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

South-Western College Publishing © Outline  Return  Holding Period Return  Yield and Appreciation  The Time Value of Money  Compounding  Compound Annual Return

South-Western College Publishing ©  Risk  Risk v.s. Uncertainty  Dispersion and the Chance of Loss  The Problem with Losses  Risk Aversion  Partitioning Risk  The Relationship between Risk and Return  The Direct Relationship  Risk, Return, and Dominance Outline

South-Western College Publishing © Return Holding period = return Ending Beginning price price Income Beginning price _ + The simplest measure of return is the holding period return.

South-Western College Publishing © Return Buy 100 shares at $25 per share Time Dividend of $0.10 per share Sell the shares at $30 per share Example : Holding period return = = 20.4% $30 - $25 + $0.10 $25

South-Western College Publishing ©  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.

South-Western College Publishing © Return Current yield is annual income divided by current price. Dividend yield is used for stocks whose 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%.

South-Western College Publishing © Return 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 College Publishing © PresentValue × ( 1 + r ) n = FutureValue where r = interest rate per period and n = number of periods Return The Time Value of Money - a dollar today is worth more than a dollar tomorrow

South-Western College Publishing © Return 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%. PresentValue × ( ) 4 = $1,000  PresentValue = $ * An annuity is a series of evenly-spaced, equal dollar payments.

South-Western College Publishing © PresentValue × ( 1 + r/n ) nt = FutureValue where r = annual interest rate and n = number of compounding periods per year t = investment horizon in years Return Compounding refers to the earning of interest on interest that is earned previously. The more frequent the compounding, the greater the interest earned.

South-Western College Publishing © 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 College Publishing © Risk Risk v.s. Uncertainty A truly risky situation must involve a chance of loss.

South-Western College Publishing © Risk 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.

South-Western College Publishing © Risk 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.

South-Western College Publishing © Risk Risk Aversion  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 risk aversion; some are more willing to take a chance than are others.

South-Western College Publishing © Risk 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 consistent, returns must be measured over consistent time intervals.

South-Western College Publishing © Risk Partitioning Risk  Undiversifiable risk - risk that must be borne by virtue of being in the market. Also known as systematic risk or market risk. Measured by beta.  Diversifiable risk - also known as unsystematic risk.

South-Western College Publishing © Risk 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.

South-Western College Publishing © 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. Partitioning Risk

South-Western College Publishing ©  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. Risk Partitioning Risk

South-Western College Publishing © The Relationship between Risk and Return Expected Return Risk Risk-free Return Riskier securities have higher expected returns.

South-Western College Publishing © The Relationship between Risk and Return Expected Return Risk Empirical financial research reveals clear evidence of the direct relationship between systematic risk and expected return. Small Company Stocks Large Company Stocks Long-term Government BondsT-bills Inflation Long-term Corporate Bonds

South-Western College Publishing © The Relationship between Risk and Return  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.

South-Western College Publishing © The Relationship between Risk and Return Expected Return Risk AB C Both A and C dominate B.

South-Western College Publishing © Review  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 are others.  A tradeoff exists between risk and return.