PA 2 Paper - Financial Management

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Ross_12e_PPT_Ch121.pptx

CHAPTER 12

SOME LESSONS FROM CAPITAL MARKET HISTORY

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Calculate the return on an investment

Discuss the historical returns on various types of investments

Discuss the historical risks on various important types of investments

Explain the implications of market efficiency

Key Concepts and Skills

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Returns

The Historical Record

Average Returns: The First Lesson

The Variability of Returns: The Second Lesson

More about Average Returns

Capital Market Efficiency

Chapter Outline

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We can examine returns in the financial markets to help us determine the appropriate returns on non-financial assets.

Lessons from capital market history

There is a reward for bearing risk.

The greater the potential reward, the greater the risk.

Risk, Return, and Financial Markets

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Section 12.1

10.4

Total dollar return =

income from investment

+ capital gain (loss) due to change in price

Example:

You bought a bond for $950 one year ago. You have received two coupons of $30 each. You can sell the bond for $975 today. What is your total dollar return?

Income = 30 + 30 = 60

Capital gain = 975 – 950 = 25

Total dollar return = 60 + 25 = $85

Dollar Returns

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10.5

Section 12.1 (A)

Lecture Tip: The issues discussed in this section need to be stressed. Many students feel that if you don’t sell a security, you won’t have to consider the capital gain or loss involved. (This is a common investor’s mistake – holding a loser too long because of reluctance to admit a bad decision was made.) Point out that non-recognition is relevant for tax purposes – only realized income must be reported. However, whether or not you have liquidated the asset is irrelevant when measuring a security’s pre-tax performance. Also, we need to annualize total returns so that we can compare the performance of different securities available in the market.

It is generally more intuitive to think in terms of percentage rather than dollar returns.

Dividend yield = income / beginning price

Capital gains yield =

(ending price – beginning price)/ beginning price

Total percentage return =

dividend yield + capital gains yield

Percentage Returns

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10.6

Section 12.1 (B)

Note that the “dividend” yield is really just the yield on cash flows received from the security (other than the selling price).

You bought a stock for $35, and you received dividends of $1.25. The stock is now selling for $40.

What is your dollar return?

Dollar return = 1.25 + (40 – 35) = $6.25

What is your percentage return?

Dividend yield = 1.25 / 35 = 3.57%

Capital gains yield = (40 – 35) / 35 = 14.29%

Total percentage return = 3.57 + 14.29 = 17.86%

Example: Calculating Returns

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10.7

Section 12.1 (B)

You might want to point out that total percentage return is also equal to total dollar return / beginning price.

Total percentage return = 6.25 / 35 = 17.86%

Financial markets allow companies, governments and individuals to increase their utility.

Savers have the ability to invest in financial assets so that they can defer consumption and earn a return to compensate them for doing so.

Borrowers have better access to the capital that is available so that they can invest in productive assets.

Financial markets also provide us with information about the returns that are required for various levels of risk.

The Importance of Financial Markets

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Section 12.2

10.8

Figure 12.4

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Section 12.2 (A)

10.9

Large-Company Stock Returns

Long-Term Government Bond Returns

U.S. Treasury Bill Returns

Year-to-Year Total Returns

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10.10

Click on each of the excel icons to see a chart of year-to-year returns similar to the charts in the text.

The charts were created using the data in Table 12.1.

The annual total return for stocks has been quite volatile.

Investment Average Return
Large Stocks 12.0%
Small Stocks 16.6%
Long-term Corporate Bonds 6.3%
Long-term Government Bonds 6.0%
U.S. Treasury Bills 3.4%
Inflation 3.0%

Average Returns

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10.11

A brief review of statistical properties may be in order at this point, particularly as it relates to the normal distribution.

The “extra” return earned for taking on risk

Treasury bills are considered to be risk-free.

The risk premium is the return over and above the risk-free rate.

Risk Premiums

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10.12

Investment Average Return Risk Premium
Large Stocks 12.0% 8.6%
Small Stocks 16.6% 13.2%
Long-term Corporate Bonds 6.3% 2.9%
Long-term Government Bonds 6.0% 2.6%
U.S. Treasury Bills 3.4% 0.0%

Table 12.3: Average Annual Returns and Risk Premiums

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10.13

Ask the students to think about why the different investments have different risk premiums.

Large stocks: 12.0 – 3.4 = 8.6

Small stocks: 16.6 – 3.4 = 13.2

LT Corp. bonds: 6.3 – 3.4 = 2.9

LT Gov’t. bonds: 6.0 – 3.4 = 2.6

Figure 12.9

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Section 12.4 (A)

10.14

Variance and standard deviation measure the volatility of asset returns.

The greater the volatility, the greater the uncertainty.

Historical variance =

sum of squared deviations from

the mean / (number of observations – 1)

Standard deviation =

square root of the variance

Variance and Standard Deviation

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10.15

Lecture Tip: Occasionally, students ask why we include the above-mean returns in measuring dispersion, since these are desirable from the investor’s viewpoint. This question provides a natural springboard for a discussion of alternative variability measures. Here we discuss semivariance as an alternative to variance.

