Investment Analysis and Portfolio Management10th Editionby Frank K. Reilly & Keith C. Brown

Chapter 1The Investment SettingQuestions to be answered:Why do individuals invest ?What is an investment ?How do we measure the rate of return on an investment ?How do investors measure risk related to alternative investments ?What factors contribute to the rate of return that an investor requires on an investment?What macroeconomic and microeconomic factors contribute to changes in the required rate of return for an investment?

Why Do Individuals Invest ?By saving money (instead of spending it), individuals forego consumption today in return for a larger consumption tomorrow.

How Do We Measure The Rate Of Return On An Investment ?The real rate of interest is the exchange rate between future consumption (future dollars) and present consumption (current dollars). Market forces determine this rate. TodayTomorrow$100$104If you are willing to exchange a certain payment of $100 today for a certain payment of $104 tomorrow, then the pure or real rate of interest is 4%

If the purchasing power of the future payment will be diminished in value due to inflation, an investor will demand an inflation premium to compensate them for the expected loss of purchasing power.

If the future payment from the investment is not certain, an investor will demand a risk premium to compensate for the investment risk.

How Do We Measure The Rate Of Return On An Investment ?

Defining an InvestmentAny investment involves a current commitment of funds for some period of time in order to derive future payments that will compensate for:the time the funds are committed (the real rate of return)the expected rate of inflation (inflation premium)uncertainty of future flow of funds (risk premium)

ReturnThe return on an investment (total gain or loss) is the change in value plus any cash distributions over a defined time period. It is expressed as a percent of the beginning-of-the-period investment. Income received on an investment plus any change in market price, usually expressed as a percent of the beginning market price of the investment. Following formula is used to measure return

Return ExampleThe stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share and shareholders just received a $1 dividend. What return was earned over the past year?

Example:Calculation of Return

Measure of Holding Period ReturnWhere:HPR = Holding period returnP0 = Beginning valueP1 = Ending valueExample of Holding Period Return: If you commit $200 to an investment at the beginning of the year and you get back $220 at the end of the year, what is your return for the period?

Alternative Formula for Holding Period Return

Measure of Equivalent Annual ReturnAnnualizing the HPRWhere:EAR = Equivalent Annual ReturnHPR = Holding Period ReturnN = Number of years Example: You bought a stock for $10 and sold it for $18 six years later. What is your HPR & EAR?

Calculating HPR & EARSolution:

Step #1:Step #2:

Class Exercises Exc. 1. On February 1, you bought 100 shares of stock in the Francesca Corporation for $34 a share and a year later you sold it for $39 a share. During the year, you received a cash dividend of $1.50 a share. Compute your HPR and HPY on this Francesca stock investment.Exc. 2. On August 15, you purchased 100 shares of stock in the Cara Cotton Company at $65 a share and a year later you sold it for $61 a share. During the year, you received dividends of $3 a share. Compute your HPR and HPY on your investment in Cara Cotton.

Mean of Historical Rates of ReturnArithmetic Mean(AM) =HPY/nWhere:AM = Arithmetic MeanGM = Geometric MeanRi = Annual HPRsN = Number of years Geometric Mean (GM), is the nth root of the product of theHPRs for n years minus one.

AM and GM

Although the arithmetic average provides a good indication of the expected rate of return for an investment during a future individual year, it is biased upward if you are attempting to measure an assets long-term performance. This is obvious for a volatile security. Consider, for example, a security that increases in price from $50 to $100 during year 1 and drops back to $50 during year 2. The annual HPYs would be:

AM or GM, which is a better measure?Investors are typically concerned with long-term performance when comparing alternative investments. GM is considered a superior measure of the long-term mean rate of return because it indicates the compound annual rate of return based on the ending value of the investment versus its beginning value.This is obvious that GM is better measure of Mean HPR for a volatile security.

ExampleYou are reviewing an investment with the following price history as of December 31st each year.

