Are Stocks Really Riskier than Bonds?

Chulho JungWilliam Shambora*Kyongwook Choi

Department of EconomicsOhio University

Bentley Hall AnnexAthens, Ohio 45701

U. S. A.

September 17, 2005

Key words: Coefficient of Variation, Risk, Irrational Behavior, GARCHJEL codes: A22, E44, I22

Abstract: Many economics principles textbooks mention that stocks and bonds are substitutes, and some textbook authors state that stocks are riskier than bonds. Most people seem to believe this idea; thus when the stock market becomes volatile, money flows from the stock market into the safe haven of the bond market. This notion, however, is not necessarily accurate and might lead people to make incorrect investment decisions. In this paper, we examine how economics textbooks treat this question and if their treatment is accurate. We find that the notion that stocks are riskier than bonds is misleading. In fact, intermediate- and long-term bonds are riskier than stocks when we measure risk by the coefficient of variation. The textbooks that provide students with this idea might lead them to make faulty investment decisions later in their lives. We examine a case where this inaccurate idea appears to lead to irrational behavior of investors in financial markets.

* Direct all correspondence to: William Shambora, Dept. of Economics, Ohio University, Athens, OH 45701, e-mail: shambora@ohio.edu, phone: 740-593-1845, fax: 740-593-0181.

Are Stocks Really Riskier Than Bonds?

1. Introduction

Most of us who teach economics entertain the hope that our students, armed with economic

knowledge and economic reasoning, will make informed decisions when confronted with real-

world choices. Toward this end we have an interest in using the most accurate information

possible both in classroom presentations and in textbook treatments. One area where economics

classes may fail at this goal and, in fact, contribute to poor decision-making is in investment

asset allocation. There is evidence that private investors not only make uninformed asset

allocation decisions, but also make decisions that lead to the opposite of their desired outcomes.

Some of this behavior may be perpetuated or exacerbated by what investors have learned in

economics classes.

In most universities, introductory economics courses are required as general education

courses for many of those who do not major in economics. These courses are presumed to

provide students with fundamental economic knowledge indispensable to everyday life. To help

students understand investment decision-making processes, instructors teach students a little

about the relationship between stocks and bonds in introductory economics (especially

macroeconomics) courses. However, they do not usually go into the details of this relationship.

In many textbooks, authors just mention that stocks and bonds are substitutes, and in some

textbooks authors say that stocks are riskier than bonds. In fact, this idea has become

“conventional wisdom”. Thus when the stock market becomes volatile, money flows from the

stock market into the assumed safe haven of the bond market. This notion, however, is not

necessarily accurate, and might lead investors to make incorrect investment decisions. In this

2

paper, we examine how economics textbooks treat this question and whether or not their

treatment is accurate. We find that the notion that stocks are riskier than bonds is misleading. We

also examine a case where this inaccurate idea appears to lead to irrational behavior of investors

in financial markets.

This paper is organized as follows. In the next section, we explain how riskiness of stocks

and bonds are handled in introductory textbooks. We provide several examples from textbooks.

In section 3, we show that stocks are not necessarily riskier than bonds. In section 4, we provide

an empirical case where this misinformation could lead to irrational behavior in financial

markets. In section 5, we summarize our conclusions.

2. Examples from Textbooks

In most principles textbooks, authors mention stocks and bonds very briefly and explain that

stocks and bonds are substitutes. Some authors, however, also briefly mention that, between

these two assets, stocks are riskier than bonds. Frank and Bernanke (2001) write, “Most financial

investors dislike risk and unpredictability and thus have a higher required rate of return for

holding risky assets like stocks than holding relatively safe assets like government bonds.”1

Stiglitz and Walsh (2002) simply state, “Shares of stock are riskier than bonds.”2 Mankiw

