# IS THE S&P 500 (“S&P”) INDEX FAIRLY VALUED AT THIS TIME?

(This article is dated September 8, 2004, for a current version, click here)

This question can be answered by looking at the current level of earnings and dividends of the S&P stocks, projecting the future rate of earnings and dividend growth and by considering the minimum return required by investors. Analysts, including myself, often apply valuation techniques to **individual** stocks. **It is actually far easier to apply these calculations to a stock index since an index constitutes a portfolio and therefore eliminates most of the random noise of unexpected events through diversification.** The index remains vulnerable to changes in interest rates and to growth in the economy but is largely insulated from the numerous random events that can impact an individual stock.

As of August 31, 2004, the S&P index was at** 1104** and had a Price Earnings Ratio (“P/E”) of 19.7 based on trailing earnings and 18.73 based on projected 2004 earnings and had a Dividend yield of 1.80%. (Source:http://www2.standardandpoors.com/spf/xls/index/SP500EPSEST.XLS). I will focus on S&P’s projected level of **18.73** based on estimated 2004 calendar year earnings.

The S&P 500 represents a portfolio of 500 stocks. For each $1104 (the index value) purchased, the underlying companies in the portfolio are therefore currently **projected** to earn $1104/18.73 = $59 in 2004 and pay a dividend of $1104 * 0.0180 = $19.90 in 2004.

When we Buy the S&P index, we can therefore think of it as being an investment or “stock” that (as of August 31, 2004) costs $1104 and currently earns $59 per year and pays a current dividend of $19.90 per year. It is worth thinking about whether or not this “stock” is a good investment at or around its recent level of $1104.

We know that the S&P index **was** at 1104 on August 31, 2004. We can estimate what the S&P **“should”** have been trading at based on the value of its ** current earnings and** **dividends and the projected growth in those earnings and dividends**. This intrinsic value approach calculates the value of the projected earnings and dividends for a ten year period and then assumes that the index is sold at a projected future P/E.

In addition to the beginning earnings and dividend level, three additional factors are required to calculate the fair value at which the S&P **should** be trading at. These are, 1. The forecast average compound growth rate in earnings and dividends over the next ten years. 2. The forecast P/E ratio at which the S&P index will be trading in ten years time. 3. The estimated rate of return required by investors.

The S&P portfolio average earnings should grow at a rate close to the growth rate of the U.S. economy in nominal (after inflation) terms. I believe a prudent estimate for this growth rate is 4% to 6% and I would focus on 5%.

The average P/E for the S&P 500 since 1935 is 15.6. However the Justifiable P/E changes with earnings expectations and the market’s required return on equities. **I have conservatively calculated that the current Justifiable P/E is in the range of only 12.5 to 14.3, even with today’s low interest rates**. This conservative calculation of the justifiable P/E assumes that, on average, the S&P 500 companies will only earn, on new investments, the 7 to 8% minimum ROEs required by investors in today’s low-interest rate environment. If companies can earn more than ROE required by investors, then it is possible to justify a P/E in the 16 range. The more optimistic we are about the level of the P/E in ten years time, the higher is the justifiable fair value level of the S&P index today.

I would estimate that a minimum (pre-tax) return required by stock investors is in the range of 7% to 9%. The higher return required by investors then the lower the price or level that investors should be willing to pay for the index today, all else being equal.

The following table calculates the value that the S&P **should** be trading at given prudent assumptions about earnings growth, the P/E ratio that will exist in ten years and the rate of return that investors require.

S&P Forecast Current Annual Earnings |
S&P Current Annual Dividends |
Earnings and Dividend Growth forecast |
P/E forecast in 10 years |
Resulting S&P in 10 years |
Required Return |
Resulting S&P Fair Value Today |

59 | 20 | 4% | 14 | 1,222 | 7% | 792 |

59 | 20 | 4% | 16 | 1,396 | 7% | 880 |

59 | 20 | 4% | 18 | 1,571 | 7% | 969 |

59 | 20 | 4% | 14 | 1,222 | 9% | 671 |

59 | 20 | 4% | 16 | 1,396 | 9% | 745 |

59 | 20 | 4% | 18 | 1,571 | 9% | 818 |

59 | 20 | 5% | 14 | 1,344 | 7% | 863 |

59 | 20 | 5% | 16 | 1,537 | 7% | 961 |

59 | 20 | 5% | 18 | 1,729 | 7% | 1,058 |

59 | 20 | 5% | 14 | 1,344 | 9% | 731 |

59 | 20 | 5% | 16 | 1,537 | 9% | 812 |

59 | 20 | 5% | 18 | 1,729 | 9% | 893 |

59 | 20 | 6% | 14 | 1,478 | 7% | 940 |

59 | 20 | 6% | 16 | 1,689 | 7% | 1,048 |

59 | 20 | 6% | 18 | 1,900 | 7% | 1,155 |

59 | 20 | 6% | 14 | 1,478 | 9% | 795 |

59 | 20 | 6% | 16 | 1,689 | 9% | 885 |

59 | 20 | 6% | 18 | 1,900 | 9% | 974 |

**Conclusions**

By changing the expected earnings growth rate, the return required by the investor and the assumed P/E ratio that will apply in ten years I can calculate that today’s S&P index should be anywhere from 671 to 1155.

My own fair-value estimate is highlighted in yellow and is 961. This assumes that investors require a minimum 7% return, that the S&P earnings and dividend will grow at 5% (3% GDP growth plus 2% inflation) and that the long run S&P P/E is 16. Higher S&P index values are implicitly assuming that earnings growth will exceed 5% annually, that the justifiable long-run P/E exceeds 16, and/or that investors require less than a 7% (pre-tax) return.

Since the S&P is currently about 1104, I conclude that it is likely overvalued.

The table illustrates quite a wide range for a reasonable fair value of the S&P. **Investors should be sobered by the fact that if investors require a 9% rate of return and if the earnings only grow at 5% (say 3% GDP plus 2% inflation) and if the S&P commands a P/E of only 14 in ten years then the fair value of the S&P today is calculated as only 731, which is 34% below the current value! **

**(Note the high light on the above paragraph was added only in August 2009, just to point out that this article in the past did indicate that the S&P could be considered high)**

Most investors would probably not admit to being happy with a 7% return, but the level of the S&P suggests that investors have bid stocks up to the point where no more than 7% is a realistic long-term return. However the return should be higher than 7 to 8% if earnings growth is significantly higher than my assumed 5%.

**My overall conclusion is that at its current level of about 1104, the S&P is probably somewhat overvalued and priced to return no more than about 7% annually**.

However, given the current relatively optimistic outlook for earnings I would rate the S&P as a Hold rather than a Sell.

It is impossible to predict where the S&P 500 index will go in the next year. But it is relatively easy to calculate whether or not it is currently overvalued based on reasonable growth expectations. Caution is warranted because the S&P can sometimes spend years in an over-valued or an under-valued-state. But ultimately, as we have recently seen, valuation does correct itself.

The good news is that although the S&P is no screaming bargain, it is currently at a better price in relation to trailing year earnings than it has been since 1997. The last time that the S&P 500 P/E was below 20 was in early 1997.

Readers should see also a similar article on the Dow Jones Industrial Average which paints a more optimistic picture. See IS THE DOW JONES INDUSTRIAL AVERAGE (“DJIA”) INDEX OVERVALUED?

Shawn C. Allen,

Editor

InvestorsFriend.com