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Chapter 7

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Learning Objectives1. Calculate realized and expected rates of return and 

risk.

2. Describe the historical pattern of financial market returns.

3. Compute geometric (or compound) and arithmetic average rates of return.

4. Explain the efficient market hypothesis and why it is important to stock prices.

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Principles Applied in This Chapter Principle 2: There is a Risk‐Return Tradeoff.

Principle 4: Market Prices Reflect Information.

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Calculating the Realized Return from an Investment Realized return or cash return measures

the gain or loss on an investment.

Example: You invested in 1 share of Apple (AAPL) for $95 and sold a year later for $200. The company did not pay any dividend during that period. What will be the cash return on this investment?

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Calculating the Realized Return from an Investment

Suppose you buy a share for $95. It pays no dividend. After 1 year you sell it for $200

Cash Return = $200 + 0 - $95 = $105

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Calculating the Realized Return from an InvestmentPercentage return cash return divided by the beginning stock price.

Rate of Return = ($200 + 0 - $95) ÷ 95= 110.53%

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Calculating Realized Rate of Return

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Calculating the Expected Return from an Investment Expected return is what the investor expects

to earn from an investment in the future.

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Table 7-2 Calculating the Expected Rate of Return for an Investment in Common Stock

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Measuring Risk The variability in returns can be quantified by

computing the Variance or Standard Deviationin investment returns.

The formula for the variance is μ μ … μ The standard deviation is √

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• Expected Return, E(r) = 0.15

• Variance = 0.0165

• Standard Deviation = 0.1285

A Brief History of the Financial Markets Investors have historically earned higher rates of return on riskier investments. However, having a higher expected rate of return simply means that investors “expect” to realize a higher return. Higher return is not guaranteed.

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Listing “Gap” The number of listed firms has fallen 

1996: 8,090 listed firms

2017: 4,336 listed firms

Fewer listed companies, higher aggregate valuation

Fewer companies choosing to go public 

More M&A, more private equity investment

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Historical Rates of Return for U.S. Financial Securities: 1926–2011

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Historical Rates of Return, 1970‐2015

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Stocks, Bonds, Commodities, and Real Estate

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Stocks, Gold and Real Esate

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Figure 7.4Historical Rates of Return in Global Markets: 1970–2011

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Figure 7.5 Investing in Emerging Markets: 1988–2011

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Lessons LearnedLesson #1: The riskier investments have historically realized higher returns.

Lesson #2: The historical returns of the higher-risk investment classes have higher standard deviations.

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Geometric vs. Arithmetic Average Rates of Return “What was the average of the yearly rates of

return?” The arithmetic average rate of return answers

the question “What was the growth rate of your

investment?” The Compound Average Annual Return

(geometric average) answers the question

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1 1 … 1 - 1

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Choosing the Right “Average”Both arithmetic average geometric average are important and correct. The following grid provides some guidance as to which average is appropriate and when:

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Question being addressed:

Appropriate Average Calculation:

What annual rate of return can we expect for next year?

The arithmetic averagerate of return calculated using annual rates of return.

What annual rate of return can we expect over a multi‐year horizon?

The CAAR calculated over a similar past period.

Computing the Geometric Average Rate of ReturnCompute the arithmetic average and CAAR for

the following stock.

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Computing Geometric Average Rate of Return Arithmetic Average= (40+(-50)) ÷ 2 = -5%

CAAR (geometric average)= [(1+R1) × (1+R2)]1/2 - 1= [(1.4) × (1+(-.5))] 1/2 - 1= -16.33%

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Computing Rates of Return What are the arithmetic and geometric rates of return?

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What Determines Stock Prices The value of an asset is the expected present value to the future cash flows.

For stocks, the future cash flows come from

Dividends

Price appreciation

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Efficient Market Hypothesis The efficient market hypothesis (EMH) states

that securities prices accurately reflect future expected cash flows and are based on all information available to investors.

An efficient market is a market in which all the available information is fully incorporated into the prices of the securities and the returns the investors earn on their investments cannot be predicted.

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The Efficient Market Hypothesis1. The weak-form efficient market

hypothesis

2. The semi-strong form efficient market hypothesis

3. The strong-form efficient market hypothesis

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Efficient Market Hypothesis

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Transaction Info

Public Info

Public & Private Info

Efficient Market Hypothesis

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Transaction Info

Public Info

Public & Private Info

Weak Form

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Efficient Market Hypothesis

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Transaction Info

Public Info

Public & Private Info

Weak Form

Semi-Strong Form

Efficient Market Hypothesis

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Transaction Info

Public Info

Public & Private Info

Weak Form

Semi-Strong Form

Strong Form

Do We Expect Financial Markets To Be Perfectly Efficient? In general, markets are expected to be at

least weak-form and semi-strong form efficient.

If there did exist simple profitable strategies, then the strategies would attract the attention of investors, who by implementing their strategies would compete away the profits.

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The Behavioral View Efficient market hypothesis is based on the assumption that investors, as a group, are rational. This view has been challenged.

If investors do not rationally process information, then markets may not accurately reflect even public information. 

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Table 7-4 Summarizing the Evidence of Anomalies to the Efficient Market Hypothesis

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