(2003) adds, “Compared to bonds, stocks offer the holder both higher risk and potentially higher

return.”3 Kennedy (2000) says, “Bonds can be risky,” and the author introduces the concept of

default risk.4 Microeconomics texts are not immune from these statements. McEachern (2003)

says, “Investors usually consider bonds less risky than stocks, although bonds involve risk as

well.”5 Gwartney, Stroup, Sobel, and Macpherson (2003) assert that stocks are riskier than

bonds if held for a short time, “but when held over lengthy periods like 20 or 30 years,

3

historically the rate of return on stocks has been both higher and less variable than that of

bonds.”6 Of all of the introductory textbooks surveyed, Taylor (2004) has the most complete

treatment of this relationship in a section called “Risk versus Return.” In that section, the

relationship between expected return and risk for various financial assets is explored in some

detail. Taylor (2004) devotes about ten pages to “Stock and Bond Markets”, a section in Chapter

16, “Physical Capital and Financial Markets”. In that section, stock and bond prices, rates of

return, and yield are discussed. In addition, behavior under uncertainty, expected return, and risk

and return theory are presented. The author presents a table comparing annual rates of return and

average size of price fluctuations for Treasury bills, long-term corporate bonds, large-company

stocks, and small-company stocks and makes the point that higher risk is associated with higher

return. The section is concluded with a discussion of diversification.

Some of the views expressed in economics textbooks, while accurate under specific sets

of circumstances or strategies, may not tell the complete story. Giving the general impression

that bonds are less risky than stocks may distort the historical relationship between stock and

bond returns. In fact, we find that intermediate- and long-term bonds, when adjusted for return,

have a higher risk than stocks.

3. Riskiness of Stocks and Bonds

In this section we discuss whether or not stocks are riskier than bonds. There are several types of

risk and different ways of comparing risk between asset classes. It is likely that many textbooks

making the statement that stocks are riskier than bonds are referring to company specific risks

associated with financial distress. Because an individual firm’s bonds have a higher claim on

assets than its equity, bonds are considered less risky in the case of financial distress; thus,

4

theoretically, the expected return on a company’s bonds should not exceed the expected return

on its stock. Company specific distress risk is diversifiable in practice and would not be a factor

in comparing diversified portfolios of stocks and bonds or stocks and a default-free bond.

In most financial literature risk and uncertainty are used interchangeably. Reilly and

Brown (2003) define risk as “the uncertainty of future outcomes” or, alternatively, “the

probability of an adverse outcome”. Portfolios can be constructed that have an assured return at

a given time horizon, therefore zero uncertainty (risk) at that particular point in time. For

example, the return on a zero coupon Treasury bond maturing ten years from now is certain if

and only if the asset is held to maturity (and the U.S. government pays its debts). However, this

strategy entails opportunity risk because, depending on how interest rates change in the market,

the best strategy may be to sell the bond before maturity and invest the proceeds in other assets.

Contrarily, the return from a stock portfolio on that same date is far from certain. From this

perspective one would again say that the stock portfolio is riskier than the bond and,

theoretically, the expected return from the stock portfolio should exceed the known return on the

bond for that period. However, in the more general case where there is no specific investment

time horizon or there is uncertainty regarding the time horizon, bondholders face reinvestment

risk as bonds mature or pay interest because future yields are uncertain. Additionally,

bondholders face risk to their principal when liquidating prior to maturity.

According to Reilly and Brown (2003) one of the most common measurements of

investment risk is the standard deviation of returns. In fact, Ibbotson (2004) defines risk as such

and it is this more generalized definition and measurement of risk that underlies our analysis.

This measurement is useful in making general historical comparisons of risk between asset

5

classes, but would not be appropriate for examining company specific risk or comparing specific

long time horizon investment strategies.

A customary method of comparing risk and return between assets that incorporates

standard deviation of returns is the coefficient of variation (CV). It is used in analyzing the risk

among dissimilar returns or returns measured in different units. Most basic finance and

investment textbooks introduce CV.7 The coefficient of variation is a measure of relative

dispersion and is calculated by dividing an asset’s standard deviation of return by its mean return

as follows:

.( )

XXCV

E X

σ= (1)

The coefficient of variation is useful as long as the expected return is greater than zero.

