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 10.3 Return Statistics 10.4 Average Stock Returns and RiskFree Returns 10.5 Risk Statistics 10.6 More on Average Returns 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 WalMart (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 WalMart (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:
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 fouryear period: Suppose your investment provides the following returns over a fouryear 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 yearbyyear historical rates of return starting in 1926 for the following five important types of financial instruments in the United States:  Largecompany Common Stocks
 Smallcompany Common Stocks
 Longterm Corporate Bonds
 Longterm 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 riskfree rate) resulting from bearing risk. The Risk Premium is the added return (over and above the riskfree rate) resulting from bearing risk. One of the most significant observations of stock market data is the longrun excess of stock return over the riskfree 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 longterm 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 oneyear Treasury bills is 2%. Suppose that The Wall Street Journal announced that the current rate for oneyear Treasury bills is 2%. What is the expected return on the market of smallcompany stocks? Recall that the average excess return on small company common stocks for the period 1926 through 2007 was 13.3%. Given a riskfree rate of 2%, we have an expected return on the market of smallcompany stocks of 15.3% = 13.3% + 2%
There is no universally agreedupon definition of risk. There is no universally agreedupon 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 bellshaped curve. A large enough sample drawn from a normal distribution looks like a bellshaped 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 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 19262007, the U.S. equity risk premium has been quite large: Over 19262007, 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 510%
 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?
Office: RCOB 18, U. of West Georgia Office Phone and Voicemail: (770)3018648 (cell) or (678)8394816 (office) Class Webpage: Ulearn Email: Ulearn (preferred) or chodges@westga.edu or chodges@gsu.edu Social Networking: Facebook, LinkedIn, and Instant Messenger mba8622@hotmail.com
Dostları ilə paylaş: 