The Investment Setting

Shahadat HosanFaculty, MBA Program

Stamford University, Bangldeshshad@asia.com

May 13, 2011

Chapter Objectives

After Studying this chapter, you would be able to answer: Why do individuals invest ? What is an investment ? How do we measure the rate of return on an investment ? How do investors measure risk related to alternative investments ? What factors contribute to the rate of return that an investor requires

on an investment? What macroeconomic and microeconomic factors contribute to

changes in the required rate of return for an investment?

Why Do Individuals Invest ?

By saving money (instead of spending it), individuals forego consumption today in return for a larger

consumption tomorrow.

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

The real rate of interest is the exchange rate between future consumption (future dollars) and present consumption (current dollars). Market forces determine this rate.

Today

Tomorrow

$100

$104If you are willing to exchange

a certain payment of $100 today for a certain payment of $104 tomorrow, then the pure or real rate of interest is 4%

If the purchasing power of the future payment will be diminished in value due to inflation, an investor will demand an inflation premium to compensate them for the expected loss of purchasing power.

If the future payment from the investment is not certain, an investor will demand a risk premium to compensate for the investment risk.

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

Defining an Investment

Any investment involves a current commitment of funds for some period of time in order to derive future payments that will compensate for: the time the funds are committed (the real rate of return) the expected rate of inflation (inflation premium) uncertainty of future flow of funds (risk premium)

Measures of Historical Rates of Return

%1010.0

$200

200 -$220

or

P

PPHPR

0

01

1.1

Where:

HPR = Holding period return

P0 = Beginning value

P1 = Ending value

Holding Period Return

Measures of Historical Rates of Return

Annualizing the HPR

111

NHPREAR

Where:

EAR = Equivalent Annual Return

HPR = Holding Period Return

N = Number of years

Example: You bought a stock for $10 and sold it for $18 six years later. What is your HPR & EAR?

Calculating HPR & EAR

Solution:

%8080.0

$10

10 -$18

or

P

PPHPR

0

01

%29.10

180.1

11

6

1

1

NHPREAR

Step #1: Step #2:

Measures of Historical Rates of Return

1 2 ... NR R RAM

N

Arithmetic Mean

1

1 21 1 ... 1 1NNGM R R R

Where:

AM = Arithmetic Mean

GM = Geometric Mean

Ri = Annual HPRs

N = Number of years

Geometric Mean

Example

You are reviewing an investment with the following price history as of December 31st each year.

Calculate: The HPR for the entire period The annual HPRs The Arithmetic mean of the annual HPRs The Geometric mean of the annual HPRs

1999 2000 2001 2002 2003 2004 2005 2006

$18.45 $21.15 $16.75 $22.45 $19.85 $24.10 $24.10 $26.50

A Portfolio of Investments

The mean historical rate of return for a portfolio of investments is measured as the weighted average of the HPRs for the individual investments in the portfolio, or the overall change in the value of the original portfolio

Computation of HoldingPeriod Return for a Portfolio

# Begin Beginning Ending Ending Market Wtd.Stock Shares Price Mkt. Value Price Mkt. Value HPR Wt. HPR

A 100,000 10$ 1,000,000$ 12$ 1,200,000$ 0.20 0.05 0.010 B 200,000 20$ 4,000,000$ 21$ 4,200,000$ 0.05 0.20 0.010 C 500,000 30$ 15,000,000$ 33$ 16,500,000$ 0.10 0.75 0.075

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

1 0

0

21,900,000 20,000,000

20,000,000

9.5%

Portfolio

P PHPR

P

Expected Rates of Return

Risk is the uncertainty whether an investment will earn its expected rate of return

Probability is the likelihood of an outcome

))(RP(

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

1

1i

ii

n

i

n

i

Risk Aversion

Much of modern finance is based on the principle that investors are risk averse

Risk aversion refers to the assumption that, all else being equal, most investors will choose the least risky alternative and that they will not accept additional risk unless they are compensated in the form of higher return

Probability Distributions

Risk-free Investment

0.00

0.20

0.40

0.60

0.80

1.00

-5% 0% 5% 10% 15%

Probability Distributions

Risky Investment with 3 Possible Returns

0.00

0.20

0.40

0.60

0.80

1.00

-30% -10% 10% 30%

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%

Measuring Risk: Historical Returns

N

HPRE i

n

1i

2i

2

HPR

Where:

= Variance (of the pop)

HPR = Holding Period Return i

E(HPR)i = Expected HPR*

N = Number of years

2

* The E(HPR) is equal to the arithmetic mean of the series of returns.

