Learning Objectives 1. Calculate realized and expected rates of - - PDF document

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Chapter 7

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Learning Objectives

1. 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 = $ 1 0 5

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Calculating the Realized Return from an Investment

Percentage return cash return divided by the beginning stock price. Rate of Return = ($200 + 0 - $95) ÷ 95 = 1 1 0 .5 3 %

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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 Deviation in 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

• f 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 7.4 Historical 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 Learned

Lesson # 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 average rate 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 Return

Compute 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 = -1 6 .3 3 %

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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 m arket hypothesis ( EMH) states that securities prices accurately reflect future expected cash flows and are based on all information available to investors.  An efficient m arket 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 Hypothesis

• 1. The w eak-form efficient m arket

hypothesis

• 2. The sem i-strong form efficient m arket

hypothesis

• 3. The strong-form efficient m arket

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

• f 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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