Calculate:The HPR for the entire period The annual HPRsThe Arithmetic mean of the annual HPRsThe Geometric mean of the annual HPRs

19992000200120022003200420052006$18.45$21.15$16.75$22.45$19.85$24.10$24.10$26.50

A Portfolio of InvestmentsThe mean historical rate of return for a portfolio of investments is measured as the weighted average of the HPRs for the individual investments in the portfolio, or the overall change in the value of the original portfolio

Investment Portfolio Collection of assets or group of assets is called investment portfolio.An efficient portfolio is one that maximizes return for a given risk level or minimizes risk for a given level of return. Return of a portfolio is the weighted average of returns on the individual component assets:

Computation of HoldingPeriod Return for a Portfolio

Expected Return and Risk

Investors and analysts often look at historical returns as a starting point for predicting the future.However, they are much more interested in what the returns on their investments will be in the future.For this reason, we need a method for estimating future or ex-ante returns.One way of doing this sensitivity analysis where probabilities are assigned to future states of nature and the returns that would be realized if a particular state of nature does occur.

Expected Rates of ReturnRisk is the uncertainty whether an investment will earn its expected rate of returnProbability is the likelihood of an outcome

Risk AversionMuch of modern finance is based on the principle that investors are risk averseRisk aversion refers to the assumption that, all else being equal, most investors will choose the least risky alternative and that they will not accept additional risk unless they are compensated in the form of higher return

Probability DistributionsRisk-free Investment

Probability DistributionsRisky Investment with 3 Possible Returns

Probability DistributionsRisky investment with ten possible rates of return

Measuring Risk: Historical ReturnsWhere: = Variance (of the pop)HPR = Holding Period Return iE(HPR)i = Expected HPR*N = Number of years * The E(HPR) is equal to the arithmetic mean of the series of returns.

Measuring Risk: Expected Rates of ReturnWhere: = VarianceRi = Return in period iE(R) = Expected ReturnPi = Probability of Ri occurringNote: Because we multiply by the probability of each return occurring, we do NOT divide by N. If each probability is the same for all returns, then the variance can be calculated by either multiplying by the probability or dividing by N.

Measure of Variance

Expected Return and Risk

Measuring Risk: Standard DeviationStandard Deviation is the square root of the varianceStandard Deviation is a measure of dispersion around the mean. The higher the standard deviation, the greater the dispersion of returns around the mean and the greater the risk.

Standard Deviation

Coefficient of VariationCoefficient of variation (CV) is a measure of relative variability CV indicates risk per unit of return, thus making comparisons easier among investments with large differences in mean returns 1.9

Why CV is considered more important?

Example of Expected Return and Risk

Expected Return and Risk

Expected Return and Risk

Expected Return and Risk

Coefficient of Variation (CV)

One problem with using standard deviation as a measure of risk is that we cannot easily make risk comparisons between two assets.The coefficient of variation overcomes this problem by measuring the amount of risk per unit of return.The higher the coefficient of variation, the more risk per return.Therefore, if given a choice, an investor would select the asset with the lower coefficient of variation

Coefficient of Variation (CV)

Example For Calculation of Holding Period Return For example, compute the holding period return if you purchased a stock for $100, received a $5 dividend, and sold the stock for $110

Calculation of Arithmetic Mean of Historical Return Through Excel What you typeWhat you see

Historical RiskHistorical RiskVarianceHistorical risk can be measured by the variability of an assets returns in relation to its average.Variance is computed by summing squared deviations and dividing by the number of observations minus one (n - 1).Squaring the differences ensures that both positive and negative deviations are given equal consideration.The sum of the squared differences is then divided by the number of observations minus one (n - 1).

Variance of Historical Return on Investment in Asset - A

Variance of Historical Return on Investment in Asset - B

Variance of Historical Return on Investment in Assets - A and B Through ExcelWhat you typeWhat you see

Standard deviation of Historical Returns on Investments

Squaring the deviations makes the variance difficult to interpret.In other words, by squaring percentages, the resulting deviations are in percent squared terms.The standard deviation simplifies interpretation by taking the square root of the squared percentages.In other words, standard deviation is in the same units as the computed average.If the average is 10%, the standard deviation might be 20%, whereas the variance would be 20% squared.