In Portfolio Selection (1959), Harry Markowitz states:

“Analyses based on [semivariance] tend to produce better portfolios than those based on [variance]. Variance considers extremely high and extremely low returns equally undesirable. An analysis based on [variance] seeks to eliminate extremes. An analysis based on [semivariance] on the other hand, concentrates on reducing losses.”

Semivariance is computed in a manner similar to the traditional variance, except that if the deviation is positive, its value is replaced by zero. We still tend to use variance instead of semivariance because semivariance tends to complicate the risk-return issue, and besides, if returns are symmetrically distributed, then variance is two times semivariance.

Year Actual Return Average Return Deviation from the Mean Squared Deviation
1 .15 .105 .045 .002025
2 .09 .105 -.015 .000225
3 .06 .105 -.045 .002025
4 .12 .105 .015 .000225
Totals .42 .00 .0045

Example: Variance and Standard Deviation

Variance = .0045 / (4-1) = .0015 Standard Deviation = .03873

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10.16

Remind students that the variance for a sample is computed by dividing the sum of the squared deviations by the number of observations – 1.

The standard deviation is just the square root.

Lecture Tip: It is sometimes difficult to get students to appreciate the risk involved in investing in common stocks. They see the large average returns and miss the variance. A simple exercise illustrating the risk of the different securities can be performed using Table 12.1. Each student (or the entire class) is given an initial investment. They are then allowed to choose a security class. Use a random number generator and the last two digits of the year to sample the distribution. The initial investment is then increased or decreased based on the return. This works best if the trials are limited to between one and five.

How volatile are mutual funds?

Morningstar provides information on mutual funds, including volatility.

Go to the Morningstar site.

Pick a fund, such as the American Funds EuroPacific Growth Fund (AEPGX).

Enter the ticker, press go, and then click “Ratings & Risk”.

Work the Web Example

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Section 12.4 (B)

10.17

Figure 12.10

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Section 12.4 (C)

10.18

The normal distribution is a symmetric, bell-shaped frequency distribution.

It is completely defined by its mean and standard deviation.

As seen in Figure 12.10, the returns appear to be at least roughly normally distributed.

Normal distribution

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Section 12.4 (D)

10.19

Figure 12.11

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10.20

2008 was one of the worst years for stock market investors in history.

The S&P 500 plunged 37 percent.

The index lost 17 percent in October alone.

From March ‘09 to Feb ‘11, the S&P 500 doubled in value.

Long-term Treasury bonds gained over 40 percent in 2008.

They lost almost 26 percent in 2009.

Recent market volatility

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Two lessons for investors from this recent volatility:

Stocks have significant risk

Diversification matters

10.21

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.

So, the answer depends on the planning period under consideration.

15 – 20 years or less: use the arithmetic

20 – 40 years or so: split the difference between them

40 + years: use the geometric

Arithmetic vs. Geometric Mean

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10.22

The calculation of an appropriate average can be extended using Blume’s formula as described in the text.

What is the arithmetic and geometric average for the following returns?

Year 1 5%

Year 2 -3%

Year 3 12%

Arithmetic average = (5 + (–3) + 12)/3 = 4.67%

Geometric average = [(1+.05) × (1-.03) × (1+.12)]1/3 – 1 = .0449 = 4.49%

Example: Computing Averages

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Section 12.5 (B)

10.23

Stock prices are in equilibrium or are “fairly” priced.

If this is true, then you should not be able to earn “abnormal” or “excess” returns.

Efficient markets DO NOT imply that investors cannot earn a positive return in the stock market.

Efficient Capital Markets

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10.24

Consider asking the students if market efficiency has increased over time.

Figure 12.14

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Section 12.6 (A)

10.25

There are many investors out there doing research.

As new information comes to market, this information is analyzed and trades are made based on this information.

Therefore, prices should reflect all available public information.

If investors stop researching stocks, then the market will not be efficient.

What Makes Markets Efficient?

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10.26

Point out that one consequence of the wider availability of information and lower transaction costs is that the market will be more volatile. It is easier to trade on “small” news instead of just big events.

It is also important to remember that not all available information is reliable information. It’s important to still do the research and not just jump on everything that crosses the news wire. The case of Emulex, discussed earlier, is an excellent example.

Daniel Tully, Chairman Emeritus of Merrill Lynch: “I’m not smart enough to know the top or the bottom of a market.”

Efficient markets do not mean that you can’t make money.

They do mean that, on average, you will earn a return that is appropriate for the risk undertaken and there is not a bias in prices that can be exploited to earn excess returns.

Market efficiency will not protect you from wrong choices if you do not diversify – you still don’t want to “put all your eggs in one basket.”

Common Misconceptions about EMH

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10.27

Lecture tip: Claims of superior performance in stock picking are very common and often hard to verify. However, if markets are semistrong form efficient, the ability to consistently earn excess returns is unlikely.

