Chapter 1 The Investment Setting Zhiqiang Wang School of Finance Dongbei University of Finance & Economics Chapter 1 The Investment Setting

The Investment Setting 1. What is An Investment? 2. Measures of Return and Risk 3. Determinants of Required Rates of Return 4. Relationship between Risk and Return Chapter 1 The Investment Setting

Chapter 1 The Investment Setting 1. What is An Investment? Why Do Individuals Invest? Investment Defined Required Rate of Return Chapter 1 The Investment Setting

Why Do Individuals Invest? By saving money (instead of spending it), individuals tradeoff present consumption for a larger future consumption. There are three factors to be considered The time the funds are committed (pure time value of money) The expected rate of inflation The uncertainty of the future payments (risk premium) Chapter 1 The Investment Setting

Pure time value of money The rate of exchange between future consumption (future dollars) and current consumption (current dollars) is the pure rate of interest People’s willingness to pay the difference for borrowing today and their desire to receive a surplus on their savings give rise to an interest rate referred to as the pure time value of money. Chapter 1 The Investment Setting

Expected rate of inflation If the future payment will be diminished in value because of inflation, then the investor will demand an interest rate higher than the pure time value of money to also cover the expected inflation expense. Chapter 1 The Investment Setting

Chapter 1 The Investment Setting Risk premium If the future payment from the investment is not certain, the investor will demand an interest rate that exceeds the pure time value of money plus the inflation rate to provide a risk premium to cover the investment risk. Chapter 1 The Investment Setting

Chapter 1 The Investment Setting Investment Defined An investment is the current commitment of dollars for a period of time to derive future payments that will compensate the investor for The time the funds are committed (pure time value of money) The expected rate of inflation The uncertainty of the future payments (risk premium) The investor is trading a known dollar amount today for some expected future stream of payments that will be greater than the current outlay. Chapter 1 The Investment Setting

Required Rate of Return Pure time value of money Pure rate of interest Nominal risk-free rate Risk premium Required rate of return, including Expected rate of inflation Chapter 1 The Investment Setting

2. Measures of Return and Risk Measures of historical rates of return Computing mean historical returns Computing expected rates of return Measuring the risk of expected rates of return Risk measures for historical returns Chapter 1 The Investment Setting

Measures of historical rates of return Holding period return (HPR) =Ending value of investment / Beginning value of investment For example, HPR=$220/$200=1.10 Annual HPR=HPR1/n Holding period yield(HPY) HPY=HPR-1 Annual HPY=annual HPR-1 For example n=2, HPR=$350/$250=1.40, Annual HPR=1.41/2 =1.1832, Annual HPY=1.1832-1=18.32% Chapter 1 The Investment Setting

Computing mean historical returns For a single investment Arithmetic mean(AM): AM=ΣHPYi/n Geometric mean(GM): GM=(ΠHPRi)1/n -1 For example AM=(15%+20%-20%)/3=5% GM=(1.151.20 0.80) 1/3-1=3.353% Year Beginning Value Ending Value HPRi HPYi 1 100.0 115.0 1.15 0.15 2 138.0 1.20 0.20 3 110.4 0.80 -0.20 Chapter 1 The Investment Setting

Computing mean historical returns The difference between AM and GM GM is considered to be 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. GM is also referred to as the time-weighted rate of return (TWRR) AM is biased upward if you attempt to measure an asset’s long-term performance. GM will be equal to AM when rates of return are the same for all years. GM will be lower than AM if the rates of return vary over the years. Chapter 1 The Investment Setting

Computation of Holding Period Yield for a Portfolio Exhibit 1.1 The mean historical rate of return for a portfolio of investments is measured as the weighted average of the HPYs for the individual investments in the portfolio. This table is in the book on page 11. It is also provided in the Investment Templates spreadsheet in an interactive spreadsheet form. Chapter 1 The Investment Setting

Calculating expected rates of return Uncertainty There is uncertainty for rate of return on one investment Random variable The rate of return on one investment is random The expected return from an investment Expected Return=ΣPiRi For example E(R)= 0.150.20+0.15(-0.20)+0.700.10=7% Economic Conditions Probability Rate of Return Strong economy, no inflation 0.15 0.20 Weak economy, above AI -0.20 No major change in the economy 0.70 0.10 Chapter 1 The Investment Setting

Chapter 1 The Investment Setting Risk Aversion The assumption that most investors will choose the least risky alternative, all else being equal and that they will not accept additional risk unless they are compensated in the form of higher return Chapter 1 The Investment Setting

Probability Distributions Exhibit 1.2 Risky Investment with 3 Possible Returns Chapter 1 The Investment Setting

Measuring the risk of expected rates of return Risk is the uncertainty Two possible measures of risk (uncertainty) Variance: σ2 =ΣPi[Ri-E(R)] 2 Standard deviation: σ For example:σ2 =0.0141, σ =0.11874 (above example) A relative measure of risk Coefficient of variation (CV) CV =Standard Deviation of returns / Expected Rate of Return For example Investment A B Expected return 0.07 0.12 Standard deviation 0.05 CV 0.71 0.58 Chapter 1 The Investment Setting

