But for those of us who trade in the short-term, stocks will always beat bonds. Even in the long-term, stocks will beat bonds as is evidenced here. But that is hardly the point. We mix our portfolio between stocks and bonds in order to avoid volatility, not necessarily to get the best return. After all, best returns are not predictable, but volatility can be. Since bonds tend to do better than stocks during market downturns, they are important to avert market shock. Any reputable financial adviser would be putting clients into at least some bonds for the sake of stability. So I think the article ignores this fundamental main point but is nonetheless a fine technical essay on the overall rationale of the long term profitability of being invested in stocks. Enjoy this wonderful weekend we're having. Today was the first time since last fall that I could go outside without a jacket.
4-2-19 AAII: Stocks v Bonds
Will Stocks Always Outperform Bonds Over
a Multi-Year Period?
Investors price stocks for higher return because of their higher
risk and dividend growth, but downturns can make bonds more favorable because
of their contractual payments.
The common stock
issued by a company is riskier than its debt, since equity is lower in the
firm’s capital structure, meaning that it has a subordinate claim to the firm’s
cash flows. In other words, interest and principal gets paid to bondholders
before equity holders receive anything. Conventional finance theory tells us
that, because of this increased risk, shareholders in the firm demand a return,
referred to as the “required return,” that is higher than the yield they would
require on the firm’s bonds. The difference between the two rates of return is
known as the equity risk premium, and according to finance theory this premium
is always positive.
But despite the
positive equity risk premium, will equity always outperform bonds in the long
run? Professor Edward McQuarrie sifted through history to show that there have
been prolonged periods during which bonds outperformed. (See “Stock
Market Charts Your Never Saw,” for instance, on SSRN.com.) His
findings are not entirely surprising but probably not a cause for concern.
About the author
Brian Haughey CFA, FRM, CAIA, is assistant professor of finance and
director of the Investment Center at Marist College in Poughkeepsie, New York.
In a rational market,
investments that are more risky promise higher returns than safer ones do. For
example, suppose that the U.S. Treasury issued a one-year bill, offering a
return of 5%. Since Treasury bills are issued at a discount, an investor would
pay $95.24 ($100 par value divided by one plus the interest rate of 5%):
$100 ÷ (1 + 0.05) =
$95.24
At maturity the
investor would receive $100, for a gain of $4.76 ($100 par value minus the
purchase price of $95.24), representing a 5% return on the investment:
$4.76 ÷ $95.24 =
0.0499 = 5%
Now imagine that a
firm, ACME Inc., also issued a 5%, one-year note at the same par value of $100
and priced at the same $95.24. Since there is a chance that ACME might go out
of business and default on the note, a rational investor would opt for the Treasury
bill that promised the same 5% return but with effectively no default risk.
Suppose there is a 1%
chance that ACME will default. That means that 99% of the time the investor
would receive $100 at maturity, but 1% of the time they would receive nothing.
We can therefore calculate that the expected future value of the ACME note is
$99.00. The math is a 99% chance of full payment times par value of $100 plus a
1% chance of full default times zero payment:
(0.99 × $100) + (0.10%
× $0) = $99.00
At the price of
$95.24, the investor who expects to receive $99 would be earning $3.76 ($99
expected future value minus $95.24 price) for an actual yield of 3.95% ($3.76 ÷
$95.24). Since this is less than the 5% promised by the Treasury bill, no
rational investor should buy the ACME note at the asking price of $95.24. In
fact, the price would have to drop to $94.29 [$99 ÷ (1 + 0.05)] to attract
investors. At that price, the ACME note’s promised yield would be 6.06%:
($100 – $94.29) ÷
$94.29 = 0.606 = 6.06%
Its expected yield,
taking default risk into account, would be 5%.
