Short Term Price Fluctuations

I recently realized that I can say a lot more about short-term price fluctuations than I had previously thought. Here it is.

Background

Rob Bennett has always been interested in the human side of investing. One of his concerns has been the emotional effect of falling prices. His concerns led to my You Can’t Count on 7% series of posts that I feature in the Guidelines section.

Just recently, Rob opened up the Talking Numbers section of PassionSaving.com, which features the Mechanics of Money--Benchmarks, Metrics, Mental Exercises and Rules of Thumb. Right off the bat, he posted Money Management Tip #2--PPx2/3/4 where PPx2 means "Panic Percentage Times Two."

Rob Bennett’s PassionSaving Web Site
PassionSaving Money Management Tips

Rob’s article grew out of a discussion at the Morningstar Web Site (Vanguard Diehards).

Morningstar Web Site

Historical Price Ranges

I extracted monthly (nominal) prices from January 1921 through December 1980 and P/E10 from Professor Robert Shiller’s database. I determined the lowest price within the following 1, 2 and 5 years (12, 24 and 60 months) and divided it by the original price. Similarly, I determined the highest price within the following 1, 2 and 5 years. Again, I expressed it as a ratio relative to the original price.

Professor Robert Shiller’s Updated Database

I sorted these ratios according to P/E10. I grouped them into ten deciles. I determined the minimum and maximum value of P/E10 in each group along with the minimum and maximum ratios within 1, 2 and 5 years.

The minimum and maximum values are independently grouped. For example, the lowest ratio within a group does not necessarily correspond to either the month with highest or the lowest value of P/E10 for that group. However, if a minimum or maximum ratio within an earlier time period is still the minimum or maximum ratio of a longer time period, it still reported as such. In particular, when a price decline hits bottom in year 2, I still report it as the minimum in year 5.

Interesting Tables

Here are the results.

Minimum monthly prices of the S&P500 within the next 1, 2 and 5 years throughout 1921-1980 relative to the initial price sorted by P/E10

P/E10..MIN(1)..MIN(2)..MIN(5)
..5.1-8.8..0.76..0.76..0.76
.8.9-10.1..0.57..0.57..0.57
10.2-11.2..0.47..0.47..0.47
11.2-12.0..0.46..0.46..0.46
12.0-13.5..0.40..0.40..0.40
13.5-15.8..0.33..0.33..0.32
15.8-17.3..0.40..0.29..0.29
17.4-18.8..0.47..0.27..0.27
18.9-21.6..0.57..0.23..0.23
21.6-32.6..0.57..0.22..0.15

Maximum monthly prices of the S&P500 within the next 1, 2 and 5 years throughout 1921-1980 relative to the initial price sorted by P/E10

P/E10..MAX(1)..MAX(2)..MAX(5)
..5.1-8.8..2.24..2.37..3.80
.8.9-10.1..1.45..1.57..3.25
10.2-11.2..1.77..2.15..2.73
11.2-12.0..1.53..1.90..2.48
12.0-13.5..1.47..1.86..2.40
13.5-15.8..1.42..1.83..2.29
15.8-17.3..1.33..1.88..2.06
17.4-18.8..1.42..1.88..1.88
18.9-21.6..1.49..1.81..1.81
21.6-32.6..1.52..1.58..1.58

Minimum Prices

Buying at bargain prices really does protect your downside risk. Starting from the lowest P/E10 levels, subsequent prices never fell below 76% of the original price and that occurred within the first year.

There is ambiguity at other levels within the Year 1 results. The rise at highest P/E10 levels indicates that a bubble is forming.

By the time that we reach Year 2, the relationship is monotonic. Higher P/E10 levels (always) translate into more danger on the downside. In terms of a single month, the downside fluctuation can fall to 40% even at middle range valuations (P/E10=12.0 to 13.5). However, such a drop is most likely to occur within the first year.

In contrast, drops at higher valuations (P/E10=15.8 to 17.3 and above) are more likely to hit bottom later.

It is not clear to me that this longer time period is a momentum effect. Maybe, it takes longer because there is farther to fall.

Maximum Prices

Bargain prices can produce fantastic returns: doubling your money within one year. The single-year upside potential is attractive at all valuations. Typically, it is in the neighborhood of 50%.

It takes the full five years (as opposed to one or two years) before the relationship between the upside potential and P/E10 becomes monotonic. Notice that, after P/E10 exceeds the 17.4 to 18.8 range, the Year 2 and Year 5 results are identical. Historically, at high valuations, the upside occurs rapidly. In this sense, the recent bubble really was different.

Even then, an upside of 1.8 within 5 years corresponds to a (nominal) price-only return in excess of 12%. A price rise of 2.5 corresponds to an annualized return of 20%.

Conclusions

These data are descriptive of what has happened. They form a reasonable starting point for determining what is likely in the future.

Today’s P/E10 is close to 27.

Judging from the past, we would expect the upside to occur sooner rather than later. The upside potential is in the neighborhood of 50%. If we reach it, it is most likely to be within the next year.

Judging from the past, the downside risk is exceptionally high.

We can anticipate a resolution within five years. This does not mean that we will hit bottom within the next five years. There is still a long way to fall before reaching historical norms.

Have fun.

John Walter Russell
November 6, 2006