1. Risk and Return Lessons from Market History
Chapter 10
Risk and Return Lessons from Market History

2. Key Concepts and Skills
Calculate the return on an investment
Compute the standard deviation of an investment’s returns
Explain the connection between historical returns and risks on various types of investments
Describe the importance of the normal distribution and its relationship to investment return
Contextualize the US market risk premium in global terms
Discern the impact on returns of the 2008 financial crisis
Differentiate between arithmetic and geometric average returns

3. How are risk and expected return related?
There are two main reasons to be concerned with this question.
When conducting discounted cash flow analysis, how should we adjust discount rates to allow for riskiness in the cash flow projections?
When saving/investing, what is the tradeoff between taking risks and our expected future wealth?

4. Graphic Representation of Returns
Dollar Returns
the sum of the cash received and the change in value of the asset, in dollars.
Dividends
Ending market value
Time 1
Initial investment
Percentage Returns
the sum of the cash received and the change in value of the asset divided by the initial investment.

5. Formulaic Definition of Returns
Dollar Return = Dividend + Change in Market Value

6. Returns: Example
Suppose you bought 100 shares of Wal-Mart (WMT) one year ago today at $50. Over the last year, you received $100 in dividends ($1 per share × 100 shares). At the end of the year, the stock sells for $60. How did you do?
Quite well. You invested $50 × 100 = $5,000. At the end of the year, you have stock worth $6,000 and cash dividends of $100. Your dollar gain was $1,100 = $ ($6,000 – $5,000).
Your percentage gain for the year is:
1,100/5,000 = 22%

7. Returns: Example $1,100 22% = $5,000 Dollar Return: $1,100 gain $100
$6,000
Time 1
-$5,000
Percentage Return:
22% =
$5,000
$1,100

8. Holding-Period Return: Example
The holding period return is the return that an investor would get when holding an investment over a period of n years, when the return during year i is given as ri:
Suppose your investment provides the following returns over a four-year period:

9. Holding-Period Returns
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

11. Returns and Volatility: A Comparison
Small Company Stocks
U.S. Treasury Bills

12. Return Statistics
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

13. Example Frequency Distribution
Frequency distribution is a histogram of yearly returns

14. Interpretation of the Example Frequency Distribution
In the example above notice that:
Small company stocks have a higher average return but a wider array (or variance) of actual returns
Large company stocks have a lower average return but a more narrow array (or variance) of actual returns.
Conclusion:
In any given observation period, it is more likely that large company stocks will produce a return near the mean than small company stocks.
On average, small company stocks produce a greater return than large company stocks, but also present a much greater likelihood of a loss in any given year

15. Historical Returns,

16. Average Stock Returns and Risk-Free Returns
US Government securities have very low volatility, or risk
US debt is considered risk free because the government can raise taxes to repay it
Consider US Treasury Bills, a discount bond that mature in less than a year
The return of such a security is often considered the “risk-free rate.
The Risk Premium is the added return (over and above the risk-free rate) resulting from bearing risk.

17. The Risk-Return Tradeoff
GENERAL RULE: The more volatile ( or risky) a return is, the greater the return will be expected to be

18. How should we measure 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.

19. Normal Distribution
A large enough sample drawn from a normal distribution looks like a bell-shaped curve.
Probability
The probability that a yearly return will fall within 20.0 percent of the mean of 12.3 percent will be approximately 2/3.
– 3s – 47.7%
– 2s – 27.7%
– 1s – 7.7%
0 12.3%
+ 1s %
+ 2s %
+ 3s %
68.26%
Return on large company common stocks
95.44%
99.74%

20. Normal Distribution
The return of large company stocks has a standard deviation of 20.5 from through 2009.
That standard deviation can be interpreted as follows:
if stock returns are approximately normally distributed, the probability that a yearly return will fall within 20.5% of the mean of 11.8% will be approximately 2/3.

21. The US Equity Risk Premium
The past US stock market risk premium has been substantial
Did US investors earn particularly large returns?
Comparison to international markets is useful:
Greater than 50% of tradable stock is not in the US
17 have an average risk premium of 7.1%
US premium is 7.4%
US Investors did well, but not dramatically better than investors internationally

22. Global Stock Market Risk Premiums

23. Conclusion: US Market Risk Premium
Apparent global MRP mean is 7.1%
Given US 7.4% mean MRP with a 19.6% standard deviation, there is a 95% probability that actual MRP is between 5.5 and 9.3 %
226 financial economists independently estimated MRP at 7%
Conclusion: US MRP estimate of 7% is reasonable barring unforeseen changes in risk environment.

24. 2008: A Year of Financial Crisis
2008 was one of the worst years for stock investors
S&P Index decreased 37%
Of 500 stocks in index 485 were down for the year
The beginning of 2009 was also bad with a 25.1% further S&P decline
From November 2007 through March 9, the S&P lost 56.8% of its value
Things turned around dramatically in the remainder of 2009, with the market gaining about 65%

25. 2008 Crisis: Lessons Learned
Global Phenomenon – No economy unscathed
Some securities performed well:
Treasury Bonds
High Quality Corporate Bonds
“Flight to Quality” Phenomenon
Reminder that stocks have significant risk and can under- as well as over-perform the mean
Argues for careful diversification
Suggests that MRP may be greater than 7% right now

26. Arithmetic vs. Geometric Mean
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.

27. Geometric Return: Example
Recall our earlier example:
So, our investor made an average of 9.58% per year, realizing a holding period return of 44.21%.