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Risk and Return

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Title: Risk and Return


1
Chapter 5
  • Risk and Return

2
CHAPTER 5 OVERVIEW
  • 5.1 Distinguishing Between Saving and Investing
  • 5.2 Types of Financial Assets
  • 5.3 Measuring Historical Returns
  • 5.4 Historical Returns
  • 5.5 Risk Concepts and Measurement
  • 5.6 Balancing Risk and Return

3
KEY TERMS
  • saving
  • investing
  • inflation
  • cash reserves
  • U.S. Treasury bills
  • U.S. Treasury notes
  • U.S. Treasury bonds
  • bonds
  • common stock
  • nominal risk-free rate
  • risk-free rate of return
  • required risk premium
  • arithmetic average returns
  • geometric mean return
  • median return
  • total return
  • nominal return
  • real return

4
Measuring Volatility
  • Standard Deviation
  • Coefficient of Variation
  • Covariance
  • Correlation
  • Investment Horizon
  • Firm-specific Risk
  • Market Risk
  • Valuation Risk
  • Reversion to the Mean
  • Interest Rate Risk
  • Credit Risk

5
WHICH IS IT?
  • Saving accumulating money to meet some
    short-term goal
  • usually through intermediary like a bank
  • money-market funds
  • Investing assuming measured risk in pursuit of
    higher rates of return over an extended period
  • long-term capital appreciation
  • growth of income

Neither saving nor investing is without risks!
6
Types of Financial Assets
  • Cash Reserves short term money market
    instruments
  • modest income with stability of principal
  • T-bills, T-notes, T-bonds
  • Bank CDs
  • Bonds interest-bearing debt obligations
  • corporate bonds
  • federal government
  • state and municipal (local) governments
  • Stock ownership stake in a corporation

7
Common stocks provide potential income from
dividends and long-term capital appreciation.
Figure 5.1
8
Stock Prices Fluctuate
  • Price swings in short term can be violent
  • Factors that influence a stocks market value
  • companys current profitability
  • company/industry growth prospects
  • interest rates
  • conditions in overall stock market
  • Over long term, stocks consistently offer best
    opportunity to stay ahead of inflation and
    increase investment value

9
Measuring Historical Returns
  • Nominal risk-free rate monetary reward for
    postponing consumption
  • Risk-free rate of return rate return investors
    can earn with no chance of default risk or
    volatility risk T-bill return
  • Required risk premium compensation investors
    demand in return for taking risks associated with
    default, inflation, volatility, or other risks

10
Measuring Historical Returns
  • Required return nominal risk-free rate
    required risk premium
  • (real risk-free rate expected
    inflation) required risk premium
  • Given a real rate of interest(real risk-free
    rate) of 3, an expected inflation premium of 5,
    and risk premiums for investments A and B of 3
    and 5, respectively, find
  • The nominal risk free rate
  • The required returns for investments A and B

11
Arithmetic Average Return
  • Simple sum of investment returns divided by the
    number of periods or securities held
  • Logical problem with thinking in linear terms
  • Arithmetic average return upwardly biased and
    inaccurate

12
Arithmetic Average Return
  • I bought a stock at 10 per share and held it for
    two years. The stock price went up to 20 at the
    end of first year and then went down to 10 at
    the end of second year. What is my holding-period
    return per year?
  • Time Return
  • 1st Yr. 100
  • 2nd Yr. -50
  • Use Arithmetic Average returns (100(-50))/2
    25 ?Correct?

13
Geometric Mean Return
  • Calculates annual investment returns accurately
    using compound rate of return earned on the
    investment over time

14
Geometric Mean Return
  • I bought a stock at 10 per share and held it for
    two years. The stock price went up to 20 at the
    end of first year and then went down to 10 at
    the end of second year. What is my holding-period
    return per year?
  • Time Return
  • 1st Yr. 100
  • 2nd Yr. -50
  • Use Geometric Mean Returns (20.5)0.5-10
    ?Correct?