Lecture Tip: Even the experts get confused about the meaning of capital market efficiency. Consider the following quote from a column in Forbes magazine: “Popular delusion three: Markets are efficient. The efficient market [sic] hypothesis, or EMH, would do credit to medieval alchemists and is about as scientific as their efforts to turn base metals into gold.” The writer is definitely not a proponent of EMH. Now consider this quote: “The truth is nobody can consistently predict the ups and downs of the market.” This statement is clearly consistent with the EMH. Ironically, the same person wrote both statements in the same column with exactly nine lines of type separating them.

Prices reflect all information, including public and private.

If the market is strong form efficient, then investors could not earn abnormal returns regardless of the information they possessed.

Empirical evidence indicates that markets are NOT strong form efficient and that insiders could earn abnormal returns.

Strong Form Efficiency

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10.28

Students are often very interested in insider trading. The case of Martha Stewart is one with which most students tend to be familiar.

Prices reflect all publicly available information including trading information, annual reports, press releases, etc.

If the market is semistrong form efficient, then investors cannot earn abnormal returns by trading on public information.

Implies that fundamental analysis will not lead to abnormal returns

Semistrong Form Efficiency

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10.29

Empirical evidence suggests that some stocks are semistrong form efficient, but not all. Larger, more closely followed stocks are more likely to be semistrong form efficient. Small, more thinly traded stocks may not be semistrong form efficient, but liquidity costs may wipe out any abnormal returns that are available.

Prices reflect all past market information such as price and volume.

If the market is weak form efficient, then investors cannot earn abnormal returns by trading on market information.

Implies that technical analysis will not lead to abnormal returns

Empirical evidence indicates that markets are generally weak form efficient.

Weak Form Efficiency

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10.30

Emphasize that just because technical analysis shouldn’t lead to abnormal returns, that doesn’t mean that you won’t earn fair returns using it – efficient markets imply that you will.

You might also want to point out that there are many technical trading rules that have never been empirically tested; so it is possible that one of them might lead to abnormal returns. But if it is well publicized, then any abnormal returns that were available will soon evaporate.

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?

What is capital market efficiency?

What are the three forms of market efficiency?

Quick Quiz

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Section 12.7

10.31

Program trading is defined as automated trading generated by computer algorithms designed to react rapidly to changes in market prices. Is it ethical for investment banking houses to operate such systems when they may generate trade activity ahead of their brokerage customers, to which they owe a fiduciary duty?

Suppose that you are an employee of a printing firm that was hired to proofread proxies that contained unannounced tender offers (and unnamed targets). Should you trade on this information, and would it be considered illegal?

Ethics Issues

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10.32

Case 2: The court decided in Chiarella v. United States that an employee of a printing firm, who was requested to proofread proxies that contained unannounced tender offers (and unnamed targets) was not guilty of insider trading because the employee determined the identity of the target through his own expertise.

Your stock investments return 8%, 12%, and -4% in consecutive years. What is the geometric return?

What is the sample standard deviation of the above returns?

Using the standard deviation and mean that you just calculated, and assuming a normal probability distribution, what is the probability of losing 3% or more?

Comprehensive Problem

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10.33

Section 12.7

(1.08 × 1.12 × .96)^.3333 – 1 = .0511

Mean = ( .08 + .12 + -.04) / 3 = .0533

Variance = (.08 - .0533)^2 + (.12 - .0533)^2 = (-.04 - .0533)^2 / (3 - 1)= .00693

Standard deviation = .00693 ^ .5 = .0833

Probability: a 3% loss (return of -3%) lies one standard deviation below the mean. There is 16% of the probability falling below that point (68% falls between -3% and 13.66%, so 16% lies below -3% and 16% lies above 13.66%).

End of Chapter

Chapter 12

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Large Companies

Long-Term Government Bonds

U.S. Treasury Bills

Large Company

1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
Year
Total Return
Large Company Stocks
0.1375
0.357
0.4508
-0.088
-0.2513
-0.436
-0.0875
0.5295
-0.0231
0.4679
0.3249
-0.3545
0.3163
-0.0143
-0.1036
-0.1202
0.2075
0.2538
0.1949
0.3621
-0.0842
0.0505
0.0499
0.1781
0.3005
0.2379
0.1839
-0.0107
0.5223
0.3162
0.0691
-0.105
0.4357
0.1201
0.0047
0.2684
-0.0875
0.227
0.1643
0.1238
-0.1006
0.2398
0.1103
-0.0843
0.0394
0.143
0.1899
-0.1469
-0.2647
0.3723
0.2393
-0.0716
0.0657
0.1861
0.325
-0.0492
0.2155
0.2256
0.0627
0.3173
0.1867
0.0525
0.1661
0.3169
-0.031
0.3046
0.0762
0.1008
0.0132
0.3758
0.2296
0.3336
0.2858
0.2104
-0.091
-0.1189
-0.221
0.2889
0.1088
0.0491
0.1579
0.0549
-0.37
0.2646
0.1506
0.0211
0.16
0.3239
0.1369
0.0141
0.1198