For the period April 1953 through September 2003 the average pre-tax nominal monthly

total return for the S&P 500 Index was about 0.95 percent as shown in Table 1. In Table 1, the

equivalent returns for the 10-year Treasuries and the 20-year Treasury bonds8 were

approximately 0.56 and 0.54 percent, respectively, while those of the 30-day and 90-day

Treasury bills were approximately 0.43 and 0.47 percent, respectively. 9 It clearly shows that the

S&P 500 Index has a higher rate of return than T-bonds or T-bills. Over the same period, the

standard deviations of the returns of the S&P 500 Index, the 10-year Treasuries and 20-year T-

bonds, and the 30-day and 90-day T-bills were approximately 3.47, 2.70, 2.19, 0.24, and 0.27

respectively, as shown in Table 1; thus the S&P 500 return had greater standard deviation than

T-bonds or T-bills.

From the raw data it appears that stocks are the most risky assets and that investors are

compensated for the risk. However, from Table 1, the S&P 500 exhibits lower CV than 10-year

6

Treasuries and 20-year T-bonds, but higher CV than T-bills. The CV of the S&P 500, 10-year

Treasuries, 20-year T-bonds, 30-day T-bills and 90-day T-bills are 3.64, 4.83, 4.01, 0.56 and

0.58, respectively. The higher CV on intermediate- and long-term bonds indicates that the

risk/reward on intermediate- and long-term bonds may exceed that of stocks, suggesting that

intermediate- and long-term bonds are riskier than stocks. When adjusting the CVs in Table 1

for bias as suggested by Breunig (2001), bonds appear even more risky than stocks.10 In other

words, stock market investors may be overcompensated for the risk they undertake relative to

that undertaken by intermediate- and long-term bond investors. This phenomenon is akin to the

“equity premium puzzle” of Mehra and Prescott (1985) where it is proposed that excess returns

on stocks can only be explained by an unfeasibly high aversion to risk. In summary, we find that

intermediate- and long-term bonds such as 10-year Treasuries or 20-year T-bonds are much more

risky than stocks when adjusted for their returns. These results are contrary to common

perceptions of the relative risk of stocks and bonds.

From Table 1, it can be seen that there were, of course, no months where losses in 30-day

Treasury bills occurred. The maximum loss in 90-day bills is also quite low. Because of the low

potential for loss, it is not surprising that the maximum return for these instruments is small. The

maximum losses in the S&P and 10-year Treasuries and 20-year T-bonds are comparatively

quite large. This is matched by relatively high maximum returns. It can be noted, however, that

the spreads between the high and low returns of the S&P and the 10-year Treasuries are almost

identical. This is further evidence that bonds may not be less risky than stocks.

Figure 1 depicts the frequency distributions of returns on S&P 500, 10-year Treasuries

and 20-year T-bonds. The distributions make it obvious that stock returns are skewed opposite

to those of bond returns, but there is no indication that the stock return tails are significantly

7

thicker than those of bond returns. It shows that the kurtosis of stock returns is about the same as

that of 20-year T-bond returns and smaller than those of T-bills and 10-year Treasury returns.

A different vantage point is obtained by looking at data presented by Ibbotson (2004).

Ibbotson (2004) compares inflation-adjusted and risk-adjusted returns for various asset classes

using annual data from 1926 through 2003. Inflation-adjusted return is calculated by

compounding [(1 + annual asset return) / (1 + annual inflation rate)] annually for 78 years. Risk-

adjusted excess return is calculated by subtracting the Treasury bill rate from the average asset

return and dividing by the standard deviation of the asset return. Table 2 shows that inflation-

adjusted return for stocks is about twenty-eight times that of long-term corporate bonds, and

about forty-four times that of long-term government bonds. In fact, Table 2 shows that the risk-

adjusted excess return for large company stocks far outweighs the equivalent return on any class

of bonds considered. This provides further evidence that stockholders are overcompensated for

the risk they undertake when compared to bondholders. The question has been raised: People

invest in bonds to be safe, but can they afford to be that safe?

