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

1

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Facets of Fundamental

Financial risk Liquidity risk

Exchange rate risk Country risk

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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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Liquidity Risk, Exchange Rate Risk,

Country Risk)

or

f(Systematic Market Risk)

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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