15
JACKRABBIT FUND How Does it Really Stack Up?
Table 5.1
16
Historical Returns
  • Total Return sum of dividends, interest income,
    and capital gains/losses
  • Average Returns arithmetic average of geometric
    mean prices
  • Median Return middle rate of returnhalf of
    values fall below median half above

17
Total Returns On Debt Equity Investments1950-1
999
18
INFLATION PROBLEM
INFLATION PROBLEM
  • Inflation general increase in cost of living
  • Nominal Return gross investment profit expressed
    as percentage
  • Real Return investment return after inflation

19
The Power of Cumulative Returns
Figure 5.2
20
Risk Concepts Measurement
  • Valuation Risk chance of loss due to relatively
    high stock prices
  • Firm-Specific Risk chance that problems with
    individual company will reduce investment value
  • Market Risk general fluctuations in stock and
    bond prices
  • Interest Rate Risk chance of loss in value of
    fixed-income investments following a rise in
    interest rates
  • Credit Risk chance of loss due to issuer default

21
Risk Measurement Concepts
  • Standard Deviation common risk measure
    volatility resulting from both upward and
    downward price movements
  • Given by
  • Coefficient of Variation relative measure of
    risk/reward relationship
  • Given by

22
Standard Deviation and Coefficient of Variation
  • Coefficient of variation, risk/reward ratio, for
    common stock is 1.11 ? when it comes to common
    stock investing, the cost of each percentage
    point of expected return is 1.11 in standard
    deviation (or risk).
  • For T-Bonds, the cost of each percentage point
    of expected return is _____ in standard
    deviation (or risk).
  • Common stocks are riskier than bonds because they
    have a higher standard deviation of annual
    returns, they involve a somewhat better
    risk/reward tradeoff.

23
Standard Deviation and Coefficient of Variation
a.Calculate the standard deviation and the
coefficient of variation for each
investment. b.On the basis of your calculation in
part a, which investment is more risky?
24
Standard Deviation and Coefficient of Variation
25
Standard Deviation and Coefficient of Variation
26
Risk Measurement Comovement
  • Comovement extent to which returns move up or
    down together
  • Covariance absolute measure of comovement
    varies between plus and minus infinity
  • Correlation relative measure of comovement
    varies between -1 and 1

27
Comovement
  • What does the correlation value of -1 imply?
  • Returns from two asset classes are perfectly
    inversely correlated.
  • A positive return of 10 in one asset class would
    correspond with a negative return of 10 in the
    other asset class.
  • What does the correlation value of 1 imply?
  • Returns from two asset classes are perfectly in
    sync.?move in lock-step fashion up and down
    together.
  • A positive return of 10 in one asset class would
    correspond with a negative return of 10 in the
    other asset class
  • What is the implication of correlation on
    portfolio formation?

28
Comovement
a.Calculate the covariance and the correlation
29
Comovement
30
Correlations in Total Returns for Stocks, Bonds,
Bills, Inflation 1950-2000
Table 5.5
  • Stocks Bonds Bills Inflation

Stocks 100.00 Bonds 20.99 100.00 Bills -11.99
33.50 100.00 Inflation -29.97 -16.88 63.12 10
0.00
Correlation in annual returns on common stocks
and the inflation rate is 29.97? an uptick in
inflation is accompanied by a downturn in stock
prices. Why??uptick in inflation rate? short-term
interest rates rise
31
Reducing Year-to-Year Volatility
  • Longer investment horizon or holding period
  • to exploit the benefit of cumulative returns
  • history tells us that risk-reward ratio tends to
    decrease as time horizon is longer for both
    stocks and bonds. (Table 5.6)
  • Broad portfolio diversification
  • Over long term, stocks provide best returns after
    inflation and taxes
  • for a person with an extended investment horizon
    since over an extended period of time stocks
    provide best returns after inflation and taxes
  • In the long run, bonds break-even (at most) after
    inflation and taxes
  • In long run, short term T-bills and money market
    investments actually deplete capital

32
SOURCES OF VOLATILITY Company or Firm-Specific
Risk
  • Company or Firm-specific Risk chance that
    problems with individual company will reduce the
    value of investment
  • Changes in overall economic environment
    inflation rate, degree of leverage (1/3 of stock
    price volatility)
  • Rise in inflation?interest rates rise?affect
    highly levered firms
  • Sector-related factors cyclical industries, tax
    code changes(15 of stock price volatility)
  • A cut in capital gains tax rate ? favor growth
    stocks whose prices rise at above-average rates
  • A cut in the amount tax paid on dividend income ?
    favor value stocks that pay above-average
    dividends
  • Industry-related factors competition,
    regulation, input costs (10 of stock price
    volatility)

