*Published on December 30th, 2014*

- See how long the S&P 500 has historically taken to revert to fair value
- Te stock market appears to be overvalued by more than 20%
- One data-driven formula that determines whether you should buy now or wait for a better price

The S&P 500 is currently trading at a P/E ratio of 20.28. The long-term historical average P/E ratio of the S&P 500 is 15.53. Based on this information, the stock market is due for a correction of about 23% to reach fair value. With the stock market historically overvalued, should investors purchase stocks at this time? This article seeks to answer that question.

### Does Value Matter?

The P/E ratio of a stock tells you how much money you have to pay for one year’s worth of earnings in a stock. A P/E ratio of 5 means you only have to pay 5 years worth of earnings, while a P/E ratio of 30 means you must pay 30 years worth of earnings.

Intuitively, the less you have to pay, the better off you will be. The historical record shows this as well. The image below shows 10 year total price returns for the S&P 500 at various starting P/E ratios.

As the image above indicates, valuation matters. All other things being equal, the less you pay for a valuable asset, the better off you are.

### Calculating Return

A stock’s total return can be calculated as follows:

- Dividends + Business Growth x Valuation Multiple Change

As an example, assume you purchases a stock for a price of $100. The stock pays $3.00 a year in dividends and has $5.00 per year in EPS for a P/E ratio of 20. Over 10 years, the stock pays you dividends each year for a total of $30 in dividends (this was not a dividend growth stock, apparently). Additionally, EPS increase from $5.00 to $10.00 per share, while the P/E ratio falls from 20 to 15. In this case, your return would be:

- +30% from dividends
- +100% from underling business growth
- -50% from valuation changes
- Total return of +80% in 10 years

As you can see from the example above, if a valuation multiple falls, your long-term total returns suffers even if the underlying business you owned experienced growth.

### Fast Growers Can’t Stay That Way Forever

Another key point is that *no business can grow at a rapid pace forever*. As an example, Apple (AAPL) has experienced rapid growth over the last decade. It *cannot* experience the same level of growth (barring some miraculous innovative new product) over the next decade because the smartphone market is much more mature and saturated than it was a decade ago. Paying a high P/E ratio for a stock discounts future growth.

Businesses have different stages of life. When a business gets out of its growth phase and into its mature stage, its growth rate falls and its P/E ratio will fall as well. Examples of businesses in the mature stage are Coca-Cola (KO), Procter & Gamble (PG), and Johnson & Johnson (JNJ). Their growth rates may fluctuate somewhat, but investors know these companies will never grow EPS at 30% a year over several years again. *They are too big to do this*. Stable companies are much easier to forecast than rapid growers because they have already exited the growth phase of business life.

### Guessing How Long a Stock Will Stay Overvalued

Here is an example of how P/E ratios discount growth: Imagine we know ahead of time (through tarot cards, of course) that a stocks fair P/E ratio is 15. Now, imagine we also know the stock will grow its EPS at 10% a year for the next several years and has a dividend yield of 2%. The stock is currently somewhat overvalued and trades a P/E ratio of 20. Should you invest in this stock?

That all depends on when you think its P/E ratio will fall. The table below shows your total return depending on what year in the future the stock’s P/E ratio will fall.

Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |

-16% | -6% | 5% | 18% | 32% |

Anything above 0% is a positive total return. With cash yields near zero, if you believe the stock will trade above fair value for 3 or more years, you are better off purchasing the overvalued stock than holding cash.

### How Long Has the S&P 500 Historically Stayed Overvalued?

The image below uses the PE 10 ratio (also called the Shiller P/E ratio) to measure the overall value of the stock market. The PE 10 ratio uses average earnings over the last 10 years instead of trailing twelve months earnings. This tweak smooths out earnings over a longer time frame and gives a more accurate view of the overall valuation level of the stock market. The historical average PE 10 ratio is 16.58. The image below shows how many years on average the S&P 500 has historically taken for its PE 10 ratio to fall to fair value or below.

The S&P 500 currently has a PE 10 ratio of 27.47. The market will likely stay overvalued for an average of 6.72 years. Just because the market has been overvalued for X number of years does not mean it is more likely for it to fall to fair value any sooner. If the stock market is overvalued next year, it will still be as likely as it was this year for the market to fall to historically fair values. The probability of a fall is not cumulative.

### Final Thoughts

Using the numbers above, investors should estimate that an overvalued stock will fall to fair value in between 5 and 7 years. In the example we used earlier (10% growth, 2% dividends, fair P/E of 15, current P/E of 20), an investor would maximize their wealth (on average) by investing in the stock instead of holding cash.

In summary, using between 5 and 7 years as the expected amount of time before a stock falls to fair value will tell you when to invest. To find the total return in 6 years of a stock use the following formula:

**((expected growth rate + dividend yield + 1)^6 x (fair P/E ratio / current P/E ratio))^(1/6) -1**

If the number is above your cash yield rate (or other investment options available), it makes sense to invest. If it is below your cash yield rate, it does not make sense to invest. Always use *conservative* growth numbers and fair P/E ratio numbers.

### Additional Sources

- Investment Formula Excel Spreadsheet Download by Sure Dividend
- Historical S&P 500 and PE 10 Data at multpl.com
- Why Total Return Trumps Growth & Value by Sure Dividend
- In Defense of The Shiller Cape Ratio by Dale Roberts on Seeking Alpha