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The Investment Setting
Shahadat HosanFaculty, MBA Program
Stamford University, [email protected]
May 13, 2011
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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?
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Why Do Individuals Invest ?
By saving money (instead of spending it), individuals forego consumption today in return for a larger
consumption tomorrow.
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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%
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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 ?
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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)
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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
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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?
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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:
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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
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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 $26.50
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A Portfolio of Investments
The mean historical rate of return for a portfolio of investments is measured as the weighted average of the HPRs for the individual investments in the portfolio, or the overall change in the value of the original portfolio
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Computation of HoldingPeriod Return for a Portfolio
# Begin Beginning Ending Ending Market Wtd.Stock Shares Price Mkt. Value Price Mkt. Value HPR Wt. HPR
A 100,000 10$ 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
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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
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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
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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 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.
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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.
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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.
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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
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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
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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
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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
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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
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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.
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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.
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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?
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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.
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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
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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
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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
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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
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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
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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
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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.
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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
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Thank You