Long-Term Bonds

1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
Long-Term Government Bonds
Year
Total Return
0.0569
0.0658
0.0115
0.0439
0.0447
-0.0215
0.0851
0.0192
0.0759
0.042
0.0513
0.0144
0.0421
0.0384
0.057
0.0047
0.018
0.0201
0.0227
0.0529
0.0054
-0.0102
0.0266
0.0458
-0.0098
-0.002
0.0243
0.0228
0.0308
-0.0073
-0.0172
0.0682
-0.0172
-0.0202
0.1121
0.022
0.0572
0.0179
0.0371
0.0093
0.0512
-0.0286
0.0225
-0.0563
0.1892
0.1124
0.0239
0.033
0.04
0.0552
0.1556
0.0038
-0.0126
0.0126
-0.0248
0.0404
0.4428
0.0129
0.1529
0.3227
0.2239
-0.0303
0.0684
0.1854
0.0774
0.1936
0.0734
0.1306
-0.0732
0.2594
0.0013
0.1202
0.1445
-0.0751
0.1722
0.0551
0.1515
0.0201
0.0812
0.0689
0.0028
0.1085
0.4178
-0.2561
0.0773
0.3575
0.018
-0.1469
0.2474
-0.0064
0.0176

T-bills

1926
1927
1928
0.0447
0.0227
0.0115
0.0088
0.0052
0.0027
0.0017
0.0017
0.0027
0.0006
0.0004
0.0004
0.0014
0.0034
0.0038
0.0038
0.0038
0.0038
0.0062
0.0106
0.0112
0.0122
0.0156
0.0175
0.0187
0.0093
0.018
0.0266
0.0328
0.0171
0.0348
0.0281
0.024
0.0282
0.0323
0.0362
0.0406
0.0494
0.0439
0.0549
0.069
0.065
0.0436
0.0423
0.0729
0.0799
0.0587
0.0507
0.0545
0.0764
0.1056
0.121
0.146
0.1094
0.0899
0.099
0.0771
0.0609
0.0588
0.0694
0.0844
0.0769
0.0543
0.0348
0.0303
0.0439
0.0561
0.0514
0.0519
0.0486
0.048
0.0598
0.0333
0.0161
0.0094
0.0114
0.0279
0.0497
0.0452
0.0124
0.0015
0.0014
0.0006
0.0008
0.0005
0.0003
0.0004
0.0021
T-Bills
Year
Total Return
0.033
0.0315
0.0405

Sheet1

Year Large-Company Stocks Long-Term Government Bonds U.S. Treasury Bills Consumer Price Index
1926 0.1375 0.0569 0.033 -0.0112
1927 0.357 0.0658 0.0315 -0.0226
1928 0.4508 0.0115 0.0405 -0.0116
1929 -0.088 0.0439 0.0447 0.0058
1930 -0.2513 0.0447 0.0227 -0.064
1931 -0.436 -0.0215 0.0115 -0.0932
1932 -0.0875 0.0851 0.0088 -0.1027
1933 0.5295 0.0192 0.0052 0.0076
1934 -0.0231 0.0759 0.0027 0.0152
1935 0.4679 0.042 0.0017 0.0299
1936 0.3249 0.0513 0.0017 0.0145
1937 -0.3545 0.0144 0.0027 0.0286
1938 0.3163 0.0421 0.0006 -0.0278
1939 -0.0143 0.0384 0.0004 0
1940 -0.1036 0.057 0.0004 0.0071
1941 -0.1202 0.0047 0.0014 0.0993
1942 0.2075 0.018 0.0034 0.0903
1943 0.2538 0.0201 0.0038 0.0296
1944 0.1949 0.0227 0.0038 0.023
1945 0.3621 0.0529 0.0038 0.0225
1946 -0.0842 0.0054 0.0038 0.1813
1947 0.0505 -0.0102 0.0062 0.0884
1948 0.0499 0.0266 0.0106 0.0299
1949 0.1781 0.0458 0.0112 -0.0207
1950 0.3005 -0.0098 0.0122 0.0593
1951 0.2379 -0.002 0.0156 0.06
1952 0.1839 0.0243 0.0175 0.0075
1953 -0.0107 0.0228 0.0187 0.0074
1954 0.5223 0.0308 0.0093 -0.0074
1955 0.3162 -0.0073 0.018 0.0037
1956 0.0691 -0.0172 0.0266 0.0299
1957 -0.105 0.0682 0.0328 0.029
1958 0.4357 -0.0172 0.0171 0.0176
1959 0.1201 -0.0202 0.0348 0.0173
1960 0.0047 0.1121 0.0281 0.0136
1961 0.2684 0.022 0.024 0.0067
1962 -0.0875 0.0572 0.0282 0.0133
1963 0.227 0.0179 0.0323 0.0164
1964 0.1643 0.0371 0.0362 0.0097
1965 0.1238 0.0093 0.0406 0.0192
1966 -0.1006 0.0512 0.0494 0.0346
1967 0.2398 -0.0286 0.0439 0.0304
1968 0.1103 0.0225 0.0549 0.0472
1969 -0.0843 -0.0563 0.069 0.062
1970 0.0394 0.1892 0.065 0.0557
1971 0.143 0.1124 0.0436 0.0327
1972 0.1899 0.0239 0.0423 0.0341
1973 -0.1469 0.033 0.0729 0.0871
1974 -0.2647 0.04 0.0799 0.1234
1975 0.3723 0.0552 0.0587 0.0694
1976 0.2393 0.1556 0.0507 0.0486
1977 -0.0716 0.0038 0.0545 0.067
1978 0.0657 -0.0126 0.0764 0.0902
1979 0.1861 0.0126 0.1056 0.1329
1980 0.325 -0.0248 0.121 0.1252
1981 -0.0492 0.0404 0.146 0.0892
1982 0.2155 0.4428 0.1094 0.0383
1983 0.2256 0.0129 0.0899 0.0379
1984 0.0627 0.1529 0.099 0.0395
1985 0.3173 0.3227 0.0771 0.038
1986 0.1867 0.2239 0.0609 0.011
1987 0.0525 -0.0303 0.0588 0.0443
1988 0.1661 0.0684 0.0694 0.0442
1989 0.3169 0.1854 0.0844 0.0465
1990 -0.031 0.0774 0.0769 0.0611
1991 0.3046 0.1936 0.0543 0.0306
1992 0.0762 0.0734 0.0348 0.029
1993 0.1008 0.1306 0.0303 0.0275
1994 0.0132 -0.0732 0.0439 0.0267
1995 0.3758 0.2594 0.0561 0.0254
1996 0.2296 0.0013 0.0514 0.0332
1997 0.3336 0.1202 0.0519 0.017
1998 0.2858 0.1445 0.0486 0.0161
1999 0.2104 -0.0751 0.048 0.0268
2000 -0.091 0.1722 0.0598 0.0339
2001 -0.1189 0.0551 0.0333 0.0155
2002 -0.221 0.1515 0.0161 0.024
2003 0.2889 0.0201 0.0094 0.019
2004 0.1088 0.0812 0.0114 0.033
2005 0.0491 0.0689 0.0279 0.034
2006 0.1579 0.0028 0.0497 0.0254
2007 0.0549 0.1085 0.0452 0.0408
2008 -0.37 0.4178 0.0124 0.0009
2009 0.2646 -0.2561 0.0015 0.0272
2010 0.1506 0.0773 0.0014 0.015
2011 0.0211 0.3575 0.0006 0.0296
2012 0.16 0.018 0.0008 0.0174
2013 0.3239 -0.1469 0.0005 0.015
2014 0.1369 0.2474 0.0003 0.0075
2015 0.0141 -0.0064 0.0004 0.0074
2016 0.1198 0.0176 0.0021 0.0211
0.117628 0.057509 0.037589 0.030752