Risk measures for historical returns To measure the risk for a series of historical rates of returns, we use the same measures as for expected returns except that we consider the historical holding period yields as follows: variance of the series holding period yield during period I expected value of the HPY that is equal to the arithmetic mean of the series the number of observations Chapter 1 The Investment Setting

3. Determinants of Required Rates of Return The real risk-free rate Factors influencing the nominal risk-free rate Risk premium Risk premium and portfolio theory Fundamental risk versus systematic risk Summary of required rate of return Chapter 1 The Investment Setting

The real risk-free rate Real risk-free rate (RFR) Pure time value of money The basic interest rate, with no inflation and no uncertainty about future flows, Influenced by time preference for consumption of income and investment opportunities in the economy Two factors influence this exchange price Subjective factor is the time preference of individuals for the consumption Objective factor is the set of investment opportunities available in the economy A positive relationship exists between the real growth rate in the economy and the real RFR Chapter 1 The Investment Setting

Factors influencing the nominal risk-free rate Two other factors influence the nominal RFR The relative ease or tightness in the capital markets The expected rate of inflation Condition in the capital market Expected rate of inflation Nominal RFR=(1+real RFR)(1+expected rate of inflation)-1 The common effect All the factors discussed thus far regarding the required rate of return affect all investments equally Chapter 1 The Investment Setting

Chapter 1 The Investment Setting Risk premium The major fundamental sources Business risk is the uncertainty of income flows caused by the nature of a firm’s business Financial risk is the uncertainty introduced by the method by which the firm finances its investments Liquidity risk is the uncertainty introduced by the secondary market for an investment Exchange rate risk is the uncertainty of returns to an investor who acquires securities in a currency different from his or her own Country risk, also called political risk, is the uncertainty of returns caused by the possibility of a major change in the political or economic environment of a country Chapter 1 The Investment Setting

Chapter 1 The Investment Setting Risk premium Total risk Risk premium= f (business risk,financial risk,liquidity risk, exchange rate risk,country risk) Chapter 1 The Investment Setting

Risk premium and portfolio theory Systematic risk and unsystematic risk systematic risk, measured by an asset’s covariance with the market portfolio. Beta measures this systematic risk of an asset. unsystematic risk, measured by the non-market (unique) variance which is not related the market portfolio but is due to unique features Under some assumptions, the risk premium for an individual earning asset is a function of the asset’s systematic risk with the aggregate market portfolio of risky assets Risk premium= f (systematic or market risk) Chapter 1 The Investment Setting

Fundamental risk versus systematic risk There is generally a significant relationship between the market measure of risk and fundamental measures of risk The two measures of risk can be complementary Risk premium= f (business risk,financial risk,liquidity risk, exchange rate risk,country risk) Risk premium= f (systematic market risk) Chapter 1 The Investment Setting

Summary required rates of return The overall required rate of return on alternative investments is determined by three variables The economy’s real RFR, i.e., the long-run real growth rate Variables that influence the nominal RFR, which included short-run ease or tightness in the capital market and the expected rate of inflation The risk premium on the investment Measures and sources of risk Measures of risk: variance of rates of return, standard deviation of rates of return, coefficient of variance of rates of return (CV), covariance of returns with the market portfolio (beta) Sources of risk: business risk, financial risk, liquidity risk, exchange rate risk, country risk Chapter 1 The Investment Setting

4. Relationship between Risk and Return Movements along the SML Changes in the slope of the SML Changes in capital market conditions or expected inflation Summary of changes in the required rate of return Chapter 1 The Investment Setting

Relationship Between Risk and Return Exhibit 1.3 (Expected) Chapter 1 The Investment Setting

Movements Along the SML Exhibit 1.4 Chapter 1 The Investment Setting

Changes in the slope of the SML A change in the slope of the SML occurs in response to a change in the attitudes of investors towards risk Exhibit 1.5 Chapter 1 The Investment Setting

Changes in capital market conditions or expected inflation A shift in the SML reflects a change in Expected real growth in the economy, Capital market conditions, The expected rate of inflation. Chapter 1 The Investment Setting

Capital Market Conditions, Expected Inflation, and the SML Exhibit 1.6 NRFR NRFR´ Expected Return Chapter 1 The Investment Setting

Summary of changes in the required rate of return The relationship between risk and the required rate of return for an investment can change in three ways A movement along the SML is caused by a change in risk characteristics of a specific investment. This change affects only the individual investment A change in the slope of the SML occurs in response to a change in the attitudes of investors towards risk A shift in the SML reflects a change in expected real growth, in market conditions such as ease or tightness of money, or a change in the rate of inflation. Again, such a change will affect all investments Chapter 1 The Investment Setting