentage return or profit that management made on each dollar of assets. The formula is:
(Net income) / (Total assets)

RETURN ON INVESTMENT (ROI)

In its most basic form, the rate of return equals net income divided by the amount of money invested. It can be applied to a particular product or piece of equipment, or to a business as a whole.

Accounting rate of return (ARR)

A method of investment appraisal that measures
the profit generated as a percentage of the
investment – see return on investment.

Internal rate of return (IRR)

A discounted cash flow technique used for investment appraisal that calculates the effective cost of capital that produces a net present value of zero from a series of future cash flows and an
initial capital investment.

Return on capital employed (ROCE)

The operating profit before interest and tax as a percentage of the total shareholders’ funds plus
the long-term debt of the business.

Return on investment (ROI)

The net profit after tax as a percentage of the shareholders’ investment in the business.

Target rate of return pricing

A method of pricing that estimates the desired return on investment to be achieved from the
fixed and working capital investment and includes that return in the price of a product/service.

Purchase returns

A contra account that reduces purchases by the amount of items purchased that were subsequently returned.

Sales returns

A contra account that offsets revenue. It represents the amount of sales made that were later returned.

internal rate of return (IRR)

The precise discount rate that makes the
present value (PV) of the future cash returns from a capital investment
exactly equal to the initial amount of capital invested. If IRR is higher
than the company’s cost-of-capital rate, the investment is an attractive
opportunity; if less, the investment is substandard from the cost-ofcapital
point of view.

return on assets (ROA)

Although there is no single uniform practice for
calculating this ratio, generally it equals operating profit (before interest
and income tax) for a year divided by the total assets that are used to
generate the profit. ROA is the key ratio to test whether a business is
earning enough on its assets to cover its cost of capital. ROA is used for
determining financial leverage gain (or loss).

return on equity (ROE)

This key ratio, expressed as a percent, equals net
income for the year divided by owners’ equity. ROE should be higher than
a business’s interest rate on debt because the owners take more risk.

return on investment (ROI)

A very general concept that refers to some
measure of income, earnings, profit, or gain over a period of time
divided by the amount of capital invested during the period. It is almost
always expressed as a percent. For a business, an important ROI measure
is its return on equity (ROE), which is computed by dividing its net
income for the period by its owners’ equity during the period.

return on sales

This ratio equals net income divided by sales revenue.

Expected Value

The value of the possible outcomes of a variable weighted by the
probabilities of each outcome

Internal Rate of Return (IRR)

The discount rate that equates the present value of the net cash
inflows with the present value of the net cash outflows
(investments). The IRR measures the profitability (rate of return) of
an investment in a project or security.

Return on Common Equity Ratio

A measure of the percentage return earned on the value of the
common equity invested in the company. It is calculated by
dividing the net income available for distribution to shareholders
by the book value of the common equity.

Return on Total Assets Ratio

A measure of the percentage return earned on the value of the
assets in the company. It is calculated by dividing the net income
available for distribution to shareholders by the book value of all
assets.

accounting rate of return (ARR)

the rate of earnings obtained on the average capital investment over the life of a capital project; computed as average annual profits divided by average investment; not based on cash flow

expected capacity

a short-run concept that represents the
anticipated level of capacity to be used by a firm in the
upcoming period, based on projected product demand

expected standard

standard set at a level that reflects what
is actually expected to occur in the future period; it anticipates
future waste and inefficiencies and allows for them;
is of limited value for control and performance evaluation purposes

internal rate of return (IRR)

the expected or actual rate of
return from a project based on, respectively, the assumed
or actual cash flows; the discount rate at which the net
present value of the cash flows equals zero

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