Standard Deviation of Historical Return on Investment in Assets - A and B Through ExcelWhat you typeWhat you see

Normal Distribution of Historical Return on Investment

Class Excercise

Portfolio of AssetsAn investment portfolio is any collection or combination of financial assets.If we assume all investors are rational and therefore risk averse, that investor will ALWAYS choose to invest in portfolios rather than in single assets.Investors will hold portfolios because he or she will diversify away a portion of the risk that is inherent in putting all your eggs in one basket.If an investor holds a single asset, he or she will fully suffer the consequences of poor performance.This is not the case for an investor who owns a diversified portfolio of assets.

DiversificationDiversification is basically used as a tool to spread the risk across the number of assets or investments.

Portfolio and DiversifiactionDiversification is enhanced depending upon the extent to which the returns on assets move together.This movement is typically measured by a statistic known as correlation as shown in Figure 6.3 below.

Portfolio and DiversificationEven if two assets are not perfectly negatively correlated, an investor can still realize diversification benefits from combining them in a portfolio as shown in Figure 6.4 below.

ExampleAssume that we wish to determine the expected value and standard deviation of returns for portfolio XY, created by combining equal portions (50% each) of assets X and Y. The forecasted returns of assets X and Y for each of the next 5 years (20132017) are given in columns 1 and 2, respectively, in the following Table.

Comparison of tow Portfolios:Positive verses negative Correlation among Returns of Assets

Portfolio of Assets A and BRecall Stocks A and B

Weighted Return of Portfolio of Assets A and BWeight : Out of available funds, 50% are invested in A, and 50% are invested in B

Comparison of Return on Investment

Same portfolio of Assets With Different Weights20% in A, 80% in B

Comparison of Different WeightSummarizing Changes in Return and Risk as the Composition of the Portfolio Changes

Number of Assets in Portfolio and Level of Risk

Determinants of Required Rates of ReturnThree factors influence an investors required rate of returnReal rate of returnExpected rate of inflation during the periodRisk

The Analysis and Estimation of the Required Rate of ReturnThe estimation of RRR is complicated by the behavior of market rates over time. First, a wide range of rates is available for alternative investments at anytime. Second, the rates of return on specific assets change dramatically over time. Third, the difference between the rates available (that is, the spread) on different assets changes over time.

Behaviour of Bond Market Rates over Time

The Real Risk Free Rate

Definition: The real risk-free rate (RRFR) is the basic interest rate, assuming no inflation and no uncertainty. This is the price charged for the risk-free exchange between current goods and future goods. We called this the pure time value of money, because the only sacrifice the investor made was deferring the use of the money for a period of time about future flows.Assumes no inflation.Assumes no uncertainty about future cash flows.Exchange price (RRFR) is influenced by two factors.Subjective Factors: Influenced by the time preference for consumption of income and Objective Factors: Investment opportunities in the economy. Investment opportunities directly depends upon long run real growth rate of the economy.

Factors Influencing the Nominal Risk-Free Rate (NRFR)Nominal rates of interest that prevail in the market are determined by real rates of interest, plus factors that will affect the nominal rate of interest, such as the expected rate of inflation and the monetary environment.Factors affecting the nominal risk free rate.Conditions of Capital Market Monetary Policy Fiscal PolicyExpected Rate of InflationAdjusting for inflation ( Fisher Equation)

Adjusting For Inflation: Fisher EquationThe nominal risk free rate of return is dependent upon:Conditions in the Capital MarketsExpected Rate of Inflation

Common EffectAll the factors discussed thus far regarding the required rate of return affect all investments equally. Whether the investment is in stocks, bonds, real estate, or machine tools, if the expected rate of inflation increases from 2 percent to 6 percent, the investors required rate of return for all investments should increase by 4 percent.

Risk PremiumA risk-free investment was defined as one for which the investor is certain of the amount and timing of the expected returns. The returns from most investments do not fit this pattern. Most investors require higher rates of return on investments if they perceive that there is any uncertainty about the expected rate of return. This increase in the required rate of return over the NRFR is the risk premium (RP).Major sources of uncertainty(1) business risk, (2) financial risk (leverage), (3) liquidity risk, (4) exchange rate risk, and (5) country (political) risk.

