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A Brief History of

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... gains if we do not sell the stock? 1-4. Computing Returns ... Financial Market History. 1-7. Financial Market History. So what do we learn from the graphs? ... – PowerPoint PPT presentation

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Title: A Brief History of


1
1
  • A Brief History of
  • Risk and Return

2
A Brief History of Risk and Return
  • Our goal in this chapter is to see what financial
    market history can tell us about risk and return.
  • There are two key observations
  • First, there is a substantial reward, on average,
    for bearing risk.
  • Second, greater risks accompany greater returns.

3
Computing Returns
  • To start us off, let us look at two measures of
    returns
  • Total dollar return is the return on an
    investment measured in dollars, accounting for
    all interim cash flows and capital gains or
    losses.
  • Do we include capital gains if we do not sell the
    stock?

4
Computing Returns
  • Total percent return is the return on an
    investment measured as a percentage of the
    original investment. The total percent return is
    the return for each dollar invested.

5
A 1 Investment in Different Types of Portfolios,
19262006.
1-5
6
Financial Market History
7
Financial Market History
  • So what do we learn from the graphs?
  • There is a strong financial incentive for
    long-term investing but. recent market behavior
    may scare off even the most ardent believers in
    long-run investing.
  • Maybe Keynes In the long run, we are all
    dead.. is more appropriate??

8
The Historical Record Total Returns on
Large-Company Stocks.
9
The Historical Record Total Returns on
Small-Company Stocks.
10
The Historical Record Total Returns on U.S.
Bonds.
11
The Historical Record Total Returns on T-bills.
12
The Historical Record Inflation.
13
Historical Average Returns
  • What measures can we use to summarize the history
    of financial market returns?
  • We can compute average returns in two ways
  • Arithmetic average returns
  • Geometric average returns

14
Arithmetic Averages versus Geometric Averages
  • The arithmetic average return answers the
    question What was your return in an average
    year over a particular period?
  • The geometric average return answers the
    question What was your average compound return
    per year over a particular period?

15
Arithmetic Averages versus Geometric Averages
  • The arithmetic average tells you what you earned
    in a typical year and what way may expect to earn
    in any given year in the future.
  • The geometric average tells you what you actually
    earned per year on average, compounded annually.
  • When we talk about average returns, we generally
    are talking about arithmetic average returns.
  • For the purpose of forecasting future returns
  • The arithmetic average is probably "too high" for
    long forecasts.
  • The geometric average is probably "too low" for
    short forecasts.

16
Blumes Formula For Estimating Returns
  • If the geometric average tends to be too high,
    and the
  • arithmetic average too low, how can we best
    estimate
  • returns?
  • Blumes formula gives an unbiased estimate.
  • Suppose we calculate averages from N years of
    data and we wish to forecast future returns over
    T years . Then forecasted returns R(T) are
    estimated as
  • R(T) geometric mean(T-1)/(N-1) arithmetic
    mean(N-T)/(N-1)

17
What Can We Learn From Average Returns?
  • Risk-free rate The rate of return on a riskless,
    i.e., certain investment.
  • Risk premium The extra return on a risky asset
    over the risk-free rate i.e., the reward for
    bearing risk.

18
How Do We Compute the Risk Premium?
  • In order to calculate an appropriate risk
    premium, we must answer two questions
  • What risk-free security do we use?
  • Do we use arithmetic or geometric average
    returns?
  • Both questions can be answered by examining why
    we are calculating the risk premium. For example,
    if we are calculating it as an input to stock
    valuation, then it makes sense to use a
    longer-term risk-free security and a geometric
    average since stock valuation tends to be an
    analysis of long-term (technically infinite)
    stream of cash flows.

19
Why Does a Risk Premium Exist?
  • Modern investment theory centers on this
    question.
  • A risk premium exists because certain securities
    are more risky than others therefore investors
    should be compensated with higher return for
    bearing this greater risk.
  • We can start our examination of risk by looking
    at variance and standard deviation of returns.

20
Return Variability Review and Concepts
  • Variance is a common measure of return
    dispersion. Sometimes, return dispersion is also
    called variability.
  • Standard deviation is the square root of the
    variance.
  • Sometimes the square root is called volatility.
  • Standard Deviation is handy because it is in the
    same "units" as the average.
  • Normal distribution A symmetric, bell-shaped
    frequency distribution that can be described with
    only an average and a standard deviation.

21
Return Variability The Statistical Tools
  • The formula for return variance is ("n" is the
    number of returns)
  • Sometimes, it is useful to use the standard
    deviation, which is related to variance like
    this

22
Frequency Distribution of Returns on Common
Stocks, 19262005
23
Historical Returns, Standard Deviations, and
Frequency Distributions 19262005
24
The Normal Distribution and Large Company Stock
Returns
25
Useful Rule of Thumb
  • In any given year, your investment has an
    approximately 1/3 chance of generating a return
    that is outside of the mean standard deviation
    for that investment.

26
Risk and Return
  • First Lesson If we are willing to bear risk,
    then we can expect to earn a risk premium, at
    least on average.
  • Second Lesson Further, the more risk we are
    willing to bear, the greater the expected risk
    premium.

27
Historical Risk and Return Trade-Off
28
Readings
  • All of Chapter 1
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