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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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= =18.32%
Chapter 1 The Investment Setting

12. 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

13. 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

14. 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

15. 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)+0.70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

16. 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

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

18. 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 = (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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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

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

30. Movements Along the SML
Exhibit 1.4
Chapter 1 The Investment Setting

31. 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

32. 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

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

34. 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