Price Probability Ranges for Key Asset Categories

by: Richard Shaw

Last week we published a visual view of price range probability cones for several securities (SPY, FXI, TLT and UUP). This article builds on the concepts in that article and provides a tabular view of the same kind of data for twenty-seven asset categories.

The two tables below show the maximum and minimum price change that statistics would suggest are probable over the 21 trading days after October 9 (last Friday), based on 21 days (1 month) and on 63 days (3 months) of historical price volatility.

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21-Day Projection Based on 21-Days of Volatility History


21-Day Projection Based on 63-Days of Volatility History


The Statistical Approach:

By measuring the standard deviation of the percentage price changes (or of the difference in natural logs of successive prices) and making the assumption of an approximately “normal” frequency distribution curve (bell shaped curve), we can estimate the range for future prices in “normal” circumstances. All bets are off in the extreme situations such as we experienced in 2008. Fortunately, price behavior is more often “normal” than not.

Note that this approach does not speak to direction, just magnitude in either the up or down direction.

Overlay Direction on Probable Price Ranges:

Since statistically estimated price ranges give no indication as to direction, additional information is needed to judge whether positive or negative price movement is likely. You might use fundamental and/or technical means of making that decision.

One approach to thinking about direction is through moving averages — the classical trend indicators. Moving averages do lag and trends can change, but moving averages are widely used as indicators of direction.

You can look at moving averages of several lengths to see how they are stacked up. For example, if each successively shorter average is above the next longer average, that is a strong positive trend indication. If each successively shorter average is below the next longer average, that is a strong negative trend indication. You might also look at the slope of one or more moving averages to indicate whether the forces at work are pushing up or pulling down.

In the tables above, information for each of four moving averages (21-days, 63-days, 126-days, and 252-days) is shown to give some indication of direction to help you work with the price probability data. For both tables the moving average data shows the ratio of each of the averages now to its value 21 days ago.

The Conical Shape of Probable Price Ranges:

Key to projecting prices is that the range of probable prices widens (with the square root of time) as the projection horizon extends farther out, creating the conical shape to the probable price range.

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68% Probability and 95% Probability:

The tables show the maximum probable price change after 21 days for +/- 1 standard deviation either way (encompassing 68% of probable prices), and for +/- 2 standard deviations (encompassing 95% of probable prices).

What lies outside of those ranges (roughly 2.5% on each side), can be quite exciting as we learn painfully upon infrequent occasions.

Multi-Year View of Probability Price Projections:

This chart of successive quarterly 95% probability price projections for the S&P 500 index might have been useful to some investors to see the problems of 2008 developing. From the beginning of the last bull in 2003 to the end in 2007, the realized price range in each calendar quarter occurred within the 95% probability projection based on the preceding 3-month daily price volatility.

Early in the first quarter of 2008, the realized price range moved outside of the 95% probability projection. That was a warning that the situation was no longer normal and was negative. The price behavior in the first quarter generated a very wide 95% projection range for the second quarter — also a warning sign that something unusual was happening. The negative trend was indicated by the raw chart and moving average cross-overs by that time as well.

The third quarter remained mostly inside the 95% boundaries, but touched the downside edge near the quarter’s end — and the downward trend was visually clear on the charts.

The combination of price behavior at or near the 95% probability level and the downward trend, should have been enough to suggest taking at least some money off the table, if not all. Something unusual — something disorderly — was developing. Ambient fundamental data was deteriorating too. “Unusual” and “disorderly” at the very least call out for heavy scrutiny, and perhaps standing aside until things are sorted out.

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By the time we reached the beginning of the first quarter of 2009, the probability cone was so wide that just about anything could happen, but with a clear down momentum. The market went well down from there.

In the second quarter of 2009, the probability range narrowed (but was still wide) and prices remained within the range. The third quarter 95% probability range narrowed again, and prices continued to remain within the conical boundaries. These were signs of a return toward normal market behavior.

We are now in the fourth quarter. The probability range is narrower than the third quarter and the trend is still up, suggesting that absent a major shock, the S&P 500 should end the year between about 930 and 1200 based on 95% probability (and based on trailing 3-month daily volatility).

The 68% probability (not shown on the chart) would put the year-end at about 990 to 1130.

Understanding and Managing Risk to Increase Gains and Limit Losses:

You need to use stop loss orders or other active measures to protect against the improbable, but can benefit by otherwise understanding and managing risks based the probable.

For example, if you are an options buyer, you would most likely want to own strike prices inside the price probability cones. However, if you were an options seller, you would most likely want to write options with strike prices outside of the price probability cones.

Similarly, if you are taking an equity position, you might want to know what statistics based on volatility tell you about the size and probability of a possible price decline, and of a possible price rise.

Probability price projections are imperfect, but potentially helpful for market interpretation when considered in combination with other fundamental and technical data.

Some Observations from the Tables:

Real estate, pipelines and oil have the widest probable percentage price ranges over the month (21 days) following last Friday (Oct 9). Bond percentage price ranges are lower than equity price ranges. Long-term bonds have wider ranges than short-term bonds. U.S. stocks have narrower ranges than non-U.S. stocks. Emerging market stocks price ranges are not terribly different from those of non-US developed markets, except for Japan. The Japanese stock market has a slightly narrower probability cone than the U.S. stock cone. Aggregate U.S. bonds, junk bonds and TIPS have similar narrow probability cones.

While several of these observations are consistent with general perceptions, some may not be so. Even if all were general perceptions, it is useful to test perceptions so that we don’t “drink the Kool-Aide” or have our mental feet in cement. Instead, we need to read the data to let the market inform and update our perceptions.

Do take note that these are short-term projections based on short-term data. Volatility changes, and this data is only useful in the short-term. It needs to be regularly updated to be of continuing help as one tool of many in your investment research and decision toolbox.


Disclosure: We own several of the securities named in this article in various managed accounts.