RISK AND RETURN BASICS

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Chapter 2

• RISK AND RETURN BASICS

2
Chapter 2 Questions

• What are the sources of investment returns?
• How can returns be measured?
• How can we compute returns on investments outside
  of their home country?

3
Chapter 2 Questions

• What is risk and how is it measured?
• How is expected return and risk estimated via
  scenario analysis?
• What are the components of an investments
  required return to investors and why might they
  change over time?

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Sources of Investment Returns

• Investments provide two basic types of return
• Income returns
• The owner of an investment has the right to any
  cash flows paid by the investment.
• Changes in price or value
• The owner of an investment receives the benefit
  of increases in value and bears the risk for any
  decreases in value.

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Income Returns

• Cash payments, usually received regularly over
  the life of the investment.
• Examples Coupon interest payments from bonds,
  Common and preferred stock dividend payments.

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Returns From Changes in Value

• Investors also experience capital gains or losses
  as the value of their investment changes over
  time.
• For example, a stock may pay a 1 dividend while
  its value falls from 30 to 25 over the same
  time period.

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Investment Strategy

• Generally, the income returns from an investment
  are in your pocket cash flows.
• Over time, your portfolio will grow much faster
  if you reinvest these cash flows and put the full
  power of compound interest in your favor.
• Dividend reinvestment plans (DRIPs) provide a
  tool for this to happen automatically similarly,
  Mutual Funds allow for automatic reinvestment of
  income.
• See Exhibit 2.5 for an illustration of the
  benefit of reinvesting income.

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Measuring Returns

• Dollar Returns
• How much money was made on an investment over
  some period of time?
• Total Dollar Return Income Price Change
• Holding Period Return
• By dividing the Total Dollar Return by the
  Purchase Price (or Beginning Price), we can
  better gauge a return by incorporating the size
  of the investment made in order to get the dollar
  return.

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Annualized Returns

• If we have return or income/price change
  information over a time period in excess of one
  year, we usually want to annualize the rate of
  return in order to facilitate comparisons with
  other investment returns.
• Another useful measure
• Return Relative Income Ending Value
• Purchase Price

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Annualized Returns

• Annualized HPR (1 HPR)1/n 1
• Annualized HPR (Return Relative)1/n 1
• With returns computed on an annualized basis,
  they are now comparable with all other annualized
  returns.

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Returns on Overseas Investments

• A holding period return on a foreign investment
  generally needs to be translated back into the
  home country return.
• If the exchange rate has changed over the life of
  the investment, the home country return (HCR) can
  be very different than the foreign return (FR).

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Returns on Foreign Investments

• HCR Relative FR Relative (Current Exchange
  Rate/Initial Exchange Rate)
• HCR(1 FR)Current Exchange Rate 1
• Initial Exchange Rate

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Measuring Historic Returns

• Starting with annualized Holding Period Returns,
  we often want to calculate some measure of the
  average return over time on an investment.
• Two commonly used measures of average
• Arithmetic Mean
• Geometric Mean

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Arithmetic Mean Return

• The arithmetic mean is the simple average of a
  series of returns.
• Calculated by summing all of the returns in the
  series and dividing by the number of values.
• RA (SHPR)/n
• Oddly enough, earning the arithmetic mean return
  for n years is not generally equivalent to the
  actual amount of money earned by the investment
  over all n time periods.

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Arithmetic Mean Example

• Year Holding Period Return
• 1 10
• 2 30
• 3 -20
• 4 0
• 5 20
• RA (SHPR)/n 40/5 8

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Geometric Mean Return

• The geometric mean is the one return that, if
  earned in each of the n years of an investments
  life, gives the same total dollar result as the
  actual investment.
• It is calculated as the nth root of the product
  of all of the n return relatives of the
  investment.
• RG P(Return Relatives)1/n 1

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Geometric Mean Example

• Year Holding Period Return Return Relative
• 1 10 1.10
• 2 30 1.30
• 3 -20 0.80
• 4 0 1.00
• 5 20 1.20
• RG (1.10)(1.30)(.80)(1.00)(1.20)1/5 1
• RG .0654 or 6.54

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Arithmetic vs. Geometric

• To ponder which is the superior measure, consider
  the same example with a 1000 initial investment.
  How much would be accumulated?
• Year Holding Period Return Investment Value
• 1 10 1,100
• 2 30 1,430
• 3 -20 1,144
• 4 0 1,144
• 5 20 1,373

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Arithmetic vs. Geometric

• How much would be accumulated if you earned the
  arithmetic mean over the same time period?
• Value 1,000 (1.08)5 1,469
• How much would be accumulated if you earned the
  geometric mean over the same time period?
• Value 1,000 (1.0654)5 1,373
• Notice that only the geometric mean gives the
  same return as the underlying series of returns.