33
SOURCES OF VOLATILITY Company or Firm-Specific
Risk
  • Significant portion of total risk if we own a
    single security
  • Becomes less and less significant as we diversify
    more and more.
  • Diversified mutual fund is a good choice to
    reduce or eliminate firm-specific risk

Diversification is the best way to limit company
risk
34
SOURCES OF VOLATILITYMarket Risk
  • Market Risk general fluctuations in stock and
    bond prices
  • Actual and anticipated changes in economic
    growth, inflation rate, interest rates
  • Changes in business climate and investor
    perceptions hope and fear
  • Popular measures of investor expectations and
    market valuation risk
  • P/E Ratios high P/E high risk low P/E low
    risk
  • Price/Book (P/B) Ratios high P/B high risk
    low P/B low risk
  • Dividend Yield Information high yield investor
    caution and concern about future business
    prospect low dividend yields investor optimism
    and enthusiasm for future business prospect

Diversification cannot eliminate market risk
Longer time horizons are best way to correct for
market risk
35
SOURCES OF VOLATILITYValuation Risk
  • Valuation Risk chance of loss due to relatively
    high stock prices
  • More than investor psychology and greed/fear
    factor
  • Economics of supply and demandbusiness
    cycle-also enters the picture
  • Expansion rising stock prices and growing
    investor enthusiasm
  • Recession stagnant or falling prices and
    investor pessimism
  • Reversion to the Mean tendency of stock and bond
    returns to return toward long-term averages

International markets may provide hedges against
valuation risk in US securities
36
SOURCES OF VOLATILITYBond Market Risk
  • Bond market subject to economic expectations as
    well
  • Bond Values extremely interest-rate-sensitive
    as interest rates rise, bond prices fall.
  • Price volatility depends on maturityterm of more
    than 10 years is more risky.
  • interest rate risk and maturity
  • Interest Rate Risk chance of loss in value of
    fixed-income investments following a rise in
    interest rates
  • credit risk and bond quality
  • Credit Risk chance of loss due to issuer default
    fail to make timely payments of principal and
    interest
  • Low quality?high credit risk vice versa.

37
Review Questions
  • 1. T F Long-term investing in stocks and bonds
    has typically resulted in rates of return that
    significantly outpaces inflation, but short-term
    losses can sometimes be substantial.
  •  
  • 2. T F After-tax rates of return on savings
    often fail to keep pace with inflation.
  • 3. T F Treasury bonds are debt obligations of
    the U.S. Treasury that have maturities of less
    than one year.

38
Review Questions
  • 4. T F Municipal bonds are interest-bearing
    securities issued by local governments that are
    typically free of federal income taxes. 
  • 5. T F The reward for postponing consumption is
    the nominal risk-free rate, which consists of the
    risk-free rate of return minus an amount equal to
    the expected rate of inflation.
  • 6. T F Required return consists of the nominal
    risk-free rate, or the risk-free rate of return
    minus an amount equal to the expected rate of
    inflation, plus the required risk premium.

39
Review Questions
  • 7. T F The arithmetic average return is an
    unbiased measure used to depict the return on
    investment over time. 
  • 8. T F The geometric mean return is an
    inappropriate measure of the compound rate of
    return earned on investment over time.
  • 9. T F U.S. Treasury bills mature in less than
    one year, and offer a good proxy for money-market
    instruments.
  • 10. T F Total return is measured by the sum of
    dividends, interest income, and capital gains or
    capital losses.

40
Review Questions
  • 11. T F If a particular investment earns a real
    return of 6 but the rate of inflation is 4, the
    return after inflation is only 2.
  •  
  • 12. T F Whereas the standard deviation is a
    relative measure of risk, the coefficient of
    variation is a useful absolute risk measure.
  •  
  • 13. T F Covariance is an absolute measure of
    comovement that varies between -1 and 1.

41
Review Questions
  • 14. T F Correlation is a relative measure of
    comovement that varies between -ì and ì.
  •  
  • 15. T F An uptick in inflation is typically
    accompanied by a downturn in stock prices.
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