Risk Return: Return on Investment
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Transcript of 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