Sheet2

Sheet3

Large Company

1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
Large-Company Stocks
Year
Total Return
Large Company Stocks
0.1375
0.357
0.4508
-0.088
-0.2513
-0.436
-0.0875
0.5295
-0.0231
0.4679
0.3249
-0.3545
0.3163
-0.0143
-0.1036
-0.1202
0.2075
0.2538
0.1949
0.3621
-0.0842
0.0505
0.0499
0.1781
0.3005
0.2379
0.1839
-0.0107
0.5223
0.3162
0.0691
-0.105
0.4357
0.1201
0.0047
0.2684
-0.0875
0.227
0.1643
0.1238
-0.1006
0.2398
0.1103
-0.0843
0.0394
0.143
0.1899
-0.1469
-0.2647
0.3723
0.2393
-0.0716
0.0657
0.1861
0.325
-0.0492
0.2155
0.2256
0.0627
0.3173
0.1867
0.0525
0.1661
0.3169
-0.031
0.3046
0.0762
0.1008
0.0132
0.3758
0.2296
0.3336
0.2858
0.2104

Long-Term Bonds

1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
Long-term Government Bonds
Year
Total Return
0.0569
0.0658
0.0115
0.0439
0.0447
-0.0215
0.0851
0.0192
0.0759
0.042
0.0513
0.0144
0.0421
0.0384
0.057
0.0047
0.018
0.0201
0.0227
0.0529
0.0054
-0.0102
0.0266
0.0458
-0.0098
-0.002
0.0243
0.0228
0.0308
-0.0073
-0.0172
0.0682
-0.0172
-0.0202
0.1121
0.022
0.0572
0.0179
0.0371
0.0093
0.0512
-0.0286
0.0225
-0.0563
0.1892
0.1124
0.0239
0.033
0.04
0.0552
0.1556
0.0038
-0.0126
0.0126
-0.0248
0.0404
0.4428
0.0129
0.1529
0.3227
0.2239
-0.0303
0.0684
0.1854
0.0774
0.1936
0.0734
0.1306
-0.0732
0.2594
0.0013
0.1202
0.1445
-0.0751
0.1722
0.0551
0.1515
0.0201
0.0812
0.0689
0.0028
0.1085
0.4178
-0.2561
0.0773
0.3575
0.018
-0.1469
0.2474
-0.0064
0.0176