Components of Fundamental RiskFive factors affect the standard deviation of returns over time.Business risk:Financial riskLiquidity riskExchange rate riskCountry risk

Business RiskBusiness risk arises due to:Uncertainty of income flows caused by the nature of a firms business Sales volatility and operating leverage determine the level of business risk.

Financial RiskFinancial risk arises due to:Uncertainty caused by the use of debt financing.Borrowing requires fixed payments which must be paid ahead of payments to stockholders.The use of debt increases uncertainty of stockholder income and causes an increase in the stocks risk premium.

Liquidity RiskLiquidity risk arises due to the uncertainty introduced by the secondary market for an investment.How long will it take to convert an investment into cash?How certain is the price that will be received?

Exchange Rate RiskExchange rate risk arises due to the uncertainty introduced by acquiring securities denominated in a currency different from that of the investor.Changes in exchange rates affect the investors return when converting an investment back into the home currency.

Country RiskCountry risk (also called political risk) refers to the uncertainty of returns caused by the possibility of a major change in the political or economic environment in a country.Individuals who invest in countries that have unstable political-economic systems must include a country risk-premium when determining their required rate of return

Risk Premium and Portfolio TheoryAn alternative view of risk has been derived from extensive work in portfolio theory and capital market theory by Markowitz (1952, 1959) and Sharpe (1964).When an asset is held in isolation, the appropriate measure of risk is standard deviationWhen an asset is held as part of a well-diversified portfolio, the appropriate measure of risk is its co-movement with the market portfolio, as measured by Beta This is also referred to as Systematic riskNon-diversifiable riskSystematic risk refers to the portion of an individual assets total variance attributable to the variability of the total market portfolio

A number of studies have examined the relationship between the market measure of risk (systematic risk) and accounting variables used to measure the fundamental risk factors, such as business risk, financial risk, and liquidity risk. The authors of these studies (especially Thompson, 1976) have generally concluded that a significant relationship exists between the market measure of risk and the fundamental measures of risk. Therefore, the two measures of risk can be complementary.

RELATIONSHIP BETWEEN RISK AND RETURNThe expected relationship between risk and return is described by Security Market Line (SML). It shows that investors increase their required rates of return as perceived risk (uncertainty) increases. The line that reflects the combination of risk and return available on alternative investments is referred to as the security market line (SML). The SML reflects the risk-return combinations available for all risky assets in the capital market at a given time. Investors would select investments that are consistent with their risk preferences; some would consider only low-risk investments, whereas others welcome high-risk investments.

SML Relationship Between Risk and ReturnBeginning with an initial SML, three changes in the SML can occur. First, individual investments can change positions on the SML because of changes in the perceived risk of the investments. Second, the slope of the SML can change because of a change in the attitudes of investors toward risk; that is, investors can change the returns they require per unit of risk.Third, the SML can experience a parallel shift due to a change in the RRFR or the expected rate of inflationi.e., anything that can change in the NRFR.

Movements along the SML

Relationship BetweenRisk and Return

Changes in the Required Rate of Return Due to Movements Along the SMLBetaRisk freeRateSecurity Market LineExpectedRateMovements along the SMLreflect changes in the market or systematicrisk of the assetLower RiskHigher Risk

Changes in the Slope of the SMLThe slope of the SML indicates the return per unit of risk required by all investorsThe market risk premium is the yield spread between the market portfolio and the risk free rate of returnThis changes over time, although the underlying reasons are not entirely clearHowever, a change in the market risk premium will affect the return required on all risky assets

Change in Market Risk PremiumExpected ReturnRmRmBetaOriginal SMLNew SMLNote that as the slope of the SML increases, so does the market risk premiumRisk Free Rate

Capital Market Conditions, Expected Inflation, and the SMLRiskOriginal SMLNew SMLRate of ReturnRisk freeRateThe SML will shift in a parallel fashion if inflation expectations, real growth expectations or capital market conditions change. This will affect the required return on all assets.

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Future TopicsChapter 2 The asset allocation decisionThe individual investor life cycleRisk tolerancePortfolio management

******This table is in the book on page 11. It is also provided in the Investment Templates spreadsheet in an interactive spreadsheet form.