CHAPTER TWO

UNDERSTANDINGRISK AND RETURN

© 2001 South-Western College Publishing

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Outline

Return Holding Period Return

Yield and Appreciation

The Time Value of Money

Compounding

Compound Annual Return

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Risk Risk vs. Uncertainty

Dispersion and the Chance of Loss

The Problem with Losses

Risk and the Time Horizon

Risk Aversion

Partitioning Risk

More on the Relationship between Riskand Return The Direct Relationship

Risk, Return, and Dominance

Outline

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Return

Holding period = return

Ending Beginning value value Income

Beginning value

_+

The simplest measure of return is the holding period return.

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Return

Buy 100 shares at $25 per share

Time

Dividend of $0.10 per share

Sell the sharesat $30 per share

Example :

Holding period return = = 20.4%$30 - $25 + $0.10

$25

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is independent of the passage of time.

when comparing investments, the periods should all be of the same length.

Return

Holding period return ...

is based on price, not total value.

adjustments need to be made for corporate actions, such as stock splits, which affect the price but not the total value.

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Return

Current yield is annual incomedivided by current price.

Dividend yield is used for stockswhose income comes exclusively from dividends.

Example :

For a stock selling for $40 and expected to pay $1 in dividends over the next year,current yield = $1 / $40 = 2.5%.

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Return

Appreciation is the increase in value of an investment independent of its yield.

It excludes accrued interest, as well as increases in value whichare due to additional deposits.

Example :

When a stock bought at $95 rises to $97.50,it has appreciated by $2.50, or $2.50 / $95 = 2.6%.

PresentValue × ( 1 + r )n = FutureValue

where r = interest rate per period and n = number of periods

Return

The time value of money is the notion that a dollar today is worth more than a dollar tomorrow. the current price of any financial asset should be the present value of its expected future cash flows.

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Return

Example :

PresentValue × ( 1 + 0.0919 )4 = $1,000

PresentValue = $703.50

What is the most that an investor would pay for a zero coupon bond which matures in 4 years' time, and has a redemption value of $1,000? The interest rate is 9.19% .

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PresentValue × ( 1 + r/n )nt = FutureValuewhere r = annual interest rate and n = number of compounding periods per year t = investment horizon in years

Return

Compounding refers to the earning of intereston interest that is earned previously.

The more frequent the compounding, the greater the interest earned.

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Return

Compound annual return is the annual interest rate that makes thetime value of money relationshiphold.

It is also known as the effective annual rate.

Example :

A nondividend-paying stock bought 4.5 years agoat $40 and sold today at $78 has a compoundannual return of R, where $40(1+R)4.5=$78.

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Risk

Risk vs. Uncertainty

A truly risky situation must involve a chance of loss.

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Risk

Dispersion and the Chance of Loss

There are 2 aspects to risk - the averageoutcome and the scattering of thepossible outcomes about this average.

A common measure of statisticaldispersion is variance.The standard deviation is the squareroot of the variance.

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Risk

The Problem with Losses

Big Losses - a large one-period losscan overwhelm a series of gains.

Small Losses - can be a problem tooif they occur too often.

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Risk

There is an important distinction between theprobability of losing money and the amountof money that may be lost.

In general, the longer a common stockinvestment is held, the lower the likelihoodthat money will be lost, but the greater theamount that may be lost.

Risk and the Time Horizon

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Risk

Risk Aversion and Rational People

A safe (certain) dollar is worth more than a risky dollar.

Risk averse persons will take risks,when they expect to be rewarded for taking the risks.

People have different degrees of riskaversion; some are more willing totake a chance than are others.

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Risk

Risk and Time

Probability theory deals with how muchand how likely, but says nothing aboutwhen.

Forecast variance increases indefinitelyas the length of the forecast period approaches infinity.

To be consistent, returns must bemeasured over consistent timeintervals.

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Risk

Partitioning Risk

Undiversifiable risk - risk that must be borne by virtue of being in the market.Also known as systematic risk ormarket risk.Measured by beta.

Diversifiable risk - also known asunsystematic risk.

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Risk

Partitioning Risk

Business risk - the variability in a firm'ssales, or its ability to sell its product.

Financial risk - associated with the financial structure of the firm.

Purchasing power risk - the possibilitythat the rate of return on an investmentwill be insufficient to offset the rise inthe cost of living.

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Risk

Interest rate risk - the chance of a lossin portfolio value due to an adversechange in interest rate.

Foreign exchange risk - the possibility of loss due to adverse changes inthe relative values of world currencies.

Partitioning Risk

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Political risk - the possibility that agovernment will interfere with a firm'spreferred manner of conducting business.

Social risk - the potentially adverse impact changing public attitudes canhave on a firm's ability to sell itsproduct.

Risk

Partitioning Risk

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More onThe Relationship between Risk and Return

ExpectedReturn

RiskRisk-free Return

Riskier securities have higher expected returns.

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The Relationship between Risk and Return

Empirical financial research reveals clear evidenceof the direct relationship between systematic riskand expected return.

ExpectedReturn

Risk

SmallCompany Stocks

LargeCompany Stocks

Long-term Government BondsT-bills

Inflation

Long-term Corporate Bonds

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The Relationship between Risk and Return

An investment alternative showsdominance over another if it offers thesame expected return for less risk,or if the security has a higher expected return than another security of comparable risk.

Equivalent assets should sell for the same price. This is known as the law of one price.

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The Relationship between Risk and Return

ExpectedReturn

Risk

A B

C

Both A and C dominate B.

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Review

A dollar today is worth more than a dollartomorrow.

A safe dollar is worth more than a riskydollar.

People have different degrees of risk aversion; some are more willing to take a chance than are others.

A tradeoff exists between risk and return.