4. A Case of Irrational Investment Behavior due to Misperception

Although few fully discuss the relative risk/reward relationships among investment choices,

many economics textbooks describe the negative relationship between interest rates and bond

prices. However, many people do not seem to understand the relationship properly. Damato

(2001) points out that based on a telephone survey conducted by American Century Investments

only 31% of investors know that bond prices decline when interest rates increase. If our

8

principles students are among those who do not understand this concept, they have probably not

read their textbook. We understand that this occasionally happens. If bond investors ignore the

effects of changing interest rates on portfolio values, it is quite possible that they poorly time the

purchase and sale of fixed income assets resulting in less than optimal overall investment returns.

Poor decision-making is especially evident when there is a stock market downturn. As

discussed in the previous sections, most people seem to believe that stocks are riskier than bonds.

Thus, when there is increased volatility in the stock market, many people move their money from

stocks to bonds (or from stock mutual funds to bond mutual funds). This kind of transfer

accelerates when people panic, particularly when there is a stock market crash. They want to

move their money to what they perceive to be a safer place. However, as previously

demonstrated, bonds may not be safer than stocks.

Misunderstanding the bond price/interest rate relationship can compound the negative

effects of believing that bonds are relatively safer than stocks. In a stock market downturn

accompanied by an economic downturn, the interest rate usually decreases rapidly. As long as

the interest rate is decreasing, the transfer of money from stocks to bonds makes sense because

bond prices are increasing, creating near-term capital gains. The problem is that this kind of

transfer from stocks to bonds usually happens late in the trend when the interest rate is near its

bottom, ensuring that bonds are being bought near their highs, resulting in eventual capital

losses. We find evidence of this from the mutual funds market.11

Figure 2 shows the relationship between yields on Aaa rated corporate bonds and net

flows into bond mutual funds for the last twenty years.12 The two series look almost like mirror

images, suggesting an inverse relationship. Such a relationship would imply that investors tend

to buy bond funds near interest rate lows and sell bond funds near interest rate highs. In fact, the

9

cumulative flow within three months before and three months after each of six peaks sums to

more than $84 billion of net outflow from bond funds. The cumulative flow within three months

of each of five troughs sums to over $117 billion of net inflow to bond funds. This suggests that

bond fund investors may indeed take action opposite to their best interest.

To investigate this anomaly, we examine the relationship between mutual fund net flows

and various financial variables suggested in the literature.13 The financial variables include the

yield spread, changes in recent and future bond interest rates, and conditional variance on stocks

and interest rates. The yield spread is measured by the spread between the 10-year Treasury and

the three-month Treasury bill. Since bond funds are primarily composed of longer-term bonds,

this variable shows how relative interest rates influence flows. The yield curve is also believed

to contain information about the future course of interest rates and the economy, which may

impact flows. The current and previous one-month changes in the Aaa bond yields are included

to account for the impact of recent interest rate history on mutual fund flows. This corresponds

with the belief that bond fund investors focus on the most recent movements in interest rates for

clues to the future course of interest rates. Aaa yields, instead of yields on other grades, are used

for several reasons. One reason is that the underlying bonds exhibit default rates closer to failure

rates of S&P stocks than do Treasury securities or lower grade bonds; we wish to avoid, as much

as is practical, bias induced by default risk. Another reason is that, according to ICI (2003),

nearly half of all bond funds are either composed of corporate bonds or a mixture of bonds. Out

of about $811 billion in bond funds, around $400 billion are corporate or strategic funds, about

$278 billion are composed of municipal bonds, and the remaining $133 billion are composed of

government bonds. Future changes in bond yields are included as expectations variables. We

include quarterly changes for the year ahead. A pattern of significantly negative changes would

10

suggest that investors invest rationally either near interest rate tops or at least do not make

systematic errors by investing near interest rate bottoms. Significantly positive coefficients

would suggest that investors make systematic errors. A trend variable is included to account for

the effects of the passage of time. Finally, stock fund flow is included in the bond fund equation

and bond fund flow is included in the stock flow equation to account for the effects of

substitution between funds.