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Scenario Analysis

• While historic returns, or past realized returns,
  are important, investment decisions are
  inherently forward-looking.
• We often employ scenario or what if? analysis
  in order to make better decisions, given the
  uncertain future.
• Scenario analysis involves looking at different
  outcomes for returns along with their associated
  probabilities of occurrence.

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Expected Rates of Return

• Expected rates of return are calculated by
  determining the possible returns (Ri) for some
  investment in the future, and weighting each
  possible return by its own probability (Pi).
• E(R) S Pi Ri

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Expected Return Example

• Economic Conditions Probability Return
• Strong .20 40
• Average .50 12
• Weak .30 -20
• E(R) .20(40) .50 (12) .30 (-20)
• E(R) 8

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What is risk?

• Risk is the uncertainty associated with the
  return on an investment.
• Risk can impact all components of return through
• Fluctuations in income returns
• Fluctuations in price changes of the investment
• Fluctuations in reinvestment rates of return.

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Sources of Risk

• Systematic Risk Factors
• Affect many investment returns simultaneously
  their impact is pervasive.
• Examples changes in interest rates and the state
  of the macro-economy.
• Asset-specific Risk Factors
• Affect only one or a small number of investment
  returns come from the characteristics of the
  specific investment.
• Examples poor management, competitive pressures.

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How can we measure risk?

• Since risk is related to variability and
  uncertainty, we can use measures of variability
  to assess risk.
• The variance and its positive square root, the
  standard deviation, are such measures.
• Measure total risk of an investment, the
  combined effects of systematic and asset-specific
  risk factors.
• Variance of Historic Returns
• s2 S(Rt-RA)2/n-1

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Standard Deviation of Historic Returns

• Year Holding Period Return
• 1 10 RA 8
• 2 30 s2 370
• 3 -20 s 19.2
• 4 0
• 5 20
• s2 (10-8)2(30-8)2(-20-8)2(0-8)2(20-8)2/4
• 448478464144/4
• 1480/4

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Coefficient of Variation

• The coefficient of variation is the ratio of the
  standard deviation divided by the return on the
  investment it is a measure of risk per unit of
  return.
• CV s/RA
• The higher the coefficient of variation, the
  riskier the investment.
• From the previous example, the coefficient of
  variation would be
• CV 19.2/8 2.40

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Measuring Risk Through Scenario Analysis

• If we are considering various scenarios of return
  in the future, we can still calculate the
  variance and standard deviation of returns, now
  just from a probability distribution.
• s2 SPi(Ri-E(R))2

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Standard Deviation of Expected Returns

• Economic Conditions Probability Return
• Strong .20 40
• Average .50 12
• Weak .30 -20
• E(R) 8
• s2 .20 (40-8)2 .50 (12-8)2 .30 (-20-8)2
• s2 448
• s 21.2 Note CV 21.2/8 2.65

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Components of Return

• Recall from Chapter 1 that the required rate of
  return on an investment is the sum of the
  risk-free rate (RFR) of return available in the
  market and a risk premium (RP) to compensate the
  investor for risk.
• Required Return RFR RP
• The Capital Market Line (CML) is a visual
  representation of how risk is rewarded in the
  market for investments.

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Components of Return Over Time

• What changes the required return on an investment
  over time?
• Anything that changes the risk-free rate or the
  investments risk premium.
• Changes in the real risk-free rate of return and
  the expected rate of inflation (both impacting
  the nominal risk-free rate, factors that shift
  the CML).
• Changes in the investments specific risk (a
  movement along the CML) and the premium required
  in the marketplace for bearing risk (changing the
  slope of the CML).