C01_Reilly1ce Lecture#1

8/22/2019 C01_Reilly1ce Lecture#1

1/48

1

Investment Analysis and PortfolioManagement

First Canadian Edition

By Reilly, Brown, Hedges, Chang


2/48

1 Chapter 1

The Investment Setting

What Is An Investment

Return and Risk Measures

Determinants of Required Returns

Relationship between Risk and Return

1-2Copyright 2010 Nelson Education Ltd.


3/48

What is an Investment?

Investment

Current commitment of $ for a period oftime in order to derive future paymentsthat will compensate for:

Time the funds are committed

Expected rate of inflation

Uncertainty of future flow of funds

Copyright 2010 Nelson Education Ltd. 1-3


4/48

Why Invest?

By investing (saving money nowinstead of spending it), individuals can

tradeoff present consumption for alarger future consumption.



5/48

Pure Rate of Interest

Exchange rate between futureconsumption (future dollars) and presentconsumption (current dollars)

Market forces determine rate

Example:

If you can exchange $100 today for $104 next year,this rate is 4% (104/100-1).



6/48

Pure Time Value of Money

People willing to pay more for the moneyborrowed and lenders desire to receive asurplus on their savings (money invested)



7/48

The Effects of Inflation

Inflation

If the future payment will be diminished in valuebecause of inflation, then the investor will

demand an interest rate higher than the puretime value of money to also cover the expectedinflation expense.



8/48

Uncertainty: Risk by any Other Name

Uncertainty

If the future payment from the investment is notcertain, the investor will demand an interest rate

that exceeds the pure time value of money plusthe inflation rate to provide a risk premium tocover the investment risk.



9/48

Required Rate of Returnon an Investment

Minimum rate of return investors require onan investment, including the pure rate ofinterest and all other risk premiums to

compensate the investor for taking theinvestment risk



10/48

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

Copyright 2010 Nelson Education Ltd.

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 theHPYs on these two stocks?

1-10

Example I:


11/48

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:


12/48

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 theHPYs on these two stocks?

1-12

Example II:


13/48

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:


14/48

Calculating Mean Historical Rates ofReturn

Suppose you have a set of annual rates ofreturn (HPYs or HPRs) for an investment.How do you measure the mean annual

return?

Do you use the arithmetic average? Or doyou use the geometric average?

It depends!



15/48

Arithmetic Mean Return (AM)

Arithmetic Mean Return (AM)

AM= HPY / nwhere HPY=the sum of all the annual HPYs

n=number of years



16/48

Geometric Mean Return (GM)

Geometric Mean Return (GM)

GM= [ HPY] 1/n -1where HPR=the product of all the annual HPRs

n=number of years



17/48

Arithmetic vs. Geometric Averages

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

When rates of return are not the same for

all years, the AM will always be higherthan the GM.

While the AM is best used as an expected

value for an individual year, while the GMis the best measure of an assets long-term performance.



18/48

Comparing Arithmetic vs. GeometricAverages: Example


Suppose you invested $100 three years ago and it is

worth $110.40 today. What are your arithmetic and

geometric average returns?

1-18


19/48

Arithmetic Average: An Example

Year Beg. Value EndingValue

HPR HPY

1 $100 $115 1.15 .15

2 115 138 1.20 .20

3 138 110.40 .80 -.20

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



20/48

Geometric Average: An Example

Year Beg. Value EndingValue

HPR HPY

1 $100 $115 1.15 .15

2 115 138 1.20 .20

3 138 110.40 .80 -.20

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%



21/48

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 overallchange 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.


E t d R t f R t


22/48

Expected Rates of ReturnWhat Do We Expect to Earn?

In previous examples, we discussed realizedhistorical rates of return.

In reality most investors are more interested in the

expected return on a future risky investment.



23/48

Risk and Expected Return

Risk refers to the uncertainty of the futureoutcomes 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 possibleoutcomes is equal to 1.0.