We also include variables for the interest rate volatility and stock market volatility

derived from a generalized autoregressive conditional heteroskedasticity (GARCH) model.14

From the GARCH model, we estimate the conditional variance of bond yields and log of stock

prices for particular time periods. Using the estimates of the conditional variance, we then

explore how the variance affects bond or stock funds net flows.

Before specifying the GARCH model, the ARIMA structure has to be determined so we

know how many lagged endogenous variables, how many differenced endogenous variables, and

how many lagged error terms to include. We estimate ARIMA models for Aaa bond rates and

log of S&P 500 stock index respectively. We find the structure to be ARIMA(1,1,13) and

ARIMA(1,1,1) respectively. The error terms are tested and found to be white noise in both

models. This means that, for our bond market equation, we use the first differenced variable,

∆BONDt, instead of BONDt, and we include the thirteen lagged error terms. Therefore, we

specify the GARCH model of bond market as:

0 1 1 1 1 12 13 ,t t t t tBOND BONDα α ε ε ε− − −∆ = + ∆ + + Φ + + ΦL (2)

1| ~ (0, ),t t tI N hε − (3)

20 1 1 1 1,t t th hγ γ ε δ− −= + + (4)

11

where BONDt is the Aaa bond rate at time t, It-1 is the set of all available information at time t-1,

and ht is the conditional variance of the error term εt. The inclusion of the lagged conditional

variance ht-1 in equation (4) differentiates the specification of the GARCH model from that of the

ARCH model; this is because the latter omits lagged variance. The GARCH specification,

therefore, generalizes the ARCH model, and allows the variance of Aaa bond rates to exhibit a

more general time dependence. This, in turn, allows us to exploit patterns and persistence in the

behavior of this variability.

For our stock market equation, we use the first differenced variable, ∆STOCKt, instead of

STOCKt , and we include the one lagged error term. Therefore, we specify the GARCH model of

stock market as:

0 1 1 1 1,t t t tSTOCK STOCKβ β ν ξν− −∆ = + ∆ + + (5)

1| ~ (0, ),t t tI N fν − (6)

20 1 1 1 1,t t tf fθ θν ζ− −= + + (7)

where STOCKt is the log of S&P 500 index at time t, It-1 is the set of all available information at

time t-1, and ft is the conditional variance of the error term tv .

Once we have estimated the GARCH model, we can investigate whether the variance or

volatility of bond and stock markets affects bond fund net flows. We do this by regressing the

bond fund net flows on the estimate of ht generated by the GARCH models and other

independent variables, so that

0 1 2 other variables ,t t t tBNFLOW h fγ γ γ η= + + + + (8)

0 1 2 other variables .t t t tSNFLOW h fα α α ω= + + + + (9)

12

where ηt and tω are error terms. Equations (8) and (9) are estimated by least squares estimation

method and we use the White heteroskedasticity consistent standard error.

All data are monthly observations from January 1984 through December 2002.

Movements in the stock market are represented by changes in the S&P 500 Index. The particular

series used is the monthly average of the index. The bond market is represented by yields on

Aaa bonds. The treasury market is represented by 10-year Treasury yield and three-month

Treasury yields. Yields for Aaa corporate bonds, 10-year Treasuries and Treasury bills are from

the Federal Reserve Board’s FRED®15 data set. T-bill yields are for the three-month constant

maturity. Aaa bond yields are Moody’s seasoned corporate Aaa bond yields, monthly averages

of daily data.

Mutual fund data are from the Investment Company Institute historical data. The data

series for the period from 1984 to 1996 are “old basis” where funds are broken into five major

categories: stock funds, bond funds, hybrid funds, taxable money market funds, and tax-exempt

money market funds. Bond funds include corporate, government, and municipal bond funds.

The “new basis” begins in 1996. Because of changes in the structure of the data there is a

discrepancy of $92 million in assets for all funds where the old and new basis overlap in January

1996. Flow data are the series for stock funds and bond funds entitled “net new flow”. This

series includes all purchases and exchanges into the funds in the category less redemptions and

exchanges out of the category.

