# investment settings

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From the book: Investment Analysis and Portfolio Management, 7th Editionby Frank K. Reilly & Keith C. BrownTRANSCRIPT

Presented BySunanda SarkerRoll NO. 161201

Batch-16MBM, BIBM

Course: Investment Course: Investment Analysis and Portfolio Analysis and Portfolio

Management (614)Management (614)Presented To

Dr. Prashanta Kumar Banerjee

Professor & Director (Research, Development

& Consultancy)BIBM

CHAPTER 1CHAPTER 1The Investment SettingThe Investment Setting

•What Is An Investment•Return and Risk Measures

•Measuring Historical Rates of Return•Computing Mean Historical Return•Calculating Expected Rates of Return•Measuring the Risk of Expected Rates of

Return•Determinants of Required Returns

What is an Investment?

Investment is the current commitment of money for a period of time in order to derive future payments that will compensate for:

• Time the funds are committed• Expected rate of inflation• Uncertainty of future flow of funds

Why Invest?

• By investing (saving money now instead of spending it), individuals can tradeoff present consumption for a larger future consumption.

Pure Time Value of Money

• People willing to pay more for the money borrowed and lenders desire to receive a surplus on their savings (money invested)

The Effects of Inflation

• Inflation‒ If the future payment will be diminished in value

because of inflation, then the investor will demand an interest rate higher than the pure time value of money to also cover the expected inflation expense.

Uncertainty: Risk by any Other Name

• Uncertainty• If the future payment from the investment is not

certain, the investor will demand an interest rate that exceeds the pure time value of money plus the inflation rate to provide a risk premium to cover the investment risk.

Required Rate of Return on an Investment

• Minimum rate of return investors require on an investment, including the pure rate of interest and all other risk premiums to compensate the investor for taking the investment risk

Measures of Historical Rates of Return

Investment of Value Beginning

Investment of Value EndingHPR

Holding Period Return:

Holding Period Yield:HPY = HPR – 1

Historical Rates of Return: What Did We Earn (Gain)?

Your investment of $250 in Stock A is worth $350 in two years while the investment of $100 in Stock B is worth $120 in six months. What are the annual HPRs and the HPYs on these two stocks?

Example I:

Your Investments Rise in Value

• Stock A– Annual HPR=HPR1/n = ($350/$250)1/2 =1.1832– Annual HPY=Annual HPR-1=1.1832-1=18.32%

• Stock B– Annual HPR=HPR1/n = ($112/$100)1/0.5 =1.2544– Annual HPY=Annual HPR-1=1.2544-1=25.44%

Example I:

Historical Rates of Return: What Did We Lose?

Your investment of $350 in Stock A is worth $250 in two years while the investment of $112 in Stock B is worth $100 in six months. What are the annual HPRs and the HPYs on these two stocks?

Example II:

Your Investments Decline in Value

• Stock A– Annual HPR=HPR1/n = ($250/$350)1/2 =.84515– Annual HPY=Annual HPR-1=.84514 - 1=-15.48%

• Stock B– Annual HPR=HPR1/n = ($100/$112)1/0.5 =.79719– Annual HPY=Annual HPR-1=.79719-1=-20.28%

Example II:

• Arithmetic Mean Return (AM)AM= HPY / n

where HPY=the sum of all the annual HPYs n=number of years

Calculating Mean Historical Rates of Return

• Geometric Mean Return (GM)GM= [ HPY] 1/n -1

where HPR=the product of all the annual HPRs n=number of years

Arithmetic vs. Geometric Averages

• When rates of return are the same for all years, the AM and the GM will be equal.

• When rates of return are not the same for all years, the AM will always be higher than the GM.

• While the AM is best used as an “expected value” for an individual year, while the GM is the best measure of an asset’s long-term performance.

Comparing Arithmetic vs. Geometric Averages: Example

Suppose you invested $100 three years ago and it is worth $110.40 today. What are your arithmetic and geometric average returns?

