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Chapter 10

Investment Returns and Aggregate Measures of

Stock Markets

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Measures of Stock Performance

Averages and Indices• Different means to calculate

an average–Price-weighted–Value-weighted–Equal-weighted–Geometric

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A Price-weighted Average

• Price of stock A $10

• Price of stock B $20

• Price-weighted average is ($10 + 20)/$2 = $15

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A Value-weighted Average

• Weights the prices by the number of shares outstanding

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A Value-weighted Average

• If number of shares outstanding of stocks A and B are–A 1,000,000–B 10,000,000

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Total Value of Each Stock

• A $10,000,000

• B $200,000,000

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Weighted Average Price

$210,000,000/(1,000,000 +10,000,000) = $19.09

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An Equal-weighted Average

• Equal dollar amount invested in each stock

• If prices are $10 and $20:– buy two shares of A for every share

of B;– $20 invested in each stock.

• Average price of a share: $40/3 = $13.33

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A Geometric Average

• Instead of dividing, take the 1/n root (the reciprocal of n)

• Average price of a share: (10)(20).5 = $14.14

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Averages and Indices

• Compare prices over time or use one year as a base

• In an index subsequent prices are expressed relative to the base year.

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Differences in Measures

• Different methods for calculating averages

• The selection of a base year

• Can produce different measures of stock performance

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Aggregate Measures of the Stock Market Include:

• Dow Jones industrial average• Standard & Poor's 500 stock

index• NYSE composite index• Value Line Stock average• Nasdaq composite index• Wilshire 5000 index

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Price Movements and Graphs

• How stock prices appear to have changed is affected by the presentation.

• Impact of absolute and relative scales

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Price Movements and Graphs

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Additional Aggregate Measures of the Stock

Market

• Russell 1000• Russell 2000• Russell 3000• S&P 400

MidCap

• S&P 600 SmallCap• S&P 1500• Nasdaq Index• Wilshire 5000

Index

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Aggregate Measures of the Stock Market

• Tend to move together

• Highly correlated

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Stock Prices

• May be deflated to determine investors' increase in purchasing power

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Percentage Change in Real Terms

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The Holding Period Return (HPR)

• The percentage earned on an investment during a period of time

• HPR = P1 + D - P0

P0

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The Holding Period Return

Major weakness :

• Does not consider the length of time

• One year and ten years are the same

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Rate of Return

• Rate that equates–the cost of an investment (cash outflow) with

–the cash inflows generated

• Gives the true annualized (compound) return

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Internal Rate of Return (r)

• Also called the dollar-weighted rate of return

• P0 = D1 + D2 +…+ Dn + Pn

(1+r) (1+r)2 (1+r)n (1+r)n

• Solve for r

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Issues with the Internal Rate of Return

• Assumes cash flows are reinvested at that internal rate of return

• Adjustments are necessary if more than one purchase or sale is made.

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Time-weighted Rate of Return

• An alternative to the internal rate of return

• Ignores the dollar amount invested

• Uses the return for each time period

• Computes the geometric average return

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Investment Returns

• Studies indicate stocks earn 9 to 12 percent annually.

• The Ibbotson results (the industry benchmark)–Large company stocks: 10.2%

–Small company stocks: 12.1%

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Ibbotson Results

• For different time horizons

Common StocksFive-year time horizon: Lowest return -2.4% (1970-1974) Higest return 28.6% (1995-1999)Ten-year time horizon: Lowest return 1.4% (1965-1974) Higest return 20.1% (1949-1958)

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Averaging Strategies

• Dollar cost averaging - the periodic purchase

• Averaging down - buying additional shares after prices fall