Complete Guide To Corporate Finance

AAA

Return, Risk And The Security Market Line - Calculating The Equity Risk Premium

In this section, we take a deeper look at the assumptions and validity of the risk premium by looking at the calculation process in action with actual data. Recall the three steps of calculating the risk premium: (1) estimate the expected return on stocks, (2) estimate the expected return on safe bonds and (3) subtract the difference to get the equity risk premium.

Step One: Estimate the Expected Total Return on Stocks
Estimating future stock returns is the most difficult (if not impossible) step. Here are the two methods of forecasting long-term stock returns:



Plugging into the Earnings Model
The earnings-based model says that the expected return is equal to the earnings yield. Consider the 15-year history of the S&P 500 Index, ending on December 31, 2003:



In the above graph, we split the S&P 500 index (violet line) into two pieces: earnings per share (green line) and the P/E multiple (blue solid line). At every point, you can multiply EPS by the P/E multiple to get the index value. For example, on the last day of December 2003, the S&P index reached 1112. At that time, the EPS of the combined companies was $45.20 and the P/E multiple therefore was 24.6x ($45.20 x 24.6 = 1112).

As the index finished the year with a P/E of almost 25, the earnings yield was 4% (1 ÷ 25 = 4%). According to the earnings-based approach, the expected real return (before inflation) was therefore 4%. The underlying intuitive idea is "mean reversion": the theory that P/E multiples cannot get too high or too low before they revert back to some natural middle ground. Consequently, a high P/E implies lower future returns and a low P/E implies higher future returns.

Graphically, we can also see why some academics warn that next decade's equity returns cannot keep pace with the double-digit returns of the 1990s. Consider the 10-year period from 1988 to 1998, omitting the acute bubble at the end of the decade. EPS grew at an annualized rate of 6.4%, but the S&P index grew a whopping 16%! The difference arose from so-called "multiple expansion": an increase in the P/E multiple from about 12 to 28x. Academic skeptics use simple logic. If you start from a base P/E multiple of about 25x at the end of 2003, you can only realize aggressive long-term returns that outpace earnings growth with further expansion of the P/E multiple.

Plugging into the Dividend Model
The dividend model says that expected return equals dividend yield plus growth in dividends (all in a percentage). Here is the dividend yield on the S&P 500 from 1988 to 2003:



The index ended 2003 with a dividend yield of 1.56%. We only need to add a long-term forecast of growth in the markets' dividends per share. One way to do this is to assume that dividend growth will track with economic growth. And we have several economic measures to choose from, including gross national product, per capita GDP and per capita gross national product.

Let's take real GDP which has been consistent over the long run at 3-4%. To use this measure for estimating future equity returns, we need to acknowledge a realistic relationship between it and dividend growth. It is a big leap to assume that 4% real GDP growth will translate into 4% growth in dividends per share. Dividend growth has rarely, if ever, kept pace with GDP growth and there are two good reasons why.

First, private entrepreneurs create a disproportionate share of economic growth; the public markets often do not participate in the economy's most rapid growth. Second, the dividend yield approach is concerned with per share growth, and there is "leakage" because companies dilute their share base by issuing stock options (while it is true that stock buybacks have an offsetting effect, they rarely compensate for stock option dilution. Publicly-traded companies are remarkably consistent "net diluters").

History tells us that real GDP growth of 4% translates, at best, into roughly 2% growth in real dividends per share, or 3% if we are really optimistic. If we add our growth forecast to the dividend yield at the end of 2003, we get about 3.5% to 4.5% (1.56% + 2 to 3% = 3.5% to 4.5%). We happen to match the 4% predicted by the earnings model, and both numbers are expressed in real terms, before inflation.

Step Two: Estimate the Expected "Risk-Free" Rate
The nearest thing to a safe long-term investment is the Treasury Inflation Protected Security (TIPS). Because the coupon payments and principal are adjusted semi-annually for inflation, the TIPS yield is already a real yield. TIPS are not truly risk-free; if interest rates move up or down, their price moves, respectively, down or up. However, if you hold a TIPS bond to maturity, you can lock in a real rate of return.