The investor should,
all else being equal, be indifferent to holding the 5% Treasury bill or the
6.06% ACME note. In reality, of course, the default risk of ACME is unknown at
inception and it may change over time. (For securities with maturities longer
than a year, the timing of a default would be another source of uncertainty.) We
should also point out that a portion of the principal may be repaid, so that
the loss could be less than 100%. Investors, however, may also be concerned
about liquidity—that is, their ability to sell the ACME note prior to maturity
if they choose to do so. Due to these uncertainties, the yield required by an
investor is likely to be even higher than the rate we calculated.
When determining the
value of future cash flows on a security that has default risk, an investor
should use a risk-adjusted discount rate greater than that used on a Treasury
bill, note or bond. This is why $100 to be paid in a year by the U.S.
government would be, in effect, considered to be worth $95.24 today in our
example, whereas $100 promised in a year by ACME would be worth only $94.29
today. The difference is due to the premium of 1.06% (6.06% – 5.00%) in the
discount rate, which compensates for the possibility of default and is a
function of both the risk of the issuer and the maturity of the investment.
Now let us turn our
attention to stocks. While there are several different ways to value a firm’s
shares, one common method is to calculate the present value of the firm’s
expected future dividends, by discounting them at the appropriate risk-adjusted
discount rate, using the dividend discount model (which is also known as the
Gordon Growth Model). In this model, the value of a stock that pays dividends
is:
Value = D1 ÷
(k – g)
Where:
§ D1 is next year’s dividend
§ k is the risk-adjusted discount rate and
§ g is the rate at which dividends are assumed
to grow each year.
The risk-adjusted
discount rate is the compensation an investor demands for parting with the
invested dollars over a period of time adjusted for the risk of losing some or
all of the money. If a firm does not pay dividends, investors can instead use
another discounted cash flow (DCF) approach to calculate the present value of
the firm’s projected future earnings, free cash flow or some other substitute
to determine the value of the stock. [See “Calculating Intrinsic Value
With the Dividend Growth Model” in the March 2014 AAII Journal for examples of other models.]
For example, suppose a
firm paid a $5 dividend this year and is expected to grow its dividend at a
rate of 4% a year into perpetuity. The investor uses a risk-adjusted discount
rate of 10% (which approximates the long-term return of large-cap stocks). Next
year’s dividend should be $5.20 ($5 current dividend times 1 plus 4% projected
growth rate). Based on this, the stock would be worth $86.67. The math is:
[$5 × (1 + 0.04)] ÷
(0.10 – 0.04) = $86.67
Clearly, the value of
the firm depends on the growth assumption. If the investor expects dividends to
grow at 5%, for example, then the stock would be worth $105:
[$5 × (1 + 0.05)] ÷
(0.10 – 0.05) = $105.00
That is not
surprising: An investor would pay more for a stock that they expect to pay them
more in dividends. The stock’s value also depends on the risk-adjusted discount
rate; a higher rate ascribes less value today to future dividends. If dividends
grow at a rate of 4%, but we use a discount rate of 15% instead, the stock’s
value would fall to $47.27:
[$5 × (1 + 0.04)] ÷
(0.15 – 0.04) = $47.27
The price is lower in
this example because the higher discount rate reflects greater perceived risk.
FIGURE 1
Stocks Versus Bonds: The Long-Term Record
Over the long term, stocks beat bonds when it comes to annualized
returns. Though stocks have historically been better at creating wealth, they
have also been more volatile, as the chart on the top shows.
The return that an
investor earns on any investment is a function of the price paid. In our last
example, the investor who pays $47.27 for the stock will earn a 15% return,
year after year, if dividends continue to grow at 4%. We can easily demonstrate
this by calculating the value of the stock one year from now. Its value will be
based on the dividend two years from now, so the stock will be worth $49.16.
The math is:
($5 × 1.042)
÷ (0.15 – 0.04) = $49.16
A stock’s value is
always based on the dividend one year from the valuation date. The value in one
year’s time depends on the dividend two years from now. In this example, we use
the current dividend of $5, growing for two years at 4%.
