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A bubble is a run-away market, in which rationality has temporarily disappeared. There is a lot of debate as to whether bubbles in the stock market ever occurred. A strong case can be made that technology stocks experienced a bubble from around f 998 to 2000. It is often called the dot-com bubble, the internet bubble, or simply the tech bubble. There is no convincing explanation based on fundamentals that can explain both why the Nasdaq Index had climbed from 2,280 in March i999 to 5,000 on March 27, 2000, and why it then dropped back to i,640 on April 4, 2001.

Method 3: Dividend or 3. Current Predictive Ratios: The third method tries to actively predict the stock market rate of Earnings Yields. return with historical dividend yields (i.e., the dividend payments received by stockholders).

Higher dividend yields should make stocks more attractive and therefore predict higher future equity premiums. The equity premium estimation is usually done in two steps: first, you must estimate a statistical regression that predicts next year's equity premium with this year's dividend yield; then, you substitute the currently prevailing dividend yield into your estimated regression to get a prediction. Unfortunately, as of 2005, current dividend yields were so low that the predicted equity premiums were negative—which is not a sensible number. Variations of this method have used interest rates of earnings yields, typically with similar results. In any case, the evidence suggests that this method has yielded poor predictions—for example, it had predicted low equity premiums in the 1990s, which was a period of superb stock market performance.

Method 4: What is 4. Philosophical Prediction: The fourth method wonders how much rate of return is required reasonable reward for to entiCe reasonable investors to switch from bonds into stocks. Even with an equity premium as low as 3%, over 25 years, an equity investor would end up with more than twice the money of a bond investor. Naturally, in an efficient market, nothing comes for free, and the reward for risk-taking should be just about fair. Therefore, equity premiums of 8% just seem too high for the amount of risk observed in the stock market. This philosophical method generally suggests equity premiums of about 1% to 3%.

Method 5: Just ask. 5. Consensus Survey: The fifth method just asks people or experts what they deem reasonable.

The ranges can vary widely, and seem to correlate with very recent stock market returns. For example, in late 2000, right after a huge run up in the stock market, surveys by Fortune or Gallup/Paine-Webber had investors expect equity premiums as high as 15%/year. (They were acutely disappointed: the stock market dropped by as much as 30% over the following two years. Maybe they just got the sign wrong?!) The consulting firm, McKinsey, uses a standard of around 5% to 6%, and the social security administration uses a standard of around 4%. A joint poll by Graham and Harvey (from Duke) and CFO magazine found that the 2005 average equity premium estimate of CFOs was around 3% per annum. And in a survey of finance professors in late 2007, the most common equity premium estimate was 5% for a 1-year horizon and 6% for a 30-year horizon.

Some recent What to choose? Welcome to the club! No one knows the true equity premium. On Monday, estimates. February 28, 2005, the CI page of the WSJ reported the following average annual after-inflation forecasts from then to 2050:

Anecdote: The Power of Compounding

Assume you invested SI in 1925. How much would you have in December 2001? If you had invested in large-firm stocks, you would have ended up with S2,279 (10.7% compound average return). If you had invested in long-term government bonds, you would have ended up with S 51 (5.3%). If you had invested in short-term Treasury bills, you would have ended up with S17 (3.8%). Of course, inflation was 3.1%, so SI in 2001 was more like SO.10 in real terms in 1926. Source: Ibbotson Associates, Chicago. U

Name

Organization

Inflation Adjusted Govmnt Corp. Stocks bonds bonds

Forecast Equity Premium

William Dudley

Goldman Sachs

5.0%

2.0%

2.5%

3.0%

Jeremy Siegel

Wharton

6.0%

1.8%

2.3%

4.2%

David Rosenberg

Merrill Lynch

4.0%

3.0%

4.0%

1.0%

Ethan Harris

Lehman Brothers

4.0%

3.5%

2.5%

0.5%

Robert Shiller

Yale

4.6%

2.2%

2.7%

2.4%

Robert LaVorgna

Deutsche Bank

6.5%

4.0%

5.0%

2.5%

Parul Jain

Nomura

4.5%

3.5%

4.0%

1.0%

John Lonski

Moody's

4.0%

2.0%

3.0%

2.0%

David Malpass

Bear Stearns

5.5%

3.5%

4.3%

2.0%

Jim Glassman

J.P. Morgan

4.0%

2.5%

3.5%

Average

The equity premium is usually quoted with respect to a short-term interest rate, because these are typically safer and therefore closer to the risk-free rate that is in the spirit of the CAPM. This is why you may want to add another 1% to the equity premium estimates in this table—long-term government bonds usually carry higher interest rates than their short-term counterparts. On the other hand, if your project is longer term, you may want to adopt a risk-free rate that is more similar to your project's duration, and thus prefer the equity premium estimates in this table. Finally, because a +20% rate of return followed by a -20% rate of return (for a 0% annual rate of return) leaves you with a two-year loss of (1 + 20%) ■ (1 - 20%) - 1 = 1.2-0.8 = -4%, if your project is long horizon, you may subtract another percent or so if you want to use annual equity premiums on long-term projects.

(Because the equity premium is a difference, inflation cancels out.)

You now know that no one can tell you the authoritative number for the equity premium. It does not exist. Everyone is guessing, but there is no way around it—you have to take a stance on the equity premium. I cannot insulate you from this problem. I could give you the arguments that you should contemplate when you are picking your number. Now I can also give you my own take: First, I have my doubts that equity premiums will return to the historical levels of 8% anytime soon. (The twentieth century was the American Century for a good reason: there were a lot of positive surprises for American investors.) I personally prefer equity premiums estimates between 2% and 4%. (Incidentally, it is my impression that there is relatively less disagreement about equity premiums forecasts today than there was just five to ten years ago.) But realize that reasonable individuals can choose equity premiums estimates as low as 1% or as high as 8%. Of course, I personally find such estimates less believable the further they are from my own personal range. And I find anything outside this 1% to 8% range just too tough to swallow. Second, whatever equity premium you do choose, be consistent. Do not use 3% for investing in

Pick a good estimate, and use it for all similar-horizon projects.

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