In the above chart, we compare the nominal 10-year Treasury yield (blue line) to its equivalent real yield (violet). The real yield simply deducts inflation. The short green line is important as it represents the 10-year TIPS yield during the year 2002. We expect the inflation-adjusted yield on the regular 10-year Treasury (violet) to track closely with the 10-year TIPS (green). At the end of 2003, they were close enough. The 10-year TIPS yield was just shy of 2%, and the real yield on the Treasury was about 2.3%. Therefore, the 2% real yield becomes our best guess at future real returns on a safe bond investment.

Step Three: Subtract the Estimated Bond Return from the Estimated Stock Return
When we subtract our forecast of bond returns from stock returns, we get an estimated equity risk premium of +1.5% to +2.5%:

All Sorts of Assumptions
This model attempts a forecast and therefore requires assumptions - enough for some experts to reject the model entirely. However, some assumptions are safer than others. If you reject the model and its outcome, it is important to understand exactly where and why you disagree with it. There are three assumptions made in this model, ranging from safe to dubious.

First, the model does assume that the entire stock market will outperform risk-free securities over the long term. But we could say this is a safe assumption because it allows for the varying returns of different sectors and the short-term vagaries of the market. Take the calendar year 2003, during which the S&P 500 jumped 26% while experiencing a modest decline in the P/E multiple.

No equity risk premium model would have predicted such a jump, but this jump does not invalidate the model. It was caused largely by phenomena that cannot be sustained over the long haul: a 17% increase in the combined forward EPS (i.e. EPS estimates for four future quarters) and an almost unbelievable 60%-plus increase in trailing EPS (according to S&P, from $27.60 to $45.20).

Second, the model requires that real growth in dividends per share - or EPS, for that matter - be limited to very low single-digit growth rates in the long run. This assumption seems secure but is reasonably debated. On the one hand, any serious study of historical returns (like those by Robert Arnott, Peter Bernstein or Jeremy Siegel) proves the sad fact that such growth rarely gets above 2% for a sustained period.

On the other hand, optimists allow for the possibility that technology could unleash a discontinuous leap in productivity that could lead to higher growth rates; who knows, maybe the new economy is just around the bend. But even if this happens, the benefits will surely accrue to selected sectors of the market rather than all stocks. Also, it is plausible that publicly traded companies could reverse their historical conduct, executing more share buybacks, granting fewer stock options and reversing the eroding effects of dilution.

Finally, the model's dubious assumption is that current valuation levels are approximately correct. We've assumed that, at the end of 2003, the P/E multiple of 25x and the price-to-dividend yield of 65x (1 ÷ 1.5% dividend yield) are going to hold going forward. Clearly, this is just a guess! If we could predict valuation changes, the full form of the equity risk premium model would read as follows:



The equity risk premium is a long-term prediction of how much the stock market will outperform safe bonds. The premium is calculated as the difference between the estimated real return on stocks and the estimated real return on safe bonds, and the model makes a key assumption that current valuation multiples are roughly correct. When the dividend yield on stocks is close enough to the TIPS yield (at the end of 2003, they were less than 50 basis points apart), the subtraction conveniently reduces the premium to a single number: the long-term growth rate of dividends paid per share.

Cost of Capital
Cost of capital is the minimum required return necessary to make a capital budgeting project, such as building a new factory, worthwhile. Cost of capital includes the cost of debt and the cost of equity.

The cost of capital determines how a company can raise money (through a stock issue, borrowing or a mix of the two). The cost of capital must equal or exceed the rate of return that a firm would receive if it invested in a different vehicle with the same level of risk. We'll discuss the cost of capital in depth in section 13 of this walkthrough. (Read more about investing and risk in 5 Essential Things You Need To Know About Every Stock You Buy and What Your Portfolio Says About You.)