A future purchaser
would be willing to pay that price if they used the same discount rate and
dividend growth assumption, so our investor could sell the stock for a $1.89
gain. Before selling, they would also collect next year’s dividend of $5.20. In
total, they would realize a 15% return (dividends plus capital appreciation
divided by purchase price):
($5.20 + $1.87) ÷
$47.27 = 0.149 = 15%
A critical point that
escapes many investors is that if markets are rational, there are only two
reasons why the investor in our example paying $47.27 would not earn a 15%
return, year after year. Either dividends grow at some rate other than what is
assumed, or when investors ultimately sell the stock, the subsequent purchaser
uses different dividend growth or risk-adjusted discount rate assumptions to
arrive at the price they are willing to pay. [In practice, investors tend to
base their risk-adjusted discount rate assumption on a stock’s beta (relative
level of volatility) at the time of purchase.]
Note that an investor
who used a risk-adjusted rate of 10% to arrive at a value of $86.67 for the
same stock and bought it at that price would earn a 10% return, assuming
dividends continued to grow at 4%.
While many textbooks,
and most practitioners, view stocks and bonds as quite different animals, they
are in fact closely related, each representing a claim on assets of the firm
with the value of each being a function of the financial health of the firm.
The key difference between them is that bond cash flows are contractual
obligations and must be paid, whereas dividends on stock, both preferred and
common, are not. Dividends are paid at the discretion of management. Rational
management should, however, overwhelmingly choose to continue to pay dividends
if there is sufficient cash to do so. [See “The Factors Driving Dividend
Policy” in the September 2017 AAII Journal.]
Investors who choose
stocks do so because of their residual claim on a firm’s earnings; while coupon
payments on bonds are generally fixed, earnings typically increase over time
and result in dividend growth that is higher than originally assumed and that is
ultimately reflected in stock appreciation. (An additional benefit for an
equity investor is that their return is a function of both income and capital
gains, the latter being recognized when the stock is sold. While the return to
a bond investor is typically taxed as income, long-term capital gains on stock
are taxed at the lower capital gains rate.)
Whether or not the
equity investor actually earns the “required return” discussed in textbooks
depends on the dividends paid, which are a function of the firm’s net earnings,
once debts, taxes and other expenses have been paid. We can explore whether
dividend growth is likely to be different than that assumed by monitoring
current business and economic conditions and using ratios such as return on
equity (ROE, or net income divided by equity) and payout (dividends per share
divided by earnings per share) to calculate the sustainable growth rate for
dividends. [A company grows when new equity is created from the reinvestment of
earnings, which is measured by the retention ratio (one minus the payout ratio)
and what earnings are generated by that new equity, measured by ROE.] As the
firm’s fortunes change, the growth rate can change.
If we accept that a
rational firm, not in financial distress, will always pay interest and
principal on its bonds, because it must, and will always choose to pay
dividends on its stocks when it has sufficient resources to do so, we can then
focus our attention on the borderline case. What happens if the firm has just
enough cash to pay current dividends, but its business suffers a downturn
resulting in reduced earnings and insufficient cash to continue paying
dividends at the current level? Management must, sooner or later, respond by
reducing or terminating the dividend.
The reduction in
earnings would cause the bond to become somewhat riskier, since the firm would
generate less cash. In the short term, the bond’s price may drop to reflect
this increased risk. As long as the firm continues to generate enough cash to
pay interest and principal, however, an investor who holds the bond to maturity
will, in the absence of any change in market interest rates, continue to earn
their promised yield. (In reality, if the slowdown is economy-wide, interest
rates are likely to drop and so the investor will earn less on their reinvested
coupons. But the investor’s total return will most likely still be positive.)
