One of the most useful tools employed by many technical commodity traders is a momentum oscillator which measures the velocity of directional price movement.

When prices move up very rapidly, at some point the commodity is considered overbought; when they move down very rapidly, the commodity is considered oversold at some point. In either case, a reaction or reversal is imminent. The slope of the momentum oscillator is directly proportional to the velocity of the move, and the distance traveled up or down by this oscillator is proportional to the magnitude of the move.

The momentum oscillator is usually characterized by a line on a chart drawn in two dimensions. The vertical axis represents magnitude or distance the indicator moves; the horizontal axis represents time. Such a momentum oscillator moves very rapidly at market turning points and then tends to slow down as the market continues the directional move. Suppose we are using closing prices to calculate the oscillator and the price is moving up daily by exactly the same increment from close to close. At some point, the oscillator begins to flatten out and eventually becomes a horizontal line. If the price begins to level out, the oscillator will begin to descend.

## Plotting the oscillator

Let's look at this concept using a simple oscillator expressed in terms of the price today minus the price "x" number of days ago — let's say 10 days ago, for example.

The easiest way to illustrate the interaction between price movement and oscillator movement is to take a straight line price relationship and plot the oscillator points used on this relationship, as shown on this page's chart.

In our illustration, we begin on Day 10 when the closing price is 48.50. The price 10 days ago on Day 1 is 50.75. So with a 10-day oscillator, today's price of 48.50 subtracted from the price 10 days ago of 50.75 results in an oscillator value of - 2.25, which is plotted below the zero line. By following this procedure each day, we develop an oscillator curve.

The oscillator curve developed by using this hypothetical situation is very interesting. As the price moves down by the same increment each day between Days 10 and 14, the oscillator curve is a horizontal line. On Day 15, the price turns up by 25 points, yet the oscillator turns up by 50 points. The oscillator is going up twice as fast as the price. The oscillator continues this rate of movement until Day 23 when its value becomes constant, although the price continues to move up at the same rate.

On Day 29, another very interesting thing happens. The price levels out at 51.00, yet the oscillator begins to go down. If the price continues to move horizontally, the oscillator will continue to descend until the 10th day, at which time both the oscillator and the price will be moving horizontally

Note the interaction of the oscillator curve and the price curve. The oscillator appears to be one step ahead of the price. That's because the oscillator, in effect, is measuring the rate of change of price movement. Between Days 14 and 23, the oscillator shows the rate of price change is very fast because the direction of the price is changing from down to up. Once the price has bottomed out and started up, then the rate of change slows down because the increments of change are measured in one direction only.

## Three problems

The oscillator can be an excellent technical tool for the trader who understands its inherent characteristics. However, there are three problems encountered in developing a meaningful oscillator:

- Erratic movement within the general oscillator configuration. Suppose that 10 days ago the price moved limit down from the previous day.Now, suppose that today the price closed the same as yesterday. When you subtract the price 10 days ago from today's price, you get an erroneously high value for the oscillator today. To overcome this, there must be some way to dampen or smooth out the extreme points used to calculate the oscillator.
- The second problem with oscillators is the scale to use on the horizontal axis. How high is high, and how low is low? The scale will change with each commodity. To overcome this problem, there must be some common denominator to apply to all commodities so the amplitude of the oscillator is relative and meaningful.
- Calculating enormous amounts of data. This is the least of the three problems.

A solution to these three problems is incorporated in the indicator which we call the Relative Strength Index (RSI):

RSI = 100 – [100 / (1 + RS)]

RS = Average of 14 days' closes UP / Average of 14 days' closes DOWN

For the first calculation of the Relative Strength Index (RSI), we need closing prices for the previous 14 days. From then on, we need only the previous day's data. The initial RSI is calculated as follows:

- Obtain the sum of the UP closes for the previous 14 days and divide this sum by 14. This is the average UP close.
- Obtain the sum of the DOWN closes for the previous 14 days and divide this sum by 14. This is the average DOWN close.
- Divide the average UP close by the average DOWN close. This is the Relative Strength (RS).
- Add 1.00 to the RS.
- Divide the result obtained in Step 4 into 100.
- Subtract the result obtained in Step 5 from 100. This is the first RSI.

## Smoothing effect

From this point on, it is necessary to use only the previous average UP close and the previous average DOWN close in calculating the next RSI.

This procedure incorporates the dampening or smoothing factor into the equation:

- To obtain the next average UP close, multiply the previous average UP close by 13, add to this amount today's UP close (if any) and divide the total by 14.

Steps 3 to 6 are the same as for the initial RSI.

The RSI approach surmounts the three basic problems of oscillators:

- Erroneous erratic movement is eliminated by the averaging technique. However, the RSI is amply responsive to price movement because an increase of the average UP close is automatically coordinated with a decrease in the average DOWN close and vice versa.
- The question, "How high is high and how low is low?" is answered because the RSI value must always fall between 0 and 100. Therefore, the daily momentum of any number of commodities can be measured on the same scale for comparison to each other and to previous highs and lows within the same commodity.
- The problem of having to keep up with mountains of previous data is also solved. After calculating the initial RSI, only the previous day's data is required for the next calculation.