Arbitrage Pricing Theory
Related Articles
  1. Investing

    3 Healthy Financial Habits for 2016

    ”Winning” investors don't just set it and forget it. They consistently take steps to adapt their investment plan in the face of changing markets.
  2. Investing

    How to Ballast a Portfolio with Bonds

    If January and early February performance is any guide, there’s a new normal in financial markets today: Heightened volatility.
  3. Economics

    The Truth about Productivity

    Why has labor market productivity slowed sharply around the world in recent years? One of the greatest economic mysteries out there.
  4. Term

    How Market Segments Work

    A market segment is a group of people who share similar qualities.
  5. Active Trading

    Market Efficiency Basics

    Market efficiency theory states that a stock’s price will fully reflect all available and relevant information at any given time.
  6. Professionals

    Is A Stockbroker Career For You?

    Becoming a stockbroker requires a broad skill set and the willingness to put in long hours. But the rewards can be enormous.
  7. Economics

    Understanding Cost-Volume Profit Analysis

    Business managers use cost-volume profit analysis to gauge the profitability of their company’s products or services.
  8. Fundamental Analysis

    5 Must-Have Metrics For Value Investors

    Focusing on certain fundamental metrics is the best way for value investors to cash in gains. Here are the most important metrics to know.
  9. Fundamental Analysis

    5 Basic Financial Ratios And What They Reveal

    Understanding financial ratios can help investors pick strong stocks and build wealth. Here are five to know.
  10. Investing

    What Investors Need to Know About Returns in 2016

    Last year wasn’t a great one for investors seeking solid returns, so here are three things we believe all investors need to know about returns in 2016.
RELATED TERMS
  1. Tight Monetary Policy

    A course of action undertaken by the Federal Reserve to constrict ...
  2. Laissez Faire

    An economic theory from the 18th century that is strongly opposed ...
  3. Short-Term Debt

    An account shown in the current liabilities portion of a company's ...
  4. Audit

    An unbiased examination and evaluation of the financial statements ...
  5. Sortino Ratio

    A modification of the Sharpe ratio that differentiates harmful ...
  6. Climate Finance

    Climate finance is a finance channel by which developed economies ...
RELATED FAQS
  1. What should I study in school to prepare for a career in corporate finance?

    Depending on which area you want to specialize in, corporate finance can be one of the most competitive fields in business. ... Read Full Answer >>
  2. Why would a company issue preference shares instead of common shares?

    Preference shares, or preferred stock, act as a hybrid between common shares and bond issues. As with any produced good or ... Read Full Answer >>
  3. What is the difference between cost of debt capital and cost of equity?

    In corporate finance, capital – the money a business uses to fund operations – comes from two sources: debt and equity. While ... Read Full Answer >>
  4. What is the difference between gross profit, operating profit and net income?

    The terms profit and income are often used interchangeably in day-to-day life. In corporate finance, however, these terms ... Read Full Answer >>
  5. What is finance?

    "Finance" is a broad term that describes two related activities: the study of how money is managed and the actual process ... Read Full Answer >>
  6. What is the difference between positive and normative economics?

    Positive economics is objective and fact based, while normative economics is subjective and value based. Positive economic ... Read Full Answer >>
Hot Definitions
  1. Harry Potter Stock Index

    A collection of stocks from companies related to the "Harry Potter" series franchise. Created by StockPickr, this index seeks ...
  2. Liquidation Margin

    Liquidation margin refers to the value of all of the equity positions in a margin account. If an investor or trader holds ...
  3. Black Swan

    An event or occurrence that deviates beyond what is normally expected of a situation and that would be extremely difficult ...
  4. Inverted Yield Curve

    An interest rate environment in which long-term debt instruments have a lower yield than short-term debt instruments of the ...
  5. Socially Responsible Investment - SRI

    An investment that is considered socially responsible because of the nature of the business the company conducts. Common ...
Trading Center