UNDERSTANDINGRISK AND RETURN

CHAPTER TWO

Practical Investment Management

Robert A. Strong

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Return Holding Period Return Yield and Appreciation The Time Value of Money Compounding Compound Annual Return

Outline

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Risk Risk vs. Uncertainty Dispersion and the Chance of Loss The Problem with Losses

• Big Losses• Small Losses• Risk and the Time Horizon

Risk Aversion• Risk Aversion and Rational People• Risk and Time

Partitioning Risk

Outline

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More on the Relationship between Risk and Return The Direct Relationship Risk, Return, and Dominance

Outline

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Introduction

A dollar today is worth more than a dollar tomorrow.

A safe dollar is worth more than a risky dollar.

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

A tradeoff exists between risk and return.

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Holding period = return

Ending Beginning value value Income

Beginning value

_+

Holding Period Return

The simplest measure of return is the holding period return.

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Buy 100 shares at $25 per share

Time

Sell the sharesat $30 per share

Dividend of $0.10 per share

Example :

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

$25

Holding Period Return

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Holding period return is independent of the passage of time. When comparing investments, the periods

should all be of the same length.

When there are stock splits or other corporate actions, care should be taken to ensure that the correct value is used for calculating the holding period return.

Holding Period Return

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Current yield is annual incomedivided by current price.

Example :

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

Yield and Appreciation

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

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

Example :

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

Yield and Appreciation

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

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P × ( 1 + r )n = F

where P = present value (i.e. price today)F = future valuer = interest rate per period

and n = number of periods

The Time Value of Money

The time value of money is the notion that a dollar today is worth more than a dollar tomorrow.

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The current price of any financial asset should be the present value of its expected future cash flows.

The Time Value of Money

Example :

P × ( 1 + 0.0919 )4 = $1,000

P = $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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Many securities pay more than one cash flow over their lives. In particular, an annuity is a series of equal and evenly spaced payments.

A convenient expression for the present value of an annuity is:

The Time Value of Money

where C = coupon or periodic payment

n r1 r

1

r

1 CP

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The Time Value of Money

Insert Figure 2.1 here.

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Compounding

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

where r = annual interest raten = number of compounding periods per year

and t = investment horizon in years

nt

n

r1PF

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

In the limit, compounding occurs continuously, and F approaches Pert.

Compounding

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

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.

Compound Annual Return

It is also known as the effective annual rate.

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A truly risky situation must involve a chance of loss.

Risk vs. Uncertainty

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Dispersion and the Chance of Loss

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

A common measure of statistical dispersion is variance. The standard deviation is the square root of the variance.

n

1i

2i xx)i(probVariance

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Dispersion and the Chance of Loss

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The Problem with Losses

Big losses - a large one-period loss can overwhelm a series of gains

Small losses - can be a problem too if they occur too often

Risk and the time horizon - as the time horizon increases, the probability of losing money decreases but the amount of money that may be lost increases.

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Small Losses

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Risk and the Time Horizon

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Risk Aversion and Rational People

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

A rational person will choose a certain dollar over a risky dollar.

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

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

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Risk Aversion and Rational People

Table 2.4 Four Risky Alternatives

Choice 1 Choice 2 Choice 3 Choice 4 ___ Resulting Resulting Resulting Resulting

Number Payoff Number Payoff Number Payoff Number Payoff

1-50 $100 1-50 $200 1-90 $ 50 1-99 $1,000

51-100 $ 90 51-100 $ 091-100 $550 100 -$89,000

Avg. $100 Avg. $100 Avg. $100 Avg. $ 100

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Risk and Time

Probability theory deals with how much and how likely, but says nothing about when.

Forecast variance increases indefinitely as the length of the forecast period approaches infinity.

To be comparable, returns must be measured over consistent time intervals.

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While the returns over a long horizon may be more uncertain, history suggests that over long periods of time, the likelihood that the investment will lose money is less.

Risk and Time

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Partitioning Risk

Undiversifiable risk is risk that must be borne by virtue of being in the market. It is also known as systematic risk or market risk, and is measured by beta.

Diversifiable risk is also known as unsystematic risk.

Total risk = undiversifiable risk + diversifiable risk

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Partitioning Risk

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

Financial risk - associated with the financial structure of the firm

Purchasing power risk - the possibility that the rate of return on an investment will be insufficient to offset the rise in the cost of living

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Partitioning Risk

Interest rate risk - the chance of a loss in portfolio value due to an adverse change in interest rate

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

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Partitioning Risk

Political risk - the possibility that a government will interfere with a firm's preferred manner of conducting business

Social risk - the potentially adverse impact changing public attitudes can have on a firm's ability to sell its product

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Partitioning Risk

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Partitioning Risk

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The Direct Relationship between Risk and Return

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Empirical financial research reveals clear evidence of the direct relationship between systematic risk and expected return, i.e. riskier securities earn higher returns on average.

The Direct Relationship between Risk and Return

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The Direct Relationship between Risk and Return

Insert Figure 2-8 here.

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Risk, Return, and Dominance

An investment alternative shows dominance over another if it offers the same 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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Risk, Return, and Dominance

Insert Figure 2-9 here.

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Return Holding Period Return Yield and Appreciation The Time Value of Money Compounding Compound Annual Return

Review

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Risk Risk vs. Uncertainty Dispersion and the Chance of Loss The Problem with Losses

• Big Losses• Small Losses• Risk and the Time Horizon

Risk Aversion• Risk Aversion and Rational People• Risk and Time

Partitioning Risk

Review

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More on the Relationship between Risk and Return The Direct Relationship Risk, Return, and Dominance

Review