Table 3 provides the estimation results. The coefficient on the conditional variance of

S&P 500 returns in the stock fund flow equation is negative and significant. The coefficients on

bond flow in the stock flow equation and stock flow in the bond flow equation are both negative

and significant. These estimates imply that when stocks are volatile people flee stocks to invest

13

in bonds since they believe that stocks are riskier than bonds. As we discussed in section 3,

however, stocks are not necessarily riskier than bonds. The coefficient estimates in the bond fund

flow equation present evidence that bond fund investors make systematic errors in timing their

purchase and sale activities. The coefficient on the term premium indicates that investors shop

for the highest current yield, possibly because they fail to grasp the implications of the term

structure of interest rates and the bond price/interest rate relationship. An increasing interest rate

spread is often a harbinger of higher interest rates to come, but bond fund investors appear to

take higher spreads as a buy signal. The coefficient on conditional variance of Aaa interest rates

is statistically significant and has a reasonable sign. It indicates that bond fund investors are

quite sensitive to interest rate volatility.

It appears that poor investment timing and asset allocation strategy indeed reduce returns

for bond fund investors. Evidence of this is provided by the coefficients on the changes in

interest rates. If investors exhibit rational behavior then the change in the future interest rate and

bond fund flow should move in opposite directions. The coefficients, however, on the quarterly

changes three, six, nine, and twelve months ahead are statistically significant at the 10% level

(note that nine month lead is significant at the 1% level) and of the same direction. It suggests

that investor behavior is not rational in the bond fund market. Such behavior is probably due to

the inaccurate commonly held notion that stocks are riskier than bonds; when the stock market

becomes volatile, money flows from the stock market into the bond market. The stock market

slide for the period 2000 through 2002 represents a good example of this phenomenon. The

coefficients on conditional variance from the stock fund flow equation suggest that investors

favor equity funds when interest rates experience high volatility and leave equity funds when the

14

stock market experiences volatility, lending support to the idea that investors are overly sensitive

to temporary changes in relative risks of stocks and bonds.

5. Conclusion

There is an impression that investors do not understand basic risk and return relationships

between stocks and bonds. We found that there may indeed be some validity to this impression.

We uncovered evidence that investors behave irrationally in their asset allocation strategy

between stock and bond mutual funds. Part of this behavior appears to stem from ignorance of

the relationship between interest rate movements and bond prices and part comes from a

mistaken belief that bonds are less risky than stocks. We looked at how introductory economics

textbooks treat these topics and discovered that investors may be ignoring the important passages

about bond pricing, but reading too much into the sections about relative riskiness between

stocks and bonds. A sampling of introductory economics textbooks revealed a number of

approaches to the topic of asset risk and return. Most textbooks introduce the inverse

relationship between interest rates and bond prices. Few, however, explore in much depth the

risk/return relationship between stocks and bonds. In fact, most simply state that stocks are

riskier than bonds.

We examined net money flows into stock and bond funds by regressing those flows on a

number of financial variables. These variables included the yield spread, past and future changes

in interest rates, and conditional variance. We found that increasing variance in bond yields

leads to withdrawals from bond funds and deposits into stock funds. Increasing variance in stock

prices leads to withdrawals from stock funds and withdrawals from stock funds (bond funds) are

15

associated with deposits into bond funds (stock funds). Increases in the interest rate term

structure (long interest rates gaining on short rates) are associated with flows into bond funds.

This indicates a willingness to chase yields despite the fact that higher spreads often signal

higher future interest rates, thus lower bond prices. Recent past and concurrent increases in

interest rates are associated with net outflows from bond funds, but future increases in interest

rates are associated with net inflows. This behavior appears to be irrational because it is return-

minimizing, leading to buying bonds when prices are high and selling when prices are low.