T-bills

1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
U.S. Treasury Bills
Year
Total Return
0.033
0.0315
0.0405
0.0447
0.0227
0.0115
0.0088
0.0052
0.0027
0.0017
0.0017
0.0027
0.0006
0.0004
0.0004
0.0014
0.0034
0.0038
0.0038
0.0038
0.0038
0.0062
0.0106
0.0112
0.0122
0.0156
0.0175
0.0187
0.0093
0.018
0.0266
0.0328
0.0171
0.0348
0.0281
0.024
0.0282
0.0323
0.0362
0.0406
0.0494
0.0439
0.0549
0.069
0.065
0.0436
0.0423
0.0729
0.0799
0.0587
0.0507
0.0545
0.0764
0.1056
0.121
0.146
0.1094
0.0899
0.099
0.0771
0.0609
0.0588
0.0694
0.0844
0.0769
0.0543
0.0348
0.0303
0.0439
0.0561
0.0514
0.0519
0.0486
0.048

Sheet1

Year Large-Company Stocks Long-Term Government Bonds U.S. Treasury Bills Consumer Price Index
1926 0.1375 0.0569 0.033 -0.0112
1927 0.357 0.0658 0.0315 -0.0226
1928 0.4508 0.0115 0.0405 -0.0116
1929 -0.088 0.0439 0.0447 0.0058
1930 -0.2513 0.0447 0.0227 -0.064
1931 -0.436 -0.0215 0.0115 -0.0932
1932 -0.0875 0.0851 0.0088 -0.1027
1933 0.5295 0.0192 0.0052 0.0076
1934 -0.0231 0.0759 0.0027 0.0152
1935 0.4679 0.042 0.0017 0.0299
1936 0.3249 0.0513 0.0017 0.0145
1937 -0.3545 0.0144 0.0027 0.0286
1938 0.3163 0.0421 0.0006 -0.0278
1939 -0.0143 0.0384 0.0004 0
1940 -0.1036 0.057 0.0004 0.0071
1941 -0.1202 0.0047 0.0014 0.0993
1942 0.2075 0.018 0.0034 0.0903
1943 0.2538 0.0201 0.0038 0.0296
1944 0.1949 0.0227 0.0038 0.023
1945 0.3621 0.0529 0.0038 0.0225
1946 -0.0842 0.0054 0.0038 0.1813
1947 0.0505 -0.0102 0.0062 0.0884
1948 0.0499 0.0266 0.0106 0.0299
1949 0.1781 0.0458 0.0112 -0.0207
1950 0.3005 -0.0098 0.0122 0.0593
1951 0.2379 -0.002 0.0156 0.06
1952 0.1839 0.0243 0.0175 0.0075
1953 -0.0107 0.0228 0.0187 0.0074
1954 0.5223 0.0308 0.0093 -0.0074
1955 0.3162 -0.0073 0.018 0.0037
1956 0.0691 -0.0172 0.0266 0.0299
1957 -0.105 0.0682 0.0328 0.029
1958 0.4357 -0.0172 0.0171 0.0176
1959 0.1201 -0.0202 0.0348 0.0173
1960 0.0047 0.1121 0.0281 0.0136
1961 0.2684 0.022 0.024 0.0067
1962 -0.0875 0.0572 0.0282 0.0133
1963 0.227 0.0179 0.0323 0.0164
1964 0.1643 0.0371 0.0362 0.0097
1965 0.1238 0.0093 0.0406 0.0192
1966 -0.1006 0.0512 0.0494 0.0346
1967 0.2398 -0.0286 0.0439 0.0304
1968 0.1103 0.0225 0.0549 0.0472
1969 -0.0843 -0.0563 0.069 0.062
1970 0.0394 0.1892 0.065 0.0557
1971 0.143 0.1124 0.0436 0.0327
1972 0.1899 0.0239 0.0423 0.0341
1973 -0.1469 0.033 0.0729 0.0871
1974 -0.2647 0.04 0.0799 0.1234
1975 0.3723 0.0552 0.0587 0.0694
1976 0.2393 0.1556 0.0507 0.0486
1977 -0.0716 0.0038 0.0545 0.067
1978 0.0657 -0.0126 0.0764 0.0902
1979 0.1861 0.0126 0.1056 0.1329
1980 0.325 -0.0248 0.121 0.1252
1981 -0.0492 0.0404 0.146 0.0892
1982 0.2155 0.4428 0.1094 0.0383
1983 0.2256 0.0129 0.0899 0.0379
1984 0.0627 0.1529 0.099 0.0395
1985 0.3173 0.3227 0.0771 0.038
1986 0.1867 0.2239 0.0609 0.011
1987 0.0525 -0.0303 0.0588 0.0443
1988 0.1661 0.0684 0.0694 0.0442
1989 0.3169 0.1854 0.0844 0.0465
1990 -0.031 0.0774 0.0769 0.0611
1991 0.3046 0.1936 0.0543 0.0306
1992 0.0762 0.0734 0.0348 0.029
1993 0.1008 0.1306 0.0303 0.0275
1994 0.0132 -0.0732 0.0439 0.0267
1995 0.3758 0.2594 0.0561 0.0254
1996 0.2296 0.0013 0.0514 0.0332
1997 0.3336 0.1202 0.0519 0.017
1998 0.2858 0.1445 0.0486 0.0161
1999 0.2104 -0.0751 0.048 0.0268
2000 -0.091 0.1722 0.0598 0.0339
2001 -0.1189 0.0551 0.0333 0.0155
2002 -0.221 0.1515 0.0161 0.024
2003 0.2889 0.0201 0.0094 0.019
2004 0.1088 0.0812 0.0114 0.033
2005 0.0491 0.0689 0.0279 0.034
2006 0.1579 0.0028 0.0497 0.0254
2007 0.0549 0.1085 0.0452 0.0408
2008 -0.37 0.4178 0.0124 0.0009
2009 0.2646 -0.2561 0.0015 0.0272
2010 0.1506 0.0773 0.0014 0.015
2011 0.0211 0.3575 0.0006 0.0296
2012 0.16 0.018 0.0008 0.0174
2013 0.3239 -0.1469 0.0005 0.015
2014 0.1369 0.2474 0.0003 0.0075
2015 0.0141 -0.0064 0.0004 0.0074
2016 0.1198 0.0176 0.0021 0.0211
0.117628 0.057509 0.037589 0.030752