24/48

Calculating Expected Returns

n

i 1

i Return)(PossibleReturn)ofyProbabilit()E(R


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

Where:

Pi = the probability of return on asset i

Ri = the return on asset i

1-24

n

i

iiRP

1

))((


25/48

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 be5%


26/48

Probability Distribution

0.00

0.20

0.40

0.60

0.80

1.00

-5% 0% 5% 10% 15%


Risk-Free Investment


27/48

Risky Investment withThree Possible Outcomes

Suppose you are considering aninvestment with 3 different potentialoutcomes as follows:


EconomicConditions

Probability Expected Return

Strong Economy 15% 20%

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

1-27


28/48

Probability Distribution

0.00

0.20

0.40

0.60

0.80

1.00

-30% -10% 10% 30%


Risky Investment with 3 PossibleReturns

C l l ti E t d R t


29/48

Calculating Expected Return on aRisky Asset

n

i

iiRPRiE

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!

0.00

0.20

0.40

0.60

0.80

1.00

-30% -10% 10% 30%

1-29


30/48

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 ofuncertainty 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 aninvestment



31/48

Risk of Expected Return

The Variance Measure


-

-

n

iiii

n

i

RERP

turn

Expected

turn

Possiblexobability

Variance

1

2

2

1

)]([

)ReRe

()(Pr

1-31


32/48


Standard Deviation ()

square root of the variance

measures the total risk

-n

iiii RERP

1

2)]([s



33/48


Coefficient of Variation (CV)

measures risk per unit of expected return

relative measure of risk


)(RE

ReturnofRateExpected

ReturnofDeviationStandardCV

s

1-33


34/48

Risk of Historical Returns

Given a series of historical returns measured byHPY, the risk of returns can be measured usingvariance and standard deviation

The formula is slightly different but the measure ofrisk is essentially the same



35/48

Variance of Historical Returns

n/HPY)](EHPY[ 2n

1i

i

2

-

s


Where:

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 arithmeticmean of the series (AM)

n = the number of observations

1-35

Three Determinants of


36/48

Three Determinants ofRequired Rate of Return

Time value of money during the time period

Expected rate of inflation during the period

Risk involved



37/48

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 theeconomy



38/48

Nominal Risk Free Rate (NRFR)

Conditions in the capital market

Expected rate of inflation

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

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



39/48

Risk Premiums: Business Risk

Uncertainty of income flows caused by the natureof a firms business

Sales volatility and operating leverage determinethe level of business risk.



40/48

Risk Premiums: Financial Risk

Uncertainty caused by the use of debt financing

Borrowing requires fixed payments which mustbe paid ahead of payments to stockholders

Use of debt increases uncertainty of stockholderincome and causes an increase in the stocks riskpremium



41/48

Risk Premiums: Liquidity Risk

How long will it take to convert an investmentinto cash?

How certain is the price that will be received?



42/48

Risk Premiums: 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 investorsreturn when converting an investment back into

the home currency.



43/48

Risk Premiums: 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 haveunstable political-economic systems must include

a country risk-premium when determining their

required rate of return.



44/48

Risk Premiums and Portfolio Theory

From a portfolio theory perspective, the relevant

risk measure for an individual asset is its co-

movement with the market portfolio.

Systematic risk relates the variance of theinvestment to the variance of the market.

Beta measures this systematic risk of an asset.

According to the portfolio theory, the risk

premium depends on the systematic risk.



45/48

Fundamental versus Systematic Risk

Fundamental risk Risk Premium= f(Business Risk, Financial Risk,

Liquidity Risk, Exchange Rate Risk, Country Risk)

Systematic risk refers to the portion of an individual assets total

variance attributable to the variability of the totalmarket portfolio.

Risk Premium= f(Systematic Market Risk)


Ri k d R t


46/48

Risk and Return:The Security Market Line (SML)

Shows relationship between risk and return for allrisky assets in the capital market at a given time

Investors select investments that are consistentwith their risk preferences.


Expected Return

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

NRFR

SecurityMarket Line

LowRisk

AverageRisk

HighRisk

The slope indicates therequired return per unit of risk


47/48

SML: Market Conditions or Inflation

A change in RRFR or expected rate ofinflation will cause a parallel shift in theSML


Risk

NRFR

Original SML

New SML

Expected Return

NRFR'

1-47


48/48

SML: Market Conditions or Inflation

When nominal risk-free rate increases, the SML willshift up, implying a higher rate of return while stillhaving the same risk premium.

Risk

NRFR

Original SML

New SML

Expected Return

NRFR'

C01_Reilly1ce Lecture#1

Documents

Transcript of C01_Reilly1ce Lecture#1