Arithmetic Average: An Example

Year Beg. Value Ending Value

HPR HPY

1 $100 $115 1.15 .152 115 138 1.20 .203 138 110.40 .80 -.20

AM= HPY / nAM=[(0.15)+(0.20)+(-0.20)] / 3 = 0.15/3=5%

GM= [ HPY] 1/n -1GM=[(1.15) x (1.20) x (0.80)]1/3 – 1

=(1.104)1/3 -1=1.03353 -1 =3.353%

Portfolio Historical Rates of Return

• Portfolio HPY‒ Mean historical rate of return for a portfolio of investments

is measured as the weighted average of the HPYs for the individual investments in the portfolio, or the overall change in the value of the original portfolio.

• The weights used in the computation are the relative beginning market values for each investment, which is often referred to as dollar-weighted or value-weighted mean rate of return.

Expected Rates of ReturnWhat Do We Expect to Earn?

• In previous examples, we discussed realized historical rates of return.

• In reality most investors are more interested in the expected return on a future risky investment.

Risk and Expected Return

• Risk refers to the uncertainty of the future outcomes of an investment• There are many possible returns/outcomes from

an investment due to the uncertainty• Probability is the likelihood of an outcome• The sum of the probabilities of all the possible

outcomes is equal to 1.0.

Calculating Expected Returns

n

i 1i Return) (Possible Return) ofy Probabilit( )E(R

)]R(P....))(R(P))(R[(P nn2211

Where:Pi = the probability of return on asset i Ri = the return on asset i

n

iii RP

1

))((

Perfect Certainty: The Risk Free Asset

• E(Ri) = ( 1) (.05) = .05 or 5%

If you invest in an asset that has an expected return 5% then it is absolutely certain your expected return will be 5%

Probability Distribution of Risk-free Investment

0.000.200.400.600.801.00

-5% 0% 5% 10% 15%

Risk-Free Investment

Risky Investment with Three Possible Outcomes

• Suppose you are considering an investment with 3 different potential outcomes as follows:

Economic Conditions

Probability Expected Return

Strong Economy 15% 20%Weak Economy 15% -20%Stable Economy 70% 10%

Probability Distribution

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-30% -10% 10% 30%

Risky Investment with 3 Possible Returns

Calculating Expected Return on a Risky Asset

n

iii RPRiE

1

))(()(

%707.)]10)(.70(.)(.15)(-.20)[(.15)(.20)( RiE

Investment in a risky asset with a probability distribution as described above, would have an expected return of 7%.

This is 2% higher than the risk free asset. In other words, investors get paid to take risk!

0.000.200.400.600.801.00

-30% -10% 10% 30%

Risk and Expected Returns

• Risk refers to the uncertainty of an investment; therefore the measure of risk should reflect the degree of the uncertainty.

• Risk of expected return reflect the degree of uncertainty that actual return will be different from the expect return.

• Common measures of risk are based on the variance of rates of return distribution of an investment

Risk of Expected Return

• The Variance Measure

n

iiii

n

i

RERP

turnExpected

turnPossiblexobability

Variance

1

2

2

1

)]([

)ReRe

()(Pr

Risk of Expected Return• Standard Deviation (σ)

• square root of the variance • measures the total risk

n

iiii RERP

1

2)]([

• Coefficient of Variation (CV)• measures risk per unit of expected return • relative measure of risk

)(RE

ReturnofRateExpectedReturnofDeviationStandardCV

Risk of Historical Returns

• Given a series of historical returns measured by HPY, the risk of returns can be measured using variance and standard deviation

• The formula is slightly different but the measure of risk is essentially the same

Variance of Historical Returns

n/HPY)](EHPY[ 2n

1ii

2

Where:

σ 2 = the variance of the series

HPY i = the holding period yield during period I

E(HPY) = the expected value of the HPY equal to the arithmetic mean of the series (AM)

n = the number of observations

Three Determinants of Required Rate of Return

• Time value of money during the time period

• Expected rate of inflation during the period

• Risk involved

Three Key Components of Total Required Rate of Return

The Real Risk Free Rate (RRFR)

• Assumes no inflation• Assumes no uncertainty about future cash flows• Influenced by time preference for consumption of

income and investment opportunities in the economy

Nominal Risk Free Rate (NRFR)

• Conditions in the capital market• Expected rate of inflation

NRFR=(1+RRFR) x (1+ Rate of Inflation) - 1NRFR=(1+RRFR) x (1+ Rate of Inflation) - 1RRFR=[(1+NRFR) / (1+ Rate of Inflation)] - 1RRFR=[(1+NRFR) / (1+ Rate of Inflation)] - 1

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