Sheet2

Sheet3

Large Company

1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
Large-Company Stocks
Year
Total Return
Large Company Stocks
0.1375
0.357
0.4508
-0.088
-0.2513
-0.436
-0.0875
0.5295
-0.0231
0.4679
0.3249
-0.3545
0.3163
-0.0143
-0.1036
-0.1202
0.2075
0.2538
0.1949
0.3621
-0.0842
0.0505
0.0499
0.1781
0.3005
0.2379
0.1839
-0.0107
0.5223
0.3162
0.0691
-0.105
0.4357
0.1201
0.0047
0.2684
-0.0875
0.227
0.1643
0.1238
-0.1006
0.2398
0.1103
-0.0843
0.0394
0.143
0.1899
-0.1469
-0.2647
0.3723
0.2393
-0.0716
0.0657
0.1861
0.325
-0.0492
0.2155
0.2256
0.0627
0.3173
0.1867
0.0525
0.1661
0.3169
-0.031
0.3046
0.0762
0.1008
0.0132
0.3758
0.2296
0.3336
0.2858
0.2104

Long-Term Bonds

1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
Long-Term Government Bonds
Year
Total Return
0.0569
0.0658
0.0115
0.0439
0.0447
-0.0215
0.0851
0.0192
0.0759
0.042
0.0513
0.0144
0.0421
0.0384
0.057
0.0047
0.018
0.0201
0.0227
0.0529
0.0054
-0.0102
0.0266
0.0458
-0.0098
-0.002
0.0243
0.0228
0.0308
-0.0073
-0.0172
0.0682
-0.0172
-0.0202
0.1121
0.022
0.0572
0.0179
0.0371
0.0093
0.0512
-0.0286
0.0225
-0.0563
0.1892
0.1124
0.0239
0.033
0.04
0.0552
0.1556
0.0038
-0.0126
0.0126
-0.0248
0.0404
0.4428
0.0129
0.1529
0.3227
0.2239
-0.0303
0.0684
0.1854
0.0774
0.1936
0.0734
0.1306
-0.0732
0.2594
0.0013
0.1202
0.1445
-0.0751

T-bills

1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
Treasury Bills
Year
Total Return
0.033
0.0315
0.0405
0.0447
0.0227
0.0115
0.0088
0.0052
0.0027
0.0017
0.0017
0.0027
0.0006
0.0004
0.0004
0.0014
0.0034
0.0038
0.0038
0.0038
0.0038
0.0062
0.0106
0.0112
0.0122
0.0156
0.0175
0.0187
0.0093
0.018
0.0266
0.0328
0.0171
0.0348
0.0281
0.024
0.0282
0.0323
0.0362
0.0406
0.0494
0.0439
0.0549
0.069
0.065
0.0436
0.0423
0.0729
0.0799
0.0587
0.0507
0.0545
0.0764
0.1056
0.121
0.146
0.1094
0.0899
0.099
0.0771
0.0609
0.0588
0.0694
0.0844
0.0769
0.0543
0.0348
0.0303
0.0439
0.0561
0.0514
0.0519
0.0486
0.048
0.0598
0.0333
0.0161
0.0094
0.0114
0.0279
0.0497
0.0452
0.0124
0.0015
0.0014
0.0006
0.0008
0.0005
0.0003
0.0004
0.0021

