Know how to calculate the return on an investment

Know how to calculate the return on an investment

• Know how to calculate the return on an investment

• Know how to calculate the standard deviation of an investment’s returns

• Understand the historical returns and risks on various types of investments

• Understand the importance of the normal distribution

• Understand the difference between arithmetic and geometric average returns

10.1 Returns

• 10.1 Returns

• 10.2 Holding-Period Returns

• 10.3 Return Statistics

• 10.4 Average Stock Returns and Risk-Free Returns

• 10.5 Risk Statistics

• 10.6 More on Average Returns

• 10.7 The U.S. Equity Risk Premium: Historical and International Perspectives

• 10.8 2008: Year of Financial Crisis

Dollar Returns

• Dollar Returns

• the sum of the cash received and the change in value of the asset, in dollars.

Dollar Return = Dividend + Change in Market Value

• Dollar Return = Dividend + Change in Market Value

Suppose you bought 100 shares of Wal-Mart (WMT) one year ago today at $45. Over the last year, you received $27 in dividends (27 cents per share × 100 shares). At the end of the year, the stock sells for $48. How did you do?

• Suppose you bought 100 shares of Wal-Mart (WMT) one year ago today at $45. Over the last year, you received $27 in dividends (27 cents per share × 100 shares). At the end of the year, the stock sells for $48. How did you do?

• You invested $45 × 100 = $4,500. At the end of the year, you have stock worth $4,800 and cash dividends of $27. Your dollar gain was $327 = $27 + ($4,800 – $4,500).

• Your percentage gain for the year is:

Dollar Return:

• Dollar Return:

• $327 gain

The holding period return is the return that an investor would get when holding an investment over a period of T years, when the return during year i is given as Ri:

• The holding period return is the return that an investor would get when holding an investment over a period of T years, when the return during year i is given as Ri:

Suppose your investment provides the following returns over a four-year period:

• Suppose your investment provides the following returns over a four-year period:

A famous set of studies dealing with rates of returns on common stocks, bonds, and Treasury bills was conducted by Roger Ibbotson and Rex Sinquefield.

• A famous set of studies dealing with rates of returns on common stocks, bonds, and Treasury bills was conducted by Roger Ibbotson and Rex Sinquefield.

• They present year-by-year historical rates of return starting in 1926 for the following five important types of financial instruments in the United States:

• Large-company Common Stocks
• Small-company Common Stocks
• Long-term Corporate Bonds
• Long-term U.S. Government Bonds
• U.S. Treasury Bills

The history of capital market returns can be summarized by describing the:

• The history of capital market returns can be summarized by describing the:

• average return
• the standard deviation of those returns
• the frequency distribution of the returns

The Risk Premium is the added return (over and above the risk-free rate) resulting from bearing risk.

• The Risk Premium is the added return (over and above the risk-free rate) resulting from bearing risk.

• One of the most significant observations of stock market data is the long-run excess of stock return over the risk-free return.

• The average excess return from large company common stocks for the period 1926 through 2007 was:
• 8.5% = 12.3% – 3.8%
• The average excess return from small company common stocks for the period 1926 through 2007 was:
• 13.3% = 17.1% – 3.8%
• The average excess return from long-term corporate bonds for the period 1926 through 2007 was:
• 2.4% = 6.2% – 3.8%

Suppose that The Wall Street Journal announced that the current rate for one-year Treasury bills is 2%.

• Suppose that The Wall Street Journal announced that the current rate for one-year Treasury bills is 2%.

• What is the expected return on the market of small-company stocks?

• Recall that the average excess return on small company common stocks for the period 1926 through 2007 was 13.3%.

• Given a risk-free rate of 2%, we have an expected return on the market of small-company stocks of 15.3% = 13.3% + 2%

There is no universally agreed-upon definition of risk.

• There is no universally agreed-upon definition of risk.

• The measures of risk that we discuss are variance and standard deviation.

• The standard deviation is the standard statistical measure of the spread of a sample, and it will be the measure we use most of this time.
• Its interpretation is facilitated by a discussion of the normal distribution.

A large enough sample drawn from a normal distribution looks like a bell-shaped curve.

• A large enough sample drawn from a normal distribution looks like a bell-shaped curve.

The 20.0% standard deviation we found for large stock returns from 1926 through 2007 can now be interpreted in the following way:

• The 20.0% standard deviation we found for large stock returns from 1926 through 2007 can now be interpreted in the following way:

• If stock returns are approximately normally distributed, the probability that a yearly return will fall within 20.0 percent of the mean of 12.3% will be approximately 2/3.

Arithmetic average – return earned in an average period over multiple periods

• Arithmetic average – return earned in an average period over multiple periods

• Geometric average – average compound return per period over multiple periods

• The geometric average will be less than the arithmetic average unless all the returns are equal.

• Which is better?

• The arithmetic average is overly optimistic for long horizons.
• The geometric average is overly pessimistic for short horizons.

Recall our earlier example:

• Recall our earlier example:

Note that the geometric average is not the same as the arithmetic average:

• Note that the geometric average is not the same as the arithmetic average:

Over 1926-2007, the U.S. equity risk premium has been quite large:

• Over 1926-2007, the U.S. equity risk premium has been quite large:

• Earlier years (beginning in 1802) provide a smaller estimate at 5.4%
• Comparable data for 1900 to 2005 put the international equity risk premium at an average of 7.1%, versus 7.4% in the U.S.

• Going forward, an estimate of 7% seems reasonable, although somewhat higher or lower numbers could also be considered rational

See Table 10.4

• See Table 10.4

• Value of United States Stock is about 45% of world total in 2008
• No other country exceeds 15%

• See Table 10.5

• Since 1922, Historical equity risk premiums are 5-10%
• Ignores “gamblers ruin” and small market issues

Large Stocks (S&P500) lost 37%

• Large Stocks (S&P500) lost 37%

• Drop was global

• Not shown, 2009 started bad (down 25% thru March), but ended up 25% for year.

Which of the investments discussed has had the highest average return and risk premium?

• Which of the investments discussed has had the highest average return and risk premium?

• Which of the investments discussed has had the highest standard deviation?

• Why is the normal distribution informative?

• What is the difference between arithmetic and geometric averages?

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