## Just one tool

The Relative Strength Index, used in conjunction with a bar chart, can provide a new dimension of interpretation for the chart reader. No single tool, method, or system is going to produce the right answers 100 of the time. However, the RSI can be a valuable input into this decision-making process.

Commodity Price Charts plots the 14-day RSI, updating the chart through Thursday of each week. Contrary to popular opinion, the choice of the number of market days used in calculating the RSI doesn't really matter because the smoothing nature of the exponential averages reduces the effect of the early days as more data is included.

To help you update the RSI values until the next issue of the charts arrives, we list the "up average" and "down average" as of Thursday on each RSI chart.

## Simplified formula

The procedure outlined earlier for beginning and updating RSIs is from J. Welles Wilder's book and his 1978 Futures Magazine story, which made the RSI a popular technical tool. The following is a simpler and faster method of computing the RSI. The results are the same as Wilder's more complicated method.

To begin a new RSI, just list the changes for 14 consecutive trading days and total the changes. Divide these totals by 14, and you will have the new up and down average. Then proceed with this formula:

RSI = 100 x U / (U + D)

U = up average; D = down average.

The example below is for T-bills. Date | Up | Down |

1/28 | +41 | |

1/29 | | -2 |

2/1 | | -60 |

2/2 | | -7 |

2/3 | +2 | |

2/4 | +1 | |

2/5 | +6 | |

2/8 | | -26 |

2/9 | +11 | |

2/10 | +14 | |

2/11 | 0 | 0 |

2/12 | | -11 |

2/16 | +28 | |

2/17 | | -18 |

Total | **103** | **124** |

1.03 / 14 = .074 = Up ave.

1.24 / 14 = .089 = Down ave.

RSI= 100 x (.074 /.163) = 45.39

To calculate the next day's RSI, multiply the up average (.074) by 13. Add the change for the day, if it is up. Divide the total by 14. Do the same for the new down average. Multiply the new down average (.089) by 13. Add the change for the day, if it is down. Divide total by 14.

Then, proceed with the formula:

RSI = 100 x U / (U + D)

For example, if T-Bills closed up 25 points the next day, calculate the new RSI as follows:

New Up ave. = .074(13) + .25/14 = .087

New Down ave. = .089(13) + 0/14 = .083

New RSI = 100 x .087 / (.087 + .083)

RSI = 51.2

Learning to use this index is a lot like learning to read a chart. The more you study the interaction between chart movement and the Relative Strength Index, the more revealing the RSI will become. If used properly, the RSI can be a very valuable tool in interpreting chart movement. Some of its uses

RSI points are plotted daily on a bar chart and, when connected, form the RSI line. Here are some things the index indicates as shown by examples from the silver chart:

Tops and bottoms — These are often indicated when the index goes above 70 or below 30. The index will usually top out or bottom out before the actual market top or bottom, giving an indication a reversal or at least a significant reaction is imminent.

The major bottom of Aug. 15 was accompanied by an RSI value below 30. The major top of Nov. 9 was preceded by an RSI value above 70. The top made on Jan. 24 was preceded by an RSI value of less than 70. This would indicate this top is less significant than the previous one and either a higher top is in the making or the long-term uptrend is running out of steam.

Chart formations — The index will display graphic chart formations which may not be obvious on a corresponding bar chart. For instance, head-and-shoulders, tops or bottoms, pennants or triangles often show up on the index to indicate breakouts and buy and sell points.

A descending triangle was formed on the RSI chart during October and early November that is not evident on the bar chart. A breakout of this triangle indicates and intermediate move in the direction of the breakout. Note also the long-term coil on the RSI chart with the large number of support points.

Failure swings — Failure swings above 70 or below 30 are very strong indications of a market reversal.

After the RSI exceeded 70 during October, the immediate downswing carried to 65. When this low point of 65 was penetrated the following week, the failure swing was completed.

After the low of Aug. 15, the RSI shot up to 41. After two downswings, this point was penetrated on the upside on Aug. 26, completing the failure swing.

Support and resistance — Areas of support and resistance often show up clearly on the index before becoming apparent on the bar chart. Trendlines on the bar chart often show up as support lines on the RSI. The mid-November break penetrated the uptrend line on the bar chart at the same time as the support level on the RSI chart.

Divergence — Divergence between price action and the RSI is a very strong indicator of a market turning point and is the single most indicative characteristic of the Relative Strength Index. Divergence occurs when the RSI is increasing and price movement is either flat or decreasing. Conversely, divergence occurs when the RSI is decreasing and price movement is either flat or increasing. Divergence does not occur at every turning point.

On the silver chart, there was divergence between the bar chart and RSI at every major turning point. The top made in November was "warned" by the RSI exceeding 70, a failure swing and divergence with the RSI turning sideways while prices continued to climb higher.

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