It is impossible to tell whether or not this irrational behavior is associated with what

investors learned or failed to learn in introductory economics classes. Nevertheless, it

underscores the need to provide accurate and complete information when these topics are

addressed. It also signifies the desirability of encouraging students to learn some of the

investment basics so that they will be better prepared to deal with a world that will require

increasing self-direction in investment decisions.

16

REFERENCES

Breunig, R. 2001. An almost unbiased estimator of the coefficient of variation. Economics Letters 70 (January): 15-19.

Damato, K. 2001. Investors turn to bonds without grasp of basics. The Wall Street Journal. November 9, 2001.

Chen, N., R. Roll, and S. Ross. 1986. Economic forces and the stock market. Journal of Business 59 (July): 383-403.

Elton, E. J., M. J. Gruber, and C. R. Blake. 1995. Fundamental economic variables, expected returns, and bond fund performance. The Journal of Finance 50 (September): 1229-1256.

Frank R., and B. Bernanke. 2001. Principles of Macroeconomics. 1st edition. NY: McGraw-Hill Irwin.

Gwartney, J. D., R.L. Stroup, R.S. Sobel, and D. Macpherson. 2003. Economics. 10th edition. OH: South-Western.

Ibbotson, R, ed. 2004. Stocks, Bonds, Bills, and Inflation®2004 Yearbook. Chicago, IL: Ibbotson and Associates.

ICI. 2003. Mutual Fund Fact Book. 43rd edition. NY: Investment Company Institute.

Kennedy, P. 2000. Macroeconomic Essentials. 2nd edition. Cambridge, MA: The MIT Press.

Mankiw, N.G. 2003. Brief Principles of Macroeconomics. 3rd edition. OH: South-Western.

Mayo, H. B. 2003. Investments. 7th edition, OH: South-Western.

McEachern, W. A. 2002. Microeconomics. 6th edition. OH: South-Western.

Mehra, R. and E. C. Prescott. 1985 The equity premium: A puzzle. Journal of Monetary Economics 15 (March): 145-162.

Reilly, F. K. and K. C. Brown. 2003. Investment Analysis and Portfolio Management. 7th edition. OH: Thomson South-Western.

Stiglitz J. E. and C. E. Walsh. 2002. Principles of Macroeconomics. 3rd edition. NY: McGraw-Hill Irwin.

Taylor, J. B. 2004. Principles of Microeconomics. 4th edition. NY: Houghton Mifflin.

17

Figure 1: Frequency Distribution for Investment Return

0

40

80

120

160

-.15 -.10 -.05 .00 .05 .10 .15 .2020 Yr Bond Return10 Yr Bond ReturnS&P 500 Return

Fre

qu

ency

Investment Return

18

Figure 2: Bond Flow vs. Aaa Bond Yield

0

4

8

12

16

-10000

0

10000

20000

84 86 88 90 92 94 96 98 00 02

Aaa Bond Yield Net Flow Bond Funds

Aa

a B

on

d Y

ield

Ne

t Flo

w B

on

d F

un

ds

Date

19

Table 1: Summary Statistics

30-day T-bill

90-day T-bill

10-year Treasury

20-year T-bond

S&P 500

Average monthly return (%) 0.4261 0.4715 0.5589 0.5447 0.9522Standard deviation (%) 0.2381 0.2722 2.7008 2.1862 3.4653CV 0.5589 0.5774 4.8324 4.0139 3.6391Bias adjusted CV* 1.7151 2.1983 5.3417 4.4672 3.1150Skewness 1.1562 1.6209 0.5093 0.4533 -0.5241Kurtosis 2.0789 4.9592 2.7102 1.6344 1.6337Maximum monthly return (%) 1.5158 2.1308 15.2347 9.9993 12.0974Minimum monthly return (%) 0.0297 -0.124 -9.3600 -6.6820 -12.302*CV is adjusted for bias per Breunig (2001). Data are from April 1953 through September 2003.

