Chapter 01-The Investment Setting

– σ2 =Σ[HPYi-E(HPY)]2 /n
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3. Determining 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
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For example
Barber, B. and J. Lyon, 1997, Detecting long-run abnormal stock returns: the empirical power and specification of test statistics, Journal of Financial Economics 43, 341-372.
– Pure time value of money – expected rate of inflation – risk premium
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2. Measuring Return and Risk
Measuring 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
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The behavior of
market rates over time
The analysis and estimation of the required rate of return are complicated by the behavior of market rates over time.
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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:
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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.
– 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%
Strong economy, no inflation
0.15
0.20
Weak economy, above AI
0.15
No major change in the economy
0.70
– E(R)=0.07
-0.20 0.10
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2
1. What is An Investment?
Investment Defined Required rate of return
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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
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.
AM=5% GM=3.353%
Year Beginning Value Ending Value HPRi HPYi
1
100.0
115.0
1.15 0.15
2
115.0
3
138.0
138.0 110.4
1.20 0.20 0.80 -0.20
Chapter 1 The Investment Setting
Chapter 1 The Investment Setting
Zhiqiang Wang
School of Finance Dongbei University of Finance & Economics
Chapter 1 The Investment Setting
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The Investment Setting
– First, a wide range of rates is available for alternative investments at any time.
– Second, the rates of return on specific assets change dramatically over time.

First, even though all these securities have promised returns based upon bond contracts, the promised annual yields during any year differ substantially.
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Measuring historical rates of return
Holding period return(HPR)
– HPR=Ending value of investment / Beginning value of investment
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Required rate of return
Pure time value of money
– Pure rate of interest
Nominal risk-free rate Risk premium Required rate of return, including
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Computing mean historical returns
For a single investment
– Arithmetic mean(AM): AM=ΣHPYi/n – Geometric mean(GM): GM=(ΠHPRi)1/n -1 – For example
– 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.
σ2 =0.0141, σ =o.11874
A relative measure of risk
– Coefficient of variation – CV=Standard Deviation of returns / Expected Rate of Return – For example, CV1=0.05/0.07=0.714, CV2=0.07/0.12=0.583
– Third, the difference between the rates available (that is, the spread) on different assets changes over time.
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The yield data in Exhibit 1.5 for alternative bonds demonstrate these three characteristics.
1. What is an Investment? 2. Measures Return and Risk 3. Determinants Required Rates of Return 4. Relationship between Risk and Return
Chapter 1 The Investment Setting
– The rate of return on one investment is random
The expected return from an investment
– Expected Return=ΣPiRi – For example
Economic Conditions
Probability Rate of Return
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Computing expected rates of return
Uncertainty
– There is uncertainty for rate of return on one investment
Random variable
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: above example