CHAPTER TWO UNDERSTANDING RISK AND RETURN Practical Investment

CHAPTER TWO UNDERSTANDING RISK AND RETURN Practical Investment Management Robert A. Strong

Outline w Return ú ú ú Holding Period Return Yield and Appreciation The Time Value of Money Compounding Compound Annual Return South-Western / Thomson Learning © 2004 2 -2

Outline w Risk ú Risk vs. Uncertainty ú Dispersion and the Chance of Loss ú The Problem with Losses • Big Losses • Small Losses • Risk and the Time Horizon ú Risk Aversion • Risk Aversion and Rational People • Risk and Time ú Partitioning Risk South-Western / Thomson Learning © 2004 2 -3

Outline w More on the Relationship between Risk and Return ú The Direct Relationship ú Risk, Return, and Dominance South-Western / Thomson Learning © 2004 2 -4

Introduction w A dollar today is worth more than a dollar tomorrow. w A safe dollar is worth more than a risky dollar. w People have different degrees of risk aversion. Some are more willing to take a chance than others. w A tradeoff exists between risk and return. South-Western / Thomson Learning © 2004 2 -5

Holding Period Return w The simplest measure of return is the holding period return. Holding period = return Ending _ Beginning + value South-Western / Thomson Learning © 2004 Income Beginning value 2 -6

Holding Period Return Example : Buy 100 shares at $25 per share Dividend of $0. 10 per share Sell the shares at $30 per share Time Holding period return = South-Western / Thomson Learning © 2004 $30 - $25 + $0. 10 $25 = 20. 4% 2 -7

Holding Period Return w Holding period return is independent of the passage of time. ú When comparing investments, the periods should all be of the same length. w 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. South-Western / Thomson Learning © 2004 2 -8

Yield and Appreciation Current yield is annual income divided by current price. Dividend yield is used for stocks whose incomes 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%. South-Western / Thomson Learning © 2004 2 -9

Yield and Appreciation is the increase in value of an investment independent of its yield. It excludes accrued interest, as well as increases in value which are 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%. South-Western / Thomson Learning © 2004 2 - 10

The Time Value of Money w The time value of money is the notion that a dollar today is worth more than a dollar tomorrow. P × ( 1 + r )n = F where P F r and n = = present value (i. e. price today) future value interest rate period number of periods South-Western / Thomson Learning © 2004 2 - 11

The Time Value of Money w The current price of any financial asset should be the present value of its expected future cash flows. Example : 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%. P × ( 1 + 0. 0919 )4 = $1, 000 P = $703. 50 South-Western / Thomson Learning © 2004 2 - 12

The Time Value of Money w Many securities pay more than one cash flow over their lives. In particular, an annuity is a series of equal and evenly spaced payments. w A convenient expression for the present value of an annuity is: where C = coupon or periodic payment South-Western / Thomson Learning © 2004 2 - 13

The Time Value of Money Insert Figure 2. 1 here. South-Western / Thomson Learning © 2004 2 - 14

Compounding w Compounding refers to the earning of interest on interest that is earned previously. where r = annual interest rate n = number of compounding periods per year and t = investment horizon in years South-Western / Thomson Learning © 2004 2 - 15

Compounding w The more frequent the compounding, the greater the interest earned. w In the limit, compounding occurs continuously, and F approaches Pert. South-Western / Thomson Learning © 2004 2 - 16

Compound Annual Return Compound annual return is the annual interest rate that makes the time value of money relationship hold. It is also known as the effective annual rate. Example : A nondividend-paying stock bought 4. 5 years ago at $40 and sold today at $78 has a compound annual return of R, where $40(1+R)4. 5=$78. South-Western / Thomson Learning © 2004 2 - 17

Risk vs. Uncertainty w A truly risky situation must involve a chance of loss. South-Western / Thomson Learning © 2004 2 - 18

Dispersion and the Chance of Loss w There are 2 aspects to risk - the average outcome and the scattering of the possible outcomes about this average. w A common measure of statistical dispersion is variance. The standard deviation is the square root of the variance. South-Western / Thomson Learning © 2004 2 - 19

