Essentials of Investment Analysis and Portfolio Management

Essentials of Investment Analysis

and Portfolio Management

by Frank K. Reilly & Keith C. Brown

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Chapter 1The Investment Setting

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Why Do Individuals Invest ?

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

(consumption choice)

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How Do We Measure the Rate Of Return On An Investment ?

The pure rate of interest is the exchange rate between future consumption and present consumption. Market forces determine this rate.

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People’s willingness to pay the difference for borrowing today and their desire to receive a surplus on their savings give rise to an interest rate referred to as the pure time value of money.

How Do We Measure the Rate Of Return On An Investment ?

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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.

How Do We Measure the Rate Of Return On An Investment ?

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If the future payment from the investment is not certain (uncertainty), 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.

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Defining an Investment

A current commitment of $ for a period of time in order to derive future payments that will compensate for:– the time the funds are

committed– the expected rate of inflation– uncertainty of future flow of

funds.

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• A central question in investments:

How investors select investments that will give them their required rate of return.

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Measures of return and risk

We have to know:• Historical rate of return for

an individual investment over one period of time

• Average historical return for an individual investment over a number of time periods

• Average return for a portfolio

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Measures of Historical Rates of Return

Holding Period Return

10.1 $200

$220 :examplefor

Investment of Value Beginning

Investment of Value EndingHPR

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Holding Period YieldHPY = HPR - 1

Prior example:1.10 - 1 = 0.10 = 10%

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Annual Holding Period Return•Annual HPR = HPR 1/n

n = number of years the investment is held

Annual Holding Period Yield•Annual HPY = Annual HPR - 1

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For instance (page 7)• A two-year HPR=$350/$250=1.4• Annual HPR=1.4 (1/2) =1.1832• Annual HPY=1.1832-1=18.32%

(Annual HPY is thus assumed constant for each year)

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• However, if the prior example is for a time period of 6 months, what is the annual HPR?

(Try it out!)

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Arithmetic Mean (AM) for an investment over a number of time periods

d yieldsding perio hol

f annual the sum oHPY

where: n

HPYAM

Computing mean historical returns

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Geometric Mean (GM)

n

n

HPRHPRHPRπ HPR

rct operato the produπ

where:

π HPRGM

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HPY for a portfolio

The mean historical rate of return for a portfolio is measured as the weighted average of the HPYs for the individual investments.

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• You can also consider the mean historical rate of return of a portfolio as the overall change in value of the original portfolio.

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Computation example of HPY for a portfolio

# Begin Beginning Ending Ending Market Wtd.

Stock Shares Price Mkt. Value Price Mkt. Value HPR HPY Wt. HPY

A 100,000 10$ 1,000,000$ 12$ 1,200,000$ 1.20 20% 0.05 0.010

B 200,000 20$ 4,000,000$ 21$ 4,200,000$ 1.05 5% 0.20 0.010

C 500,000 30$ 15,000,000$ 33$ 16,500,000$ 1.10 10% 0.75 0.075

Total 20,000,000$ 21,900,000$ 0.095

21,900,000$

20,000,000$

HPY = 1.095 - 1 = 0.095

= 9.5%

HPR = = 1.095

Exhibit 1.1

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Expected Rates of Return

• Risk: uncertainty that an investment will earn its expected rate of return (historical return=realized return)

• Point estimate: He/she expects to earns 10% over a year.

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Computing expected return

n

iii

nn

n

i

i

RP

RPRPRP

) E(R

1

2211

1

...

Return) (Possible Return) ofty (Probabili

Return Expected

See the detailed computation shown on page 12.

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Probability DistributionsRisk-free Investment (perfect certainty)

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 rates of returns

0.00

0.20

0.40

0.60

0.80

1.00

-30% -20% -10% 0% 10% 20% 30%

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Probability Distributions

Risky investment with 10 possible rates of return

0.00

0.20

0.40

0.60

0.80

1.00

-40% -30% -20% -10% 0% 10% 20% 30% 40% 50%

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Risk Aversion

Most investors will choose the least risky alternative, all else being equal and that they will not accept additional risk unless they are compensated in the form of higher return.

Compare the perfect certainty case and the risky investment case on page 12.

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Measuring the risk of expected rates of return

n

iiii

n

i

RERP1

2

2

1

)]([

Return) Expected-Return (Possibley)Probabilit(

Variance

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Standard deviation is the square root of the variance =

Measuring the risk of expected rates of return

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Coefficient of variation (CV) a measure of relative variability that indicates risk per unit of return.

E(R)

σC.V. i

Measuring the risk of expected rates of return

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/n(HPY)]E[HPYσn

ii

2

1

2

1.10

Measuring the risk of historical rates of return

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Determinants of required rates of return

• Time value of money• Expected rate of inflation• Risk involved

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• Required rate of return: the minimum rate of return to compensate for deferring consumption.

Find out the characteristics of the yield data in Exhibit 1.5:

1. Cross-section2. Time series3. Yield spread

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The components that determine the required rate of return

• The basic interest rate• Assumes no inflation• Assumes no uncertainty about future cash

flows.• Pure time value of money• Influenced by time preference for consumption

of income (subjective) and investment opportunities in the economy (objective)

The Real Risk Free Rate (RRFR)

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Real RFR = 1Inflation) of Rate(1

RFR) Nominal1(

1+Nominal RFR=(1+Real RFR)(1+Rate of Inflation)

Factors for nominal risk-free rate (NRFR)

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• Real RFR is quite stable over time.

• Nominal RFR can be affected by– The relative ease or tightness in the

capital markets – Expected rate of inflation

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Risk Premium

• We demand a higher return on an investment if we perceive that its uncertainty about expected return is higher.

• The increase in required return over the NRFR is called risk premium.

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The major sources of uncertainty (fundamental risk)

• Business risk• Financial risk• Liquidity risk• Exchange rate risk• Country risk

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Business Risk

• Uncertainty of income flows• Sales or earnings volatility

leverage affects the level of business risk.

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Financial Risk (financial leverage)

• Uncertainty caused by the use of debt financing.

• Borrowing requires fixed payments which must be paid ahead of payments to stockholders.

• The use of debt increases uncertainty of stockholder income and causes an increase in the stock’s 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

investment into cash?– How certain is the price that will be

received?

• US T-bills has almost no liquidity risk.

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Exchange Rate Risk• Uncertainty of return is

introduced by acquiring securities denominated in a foreign currency.

• To measure exchange rate risk:Use absolute variability of exchange

rate relative to a composite exchange rate.

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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.

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Risk Premium

Basically,Risk premium= f (Business

Risk, Financial Risk, Liquidity Risk, Exchange Rate Risk, Country Risk)

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Pages 22-27•Risk premium and portfolio theory •Fundamental risk vs systematic risk•Relationship between risk and return→Will be further discussed in the later chapters

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Exercises

• Do Problem 1, 5, 7, 9. • Read Appendix of Chapter 1 (This

is extra reading. Of course you need to read the contents of all chapters we discuss!)

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• Fundamental risk comprises business risk, financial risk, liquidity risk,

exchange rate risk, and country risk• Systematic risk refers to the portion

of an individual asset’s total variance attributable to the variability of the total market portfolio