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**The Investment Setting**

Shahadat Hosan Faculty, MBA Program Stamford University, Bangldesh 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. Tomorrow If 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% $104 $100 Today

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

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.

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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**

1.1 Holding Period Return Where: HPR = Holding period return P0 = Beginning value P1 = Ending value

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**Measures of Historical Rates of Return**

Annualizing the HPR 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: Step #1: Step #2:

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**Measures of Historical Rates of Return**

Arithmetic Mean 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 $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 Holding Period Return for a Portfolio**

This table is in the book on page 11. It is also provided in the Investment Templates spreadsheet in an interactive spreadsheet form.

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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

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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

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**Probability Distributions**

Risky Investment with 3 Possible Returns

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**Probability Distributions**

Risky investment with ten possible rates of return

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**Measuring Risk: Historical Returns**

Where: = Variance (of the pop) HPR = Holding Period Return i E(HPR)i = Expected HPR* N = Number of years * The E(HPR) is equal to the arithmetic mean of the series of returns.

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**Measuring Risk: Expected Rates of Return**

Where: = Variance Ri = Return in period i E(R) = Expected Return Pi = Probability of Ri occurring 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 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**

1.9 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

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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**

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 Between Risk and Return**

(Expected) Rate of Return Beta Risk free Rate Security Market Line (SML) Low Risk Average High Slope of the SML indicates the required return per unit of risk

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

Expected Rate Lower Risk Higher Risk Security Market Line Movements along the SML reflect changes in the market or systematic risk of the asset Risk free Rate Beta

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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**

Note that as the slope of the SML increases, so does the market risk premium Expected Return New SML Rm´ Original SML Rm Risk Free Rate Beta

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**Capital Market Conditions, Expected Inflation, and the SML**

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. Rate of Return New SML Original SML Risk free Rate Risk

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**The Internet Investments Online**

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Thank You

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Chapter 4 Risk and Rates of Return © 2005 Thomson/South-Western.

Chapter 4 Risk and Rates of Return © 2005 Thomson/South-Western.

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