Dispersion and the Chance of Loss Insert Figure 2 -3 here. South-Western / Thomson Learning © 2004 2 - 20

The Problem with Losses w Big losses - a large one-period loss can overwhelm a series of gains w Small losses - can be a problem too if they occur too often w 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. South-Western / Thomson Learning © 2004 2 - 21

Small Losses Insert Figure 2 -4 here. South-Western / Thomson Learning © 2004 2 - 22

Risk and the Time Horizon South-Western / Thomson Learning © 2004 2 - 23

Risk Aversion and Rational People w A safe (certain) dollar is worth more than a risky dollar. w A rational person will choose a certain dollar over a risky dollar. w Risk averse persons will take risks, when they expect to be rewarded for taking the risks. w People have different degrees of risk aversion. Some are more willing to take a chance than others. South-Western / Thomson Learning © 2004 2 - 24

Risk Aversion and Rational People Choice 1 Resulting Choice 2 Choice 3 Resulting Payoff Resulting Number Payoff Number 1 -50 $100 1 -50 $200 1 -90 $ 50 1 -99 51 -100 $ 90 51 -100 $ 91 -100 $550 100 Avg. $100 Avg. 0 Number Choice 4 ___ Payoff Number Payoff $1, 000 -$89, 000 $ 100 Table 2. 4 Four Risky Alternatives South-Western / Thomson Learning © 2004 2 - 25

Risk and Time w Probability theory deals with how much and how likely, but says nothing about when. w Forecast variance increases indefinitely as the length of the forecast period approaches infinity. w To be comparable, returns must be measured over consistent time intervals. South-Western / Thomson Learning © 2004 2 - 26

Risk and Time w 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. South-Western / Thomson Learning © 2004 2 - 27

Partitioning Risk w 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. w Diversifiable risk is also known as unsystematic risk. w Total risk = undiversifiable risk + diversifiable risk South-Western / Thomson Learning © 2004 2 - 28

Partitioning Risk w Business risk - the variability in a firm's sales, or its ability to sell its product w Financial risk - associated with the financial structure of the firm w 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 South-Western / Thomson Learning © 2004 2 - 29

Partitioning Risk w Interest rate risk - the chance of a loss in portfolio value due to an adverse change in interest rate w Foreign exchange risk - the possibility of loss due to adverse changes in the relative values of world currencies South-Western / Thomson Learning © 2004 2 - 30

Partitioning Risk w Political risk - the possibility that a government will interfere with a firm's preferred manner of conducting business w Social risk - the potentially adverse impact changing public attitudes can have on a firm's ability to sell its product South-Western / Thomson Learning © 2004 2 - 31

Partitioning Risk Insert Figure 2 -5 here. South-Western / Thomson Learning © 2004 2 - 32

Partitioning Risk Insert Figure 2 -6 here. South-Western / Thomson Learning © 2004 2 - 33

The Direct Relationship between Risk and Return Insert Figure 2 -7 here. South-Western / Thomson Learning © 2004 2 - 34

The Direct Relationship between Risk and Return w 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. South-Western / Thomson Learning © 2004 2 - 35

The Direct Relationship between Risk and Return Insert Figure 2 -8 here. South-Western / Thomson Learning © 2004 2 - 36

Risk, Return, and Dominance w 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. w Equivalent assets should sell for the same price. This is known as the law of one price. South-Western / Thomson Learning © 2004 2 - 37

Risk, Return, and Dominance Insert Figure 2 -9 here. South-Western / Thomson Learning © 2004 2 - 38

Review w Return ú ú ú Holding Period Return Yield and Appreciation The Time Value of Money Compounding Compound Annual Return South-Western / Thomson Learning © 2004 2 - 39

Review w Risk ú Risk vs. Uncertainty ú Dispersion and the Chance of Loss ú The Problem with Losses • Big Losses • Small Losses • Risk and the Time Horizon ú Risk Aversion • Risk Aversion and Rational People • Risk and Time ú Partitioning Risk South-Western / Thomson Learning © 2004 2 - 40

Review w More on the Relationship between Risk and Return ú The Direct Relationship ú Risk, Return, and Dominance South-Western / Thomson Learning © 2004 2 - 41