20

Table 2: Inflation-adjusted and Risk-adjusted Returns from Ibbotson Data

Series Inflation-adjusted Return Risk-adjusted Return Large Company Stocks 223.019 0.422Long-Term Corporate Bonds 7.721 0.279Long-Term Government Bonds 5.029 0.213Intermediate-Term Government Bonds 5.029 0.298Treasury Bills 0.696 ─Note that all returns are obtained from Stocks, Bonds, Bills, and Inflation 2004 Year book Tables 2-1 and 6-7.

Return series are from 1926 to 2003. Inflation-adjusted returns are calculated by ( ) 78(1 Return) / (1+Inflation) 1+ − .

Risk-adjusted returns are calculated by ( )i i(R ) /fR σ− , where iR is the return on each asset and fR is the return on

a risk-free proxy (Treasury bills).

21

Table 3: Bond and Stock Flow Regression Estimates

Variables Bond Fund Flow Stock Fund Flow Constant 4.358 (2.174)** -1.104 (3.655) Trend -0.003 (0.009) 0.100 (0.017)***

Term Premium 0.806 (0.279)*** 0.132 (0.544) ∆Aaat-1 -4.889 (1.578)*** 1.292 (2.301) ∆Aaat -6.132 (1.526)*** -1.239 (2.648) ∆Aaat+3 0.556 (1.446) 3.061 (2.636) ∆Aaat+6 2.606 (1.622)* -1.633 (2.788) ∆Aaat+9 4.428 (1.420)*** 0.295 (2.578) ∆Aaat+12 2.464 (1.553)* 2.884 (2.661) Aaa Conditional Variance -16.891 (6.025)*** 18.852 (11.380)*

S&P 500 Conditional Variance 18.613 (38.165) -141.796 (39.897)***

Stock Fund Flow -0.096 (0.043)*** ─ Bond Fund Flow ─ -0.343 (0.194)*

Adjusted R2 0.256 0.397*Significant at the 10% level. **Significant at the 5% level. ***Significant at the 1% level. Sample Period is 1984:03 – 2001:12. The numbers in parenthesis are standard errors.

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NOTES

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1 See Page 282. 2 See Page 387.3 See Page 156.4 See Page 144.5 See Page 294.6 See Page 686.7 See, for example, Mayo (2003).8 Typically, 10-year Treasuries are known as intermediate-term bonds and 20-year T-bonds are long-term bonds.9 The data for T-bonds and T-bills are from CRSP. Monthly total return data from April 1953 through September 2003 are used since this period overlaps the S&P 500 total return data via Standard & Poors Corp. We do not include corporate bonds in comparison since the equivalent data (total return data) are not available for corporate bonds.10 Breunig (2001) demonstrates that CV estimates are biased in skewed distributions. In negatively skewed distributions, like that of S&P returns, the CV is overestimated, and in positively skewed returns such as bonds, the bias is the opposite. This indicates that the relative risk of bonds to stocks may be even greater than implied by our CV estimates. See Table 1 for return distribution information and bias-adjusted CV estimates.11 Most mutual funds fall into one of three categories: stock funds, which invest in equity securities, bond funds, which invest in fixed income securities, and money market funds, which invest in very short-term interest-paying assets. If investors do not understand relative risk and reward or basic interest rate and pricing relationships, their strategies in timing purchases and sales as well as in asset allocation may result in sub-optimal returns on mutual fund assets and could even create problems for fund managers who are forced to take or reduce positions at the wrong time.12 We use the Aaa interest rate instead of Treasuries rates in this section since the majority of bond funds under consideration are composed of corporate bonds.13 Previous literature suggests that returns on common stock (e.g., Chen, Roll, and Ross (1986)) and bonds (e.g., Elton, Gruber, and Blake (1995)) can be explained by variables such as market returns, risk, term premium, inflation, and economic performance.14The original autoregressive conditional heteroskedasticity (ARCH) model was developed by Engle (1982). Bollerslev (1986) extends the ARCH model to a GARCH model. The GARCH model differs from the ARCH model in that the former conditions current variance on lagged variance, as is shown in the specification of our model.15 These data can be found at http://research.stlouisfed.org/fred2/.