Sheet1

Year Large-Company Stocks Long-Term Government Bonds U.S. Treasury Bills Consumer Price Index
1926 0.1375 0.0569 0.033 -0.0112
1927 0.357 0.0658 0.0315 -0.0226
1928 0.4508 0.0115 0.0405 -0.0116
1929 -0.088 0.0439 0.0447 0.0058
1930 -0.2513 0.0447 0.0227 -0.064
1931 -0.436 -0.0215 0.0115 -0.0932
1932 -0.0875 0.0851 0.0088 -0.1027
1933 0.5295 0.0192 0.0052 0.0076
1934 -0.0231 0.0759 0.0027 0.0152
1935 0.4679 0.042 0.0017 0.0299
1936 0.3249 0.0513 0.0017 0.0145
1937 -0.3545 0.0144 0.0027 0.0286
1938 0.3163 0.0421 0.0006 -0.0278
1939 -0.0143 0.0384 0.0004 0
1940 -0.1036 0.057 0.0004 0.0071
1941 -0.1202 0.0047 0.0014 0.0993
1942 0.2075 0.018 0.0034 0.0903
1943 0.2538 0.0201 0.0038 0.0296
1944 0.1949 0.0227 0.0038 0.023
1945 0.3621 0.0529 0.0038 0.0225
1946 -0.0842 0.0054 0.0038 0.1813
1947 0.0505 -0.0102 0.0062 0.0884
1948 0.0499 0.0266 0.0106 0.0299
1949 0.1781 0.0458 0.0112 -0.0207
1950 0.3005 -0.0098 0.0122 0.0593
1951 0.2379 -0.002 0.0156 0.06
1952 0.1839 0.0243 0.0175 0.0075
1953 -0.0107 0.0228 0.0187 0.0074
1954 0.5223 0.0308 0.0093 -0.0074
1955 0.3162 -0.0073 0.018 0.0037
1956 0.0691 -0.0172 0.0266 0.0299
1957 -0.105 0.0682 0.0328 0.029
1958 0.4357 -0.0172 0.0171 0.0176
1959 0.1201 -0.0202 0.0348 0.0173
1960 0.0047 0.1121 0.0281 0.0136
1961 0.2684 0.022 0.024 0.0067
1962 -0.0875 0.0572 0.0282 0.0133
1963 0.227 0.0179 0.0323 0.0164
1964 0.1643 0.0371 0.0362 0.0097
1965 0.1238 0.0093 0.0406 0.0192
1966 -0.1006 0.0512 0.0494 0.0346
1967 0.2398 -0.0286 0.0439 0.0304
1968 0.1103 0.0225 0.0549 0.0472
1969 -0.0843 -0.0563 0.069 0.062
1970 0.0394 0.1892 0.065 0.0557
1971 0.143 0.1124 0.0436 0.0327
1972 0.1899 0.0239 0.0423 0.0341
1973 -0.1469 0.033 0.0729 0.0871
1974 -0.2647 0.04 0.0799 0.1234
1975 0.3723 0.0552 0.0587 0.0694
1976 0.2393 0.1556 0.0507 0.0486
1977 -0.0716 0.0038 0.0545 0.067
1978 0.0657 -0.0126 0.0764 0.0902
1979 0.1861 0.0126 0.1056 0.1329
1980 0.325 -0.0248 0.121 0.1252
1981 -0.0492 0.0404 0.146 0.0892
1982 0.2155 0.4428 0.1094 0.0383
1983 0.2256 0.0129 0.0899 0.0379
1984 0.0627 0.1529 0.099 0.0395
1985 0.3173 0.3227 0.0771 0.038
1986 0.1867 0.2239 0.0609 0.011
1987 0.0525 -0.0303 0.0588 0.0443
1988 0.1661 0.0684 0.0694 0.0442
1989 0.3169 0.1854 0.0844 0.0465
1990 -0.031 0.0774 0.0769 0.0611
1991 0.3046 0.1936 0.0543 0.0306
1992 0.0762 0.0734 0.0348 0.029
1993 0.1008 0.1306 0.0303 0.0275
1994 0.0132 -0.0732 0.0439 0.0267
1995 0.3758 0.2594 0.0561 0.0254
1996 0.2296 0.0013 0.0514 0.0332
1997 0.3336 0.1202 0.0519 0.017
1998 0.2858 0.1445 0.0486 0.0161
1999 0.2104 -0.0751 0.048 0.0268
2000 -0.091 0.1722 0.0598 0.0339
2001 -0.1189 0.0551 0.0333 0.0155
2002 -0.221 0.1515 0.0161 0.024
2003 0.2889 0.0201 0.0094 0.019
2004 0.1088 0.0812 0.0114 0.033
2005 0.0491 0.0689 0.0279 0.034
2006 0.1579 0.0028 0.0497 0.0254
2007 0.0549 0.1085 0.0452 0.0408
2008 -0.37 0.4178 0.0124 0.0009
2009 0.2646 -0.2561 0.0015 0.0272
2010 0.1506 0.0773 0.0014 0.015
2011 0.0211 0.3575 0.0006 0.0296
2012 0.16 0.018 0.0008 0.0174
2013 0.3239 -0.1469 0.0005 0.015
2014 0.1369 0.2474 0.0003 0.0075
2015 0.0141 -0.0064 0.0004 0.0074
2016 0.1198 0.0176 0.0021 0.0211
0.117628 0.057509 0.037589 0.030752

Sheet2

Sheet3