Measuring Risk: Expected Rates of Return

22i i

1

(P ) R E(R)n

i

Where:

= Variance

Ri = Return in period i

E(R) = Expected Return

Pi = Probability of Ri occurring

2

Note: Because we multiply by the probability of each return

occurring, we do NOT divide by N. If each probability is the

same for all returns, then the variance can be calculated by

either multiplying by the probability or dividing by N.

Measuring Risk: Standard Deviation

Standard Deviation is the square root of the variance

2i i i

1

1

22

i i i1

P[R -E(R )]

P [R -E(R )]

n

i

n

i

Standard Deviation is a measure of dispersion around the mean. The higher the standard deviation, the greater the dispersion of returns

around the mean and the greater the risk.

Coefficient of Variation Coefficient of variation (CV) is a measure of

relative variability CV indicates risk per unit of return, thus making

comparisons easier among investments with large differences in mean returns

1.9

i

E(R)

Standard Deviation of ReturnsCV

Expected Rate of Return

Determinants of Required Rates of Return

Three factors influence an investor’s required rate of return Real rate of return Expected rate of inflation during the period Risk

The Real Risk Free Rate

Assumes no inflation. Assumes no uncertainty about future cash

flows. Influenced by the time preference for

consumption of income and investment opportunities in the economy

Adjusting For Inflation:Fisher Equation

1 1 1Nominal Real Expected Inflation

The nominal risk free rate of return is dependent upon: Conditions in the Capital Markets Expected Rate of Inflation

Components of Fundamental Risk

Five factors affect the standard deviation of returns over time. Business risk: Financial risk Liquidity risk Exchange rate risk Country risk

Business Risk

Business risk arises due to: Uncertainty of income flows caused by the nature of a

firm’s business Sales volatility and operating leverage determine the

level of business risk.

Financial Risk

Financial risk arises due to: 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.

Liquidity Risk Liquidity risk arises due to the uncertainty

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?

Exchange Rate Risk

Exchange rate risk arises due to the uncertainty introduced by acquiring securities denominated in a currency different from that of the investor.

Changes in exchange rates affect the investors return when converting an investment back into the “home” currency.

Country Risk Country risk (also called political risk) refers to 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 their required rate of return

Risk Premium and Portfolio Theory

When an asset is held in isolation, the appropriate measure of risk is standard deviation

When an asset is held as part of a well-diversified portfolio, the appropriate measure of risk is its co-movement with the market portfolio, as measured by Beta

This is also referred to as Systematic risk Nondiversifiable risk

• Systematic risk refers to the portion of an individual asset’s total variance attributable to the variability of the total market portfolio

Relationship BetweenRisk and Return

(Expected)Rate of Return

Beta

Risk freeRate

Security Market Line

(SML)

Low

Risk

Average

Risk

High

Risk

Slope of the SML indicates therequired return per unit of risk

Changes in the Required Rate of Return Due to Movements Along the SML

Beta

Risk freeRate

Security Market Line

ExpectedRate

Movements along the SMLreflect changes in the market or systematic

risk of the asset

Lower Risk

Higher Risk

Changes in the Slope of the SML

The slope of the SML indicates the return per unit of risk required by all investors

The market risk premium is the yield spread between the market portfolio and the risk free rate of return

This changes over time, although the underlying reasons are not entirely clear

However, a change in the market risk premium will affect the return required on all risky assets

Change in Market Risk Premium

Expected Return

Rm´

Rm

Beta

Original SML

New SML

Note that as the slope of the SML increases,

so does the market risk premium

Risk Free Rate

Capital Market Conditions, Expected Inflation, and the SML

Risk

Original SML

New SML

Rate of Return

Risk freeRate

The SML will shift in a parallel fashion if inflation expectations, real growth expectations or capital

market conditions change. This will affect the required return on all assets.

The InternetInvestments Online

http://www.finpipe.com

http://www.investorguide.com

http://www.aaii.com

http://www.economist.com

http://www.online.wsj.com

http://www.forbes.com

http://www.barrons.com

http://fisher.osu.edu/fin/journal/jofsites.htm

http://www.ft.com

http://www.fortune.com

http://www.smartmoney.com

http://www.worth.com

http://www.money.cnn.com

Thank You