Risk and Return

1
Chapter 5

• Risk and Return

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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

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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

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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

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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!
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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

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Common stocks provide potential income from
dividends and long-term capital appreciation.
Figure 5.1
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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

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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

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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

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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

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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?

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Geometric Mean Return

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

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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?

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JACKRABBIT FUND How Does it Really Stack Up?
Table 5.1
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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

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Total Returns On Debt Equity Investments1950-1
999
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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

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The Power of Cumulative Returns
Figure 5.2
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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

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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

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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.

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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?
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Standard Deviation and Coefficient of Variation
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Standard Deviation and Coefficient of Variation
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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

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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?

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Comovement
a.Calculate the covariance and the correlation
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Comovement
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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
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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

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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)

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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
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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
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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
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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.

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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.

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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.

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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.

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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.

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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.