Risk Return: Return on Investment

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    Return On An Investment

    The pure rate of interest:

    Exchange rate between future

    consumption (future dollars) andpresent consumption (current

    dollars).

    Market forces determine this rate

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    Peoples willingness to pay the

    difference for borrowing today andtheir desire to receive a surplus on

    their savings give rise to an interest

    rate referred to as the pure timevalue of money.

    Return On An Investment

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    If the future payment will bediminished in value because ofinflation, then the investor willdemand an interest rate higher thanthe pure time value of money toalso cover the expected inflationexpense.

    Return On An Investment

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    If the future payment from theinvestment is not certain, the

    investor will demand an interestrate that exceeds the pure timevalue of money plus the inflation

    rate to provide a risk premium tocover the investment risk.

    Return On An Investment

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    Measures ofHistorical Rates of Return

    Holding Period Return

    10.1$200

    $220

    InvestmentofValueBeginning

    InvestmentofValueEndingHPR

    ==

    =

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    Measures ofHistorical Rates of Return

    Holding Period Yield

    HPY = HPR - 11.10 - 1 = 0.10 = 10%

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    Annual Holding Period ReturnAnnual HPR = HPR1/n

    where n = number of years investment is held

    Annual Holding Period YieldAnnual HPY = Annual HPR - 1

    Measures ofHistorical Rates of Return

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    Measures ofHistorical Rates of Return

    Arithmetic Mean

    yieldsperiodholdingannualofsumtheHPY

    :whereHPY/AM

    =

    = n

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    Measures ofHistorical Rates of Return

    Geometric Mean

    [ ]

    ( ) ( ) ( )n

    n

    HPRHPRHPR

    :followsasreturnsperiodholdingannualtheofproductthe

    :where 1HPRGM

    21

    1

    =

    =

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    MEASURING HISTORICAL RETURN

    TOTAL RETURN

    C+ (PE

    - PB)

    R =

    PB

    RETURN RELATIVE

    C+ PE

    RETURN RELATIVE = PB

    CUMULATIVE WEALTH INDEX

    CWIn

    = WI0 (1+R1) (1+R2) (1+Rn)

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    Expected Rates of Return

    Risk is uncertainty that an

    investment will earn its expectedrate of return

    Probability is the likelihood of an

    outcome

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    Expected Rates of Return

    =

    =n

    i 1

    i

    Return)(PossibleReturn)ofyProbabilit(

    )E(RReturnExpected

    )R(P....))(R(P))(R[(P nn2211 +++

    ))(RP(1

    ii

    n

    i

    =

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    Probability Distributions

    Risk-free Investment

    0.00

    0.20

    0.40

    0.60

    0.80

    1.00

    -5% 0% 5% 10% 15%

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    Probability Distributions

    Risky Investment with 3 Possible Returns

    0.00

    0.20

    0.40

    0.60

    0.80

    1.00

    -30% -10% 10% 30%

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    Probability Distributions

    Risky investment with ten possible rates of return

    0.00

    0.20

    0.40

    0.60

    0.80

    1.00

    -40% -20% 0% 20% 40%

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    Measuring the Risk of

    Expected Rates of Return

    2

    n

    1iReturn)Expected-Return(Possibley)Probabilit(

    )(Variance

    =

    =

    2iii

    1

    )]E(R)[RP( =n

    i

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    Measuring the Risk of

    Expected Rates of ReturnStandard Deviation is the square

    root of the variance

    =n

    i 1

    2iii )]E(R-[RP

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    Measuring the Risk of

    Expected Rates of ReturnCoefficient of variation (CV) a measure ofrelative variability that indicates risk per unit

    of returnStandard Deviation of Returns

    Expected Rate of Returns

    E(R)i=

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    Measuring the Risk ofHistorical Rates of Return

    variance of the series

    holding period yield during period I

    expected value of the HPY that is equalto the arithmetic mean of the series

    the number of observations

    2/nn

    1i

    i

    2 HPY)(EHPY[=

    =

    =

    =

    =

    =

    n

    E(HPY)

    HPY i

    2

    D i f

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    Determinants ofRequired Rates of Return

    Time value of money during the

    period of investment

    Expected rate of inflation during

    the period

    Risk involved

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    The Real Risk Free Rate

    (RRFR)Assumes no inflation.

    Assumes no uncertainty about futurecash flows.

    Influenced by time preference for

    consumption of income andinvestment opportunities in theeconomy

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    Adjusting For Inflation

    Real RFR =

    1Inflation)ofRate(1RFR)Nominal1(

    ++

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    Nominal Risk-Free Rate

    Dependent upon

    Conditions in the Capital MarketsExpected Rate of Inflation

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    Adjusting For Inflation

    Nominal RFR =(1+Real RFR) x (1+Expected Rate of Inflation) -

    1

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    Facets of Fundamental

    Risk Business risk

    Financial risk Liquidity risk

    Exchange rate risk Country risk

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    Business Risk

    Uncertainty of income flows caused by

    the nature of a firms business

    Sales volatility and operating leverage

    determine the level of business risk.

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    Financial Risk

    Uncertainty caused by the use of debtfinancing.

    Borrowing requires fixed payments whichmust be paid ahead of payments tostockholders.

    The use of debt increases uncertainty ofstockholder income and causes an increase inthe stocks risk premium.

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    Liquidity Risk

    Uncertainty is introduced by the secondary

    market for an investment.

    How long will it take to convert an investmentinto cash?

    How certain is the price that will be received?

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    Exchange Rate Risk

    Uncertainty of return is introduced by

    acquiring securities denominated in a

    currency different from that of the investor.

    Changes in exchange rates affect the

    investors return when converting aninvestment back into the home currency.

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    Country Risk

    Political risk is the uncertainty of returns caused

    by the possibility of a major change in the

    political or economic environment in a country. Individuals who invest in countries that have

    unstable political-economic systems must include

    a country risk-premium when determining theirrequired rate of return

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    Risk Premium

    f(Business Risk, Financial Risk,

    Liquidity Risk, Exchange Rate Risk,

    Country Risk)

    or

    f(Systematic Market Risk)

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    Risk Premium

    and Portfolio Theory The relevant risk measure for an

    individual asset is its co-movement withthe market portfolio

    Systematic risk relates the variance ofthe investment to the variance of the

    market Beta measures this systematic risk of an

    asset

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    Fundamental Risk

    versus Systematic Risk Fundamental risk comprises business risk,

    financial risk, liquidity risk, exchange rate

    risk, and country risk

    Systematic risk refers to the portion of an

    individual assets total variance attributableto the variability of the total market portfolio

    R l ti hi B t

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    Relationship BetweenRisk and Return

    Rateof Return

    Risk(business risk, etc., or systematic risk-beta)

    RFR

    SecurityMarket Line

    LowRisk

    AverageRisk

    HighRisk

    The slope indicates therequired return per unit of r

    (Expected)

    EVALUATION OF VARIOUS INVESTMENT AVENUES

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    EVALUATION OF VARIOUS INVESTMENT AVENUES

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