Dividend Discount Model
The constant growth dividend discount model (also known as the
Gordon Growth Model) assumes that a company is growing at a constant rate. It
is best used for large, stable companies that have consistent earnings and
dividends. However, small- and medium-sized firms that are growing their
earnings and dividends steadily can be valued using this approach as well. The
formula for the constant growth model is:
Stock price = D1 ÷ (k – g)
Where:
- D1 = dividend for the coming year
- k = required rate of return; k must be greater than g
- g = growth rate of dividends
(Decimals, not percentages, must be used for the model to work.)
As with any model, the output generated is only as good as the
quality of the factors going into the calculation. Dividends and earnings
information is widely available, but the required rate of return and growth
rate of dividends require assumptions to be made.
A common formula for estimating the possible required rate of
return is:
Required rate of return for equity = risk-free rate + (market
risk premium × beta for equity).
The risk-free rate used in this calculation is the yield on
long-term Treasuries, such as a 30-year Treasury bond. The reasoning behind
using a long-term bond is that equities are thought of as indefinite holdings;
therefore, the risk-free rate should be a very long-term risk-free rate.
According to Ibbotson Associates, long-term Treasuries annualized a total
return of 5.5% over the 90-year period ending in 2017.
The market risk premium is the expected return of the stock market
less the risk-free rate. In short, it is the return required to entice
investors to purchase risky assets instead of simply purchasing risk-free
assets. A good estimate of this figure is the historical market risk premium of
the S&P 500 index.
According to Ibbotson Associates, the S&P 500 gained 10.2%
annually over the same 90-year period. Therefore, the market risk premium is
4.7% (10.2% – 5.5%). It is worth noting that there are a number of economists
who believe our stock market will not be able to achieve the same type of
returns we have experienced over the long run. However, this opinion is hard to
substantiate, and using a long-term historical market risk premium is
considered a sound procedure.
—AAII
—AAII
The equity investor,
however, would see the value of their shares drop, for two reasons. First, the
stream of dividends would no longer grow as expected, but would likely be
reduced or even terminated and the stock’s present value would drop. Second,
since the firm is riskier, the risk-adjusted discount rate should increase,
further reducing the present value of future dividends. The equity investor’s
return would drop below what they expected (which was equal to the
risk-adjusted discount rate) since their current income, in the form of
dividends, would diminish. The investor would see reduced—or even
negative—capital gain, due to the decrease in the value of the stock.
If the reduction in
the firm’s earnings, and consequently in its dividends, continued year after
year, the value of the stock would also continue to drop each year in lockstep.
It’s possible, of course, that the market might anticipate this continued
deterioration in the firm’s fortunes and drive the stock price down below that
projected by the dividend discount model.
If such a downturn
were to occur across multiple firms, the broad bond market would likely
continue to show positive returns, while the broad equity market would show
negative returns. One could argue that the Federal Reserve would respond to
such a broad slowdown by cutting rates or by implementing some other stimulus,
thereby possibly reducing the risk-adjusted discount rate. Nevertheless, a
prolonged period of declining equity prices, over a period of multiple years,
despite positive bond market returns, is a plausible scenario.
Are we likely to see a
period of McQuarrie-esque returns where stocks realize lower returns relative
to bonds over the 30 years? Such a scenario is only likely if long-term
earnings growth for stocks is substantially less than what is currently
anticipated. Favoring stocks is the favorable energy situation in the U.S., the
arrival of the long-anticipated productivity dividend of technology spending
(as evidenced by the growth in artificial intelligence, big data,
virtualization, robotics and autonomous machines) and the general growth in
economic activity due to human ingenuity and innovation. These should help
long-term earnings and dividend growth.
Both earnings growth
and dividends have historically helped stocks to outperform over the long run,
as Figure 1shows.
Blending bonds with stocks in a portfolio has tended to reduce volatility, with
falling rates since the late 1980s helping to boost the returns of bonds.
Brian Haughey CFA, FRM, CAIA, is
assistant professor of finance and director of the Investment Center at Marist
College in Poughkeepsie, New York.
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