**Momentum and Strength**

Even though I recently shot an arrow directly at the subject with my dismissal of the value of many indicators , I think it would be good to investigate the math behind indicators. A full understanding can only enhance the ability to understand the market.

To start with it might help to define the difference between Momentum and Strength. Momentum and Strength are two commonly misused terms even though they are two of the most important indicators used. Speaking the same language is always helpful.

Momentum measures the rate of change. I like to see it as a ball being tossed to a friend, and I envision the arc created by the ball as it approaches it's peak. The rate at which it ascends decreases until at the very top the momentum is zero and finally turns negative.

Mathematically Momentum can be expressed as

Momentum = Velocity[now] - Velocity[before].

That's pretty simple, but exactly what is Velocity?

Velocity is change divided by time. It's like 20 miles per hour which is an expression of speed.

So lets say the price changed by +10 points over the past 5 days The Velocity is +10 points / 5 days. So we would say the Velocity is 2. Velocity is an expression of speed, not an express acceleration or deceleration.

So going back to our description of Momentum

Momentum = Velocity[now] - Velocity[before].

By subtracting the previous average speed of the market from the current speed we can see if Price is gaining or loosing Momentum. Now let's say tomorrows price is 2 points lower than 5 days before, going from +10 to +8. Our velocity will have changed from 2 to 1.6 (+8/5= 1.6)

As the ball looses upward momentum (Not Travel Speed) it finally goes from positive to negative at the peak.

Charting this arc helps us see a pattern of rising Momentum peaking and then falling just as a ball would travel to our friend.

Here's the basic formula for Momentum.

The brackets [ number ] describe how many bars back to look for the value

# Momentum

input length = 12;

plot Momentum = close - close[length];

So what is Strength?

Strength is a comparison of upward movement to downward movement

There are different ways to calculate this. This first example is from Wikipeadia. It's a little more difficult to write and understand than the next example. But I want to demonstrate that there are different ways to express Strength.

input Length = 14;

def delta = close[0] - close[1];

def D= if delta > 0 then 0 else delta; # Don't count this if it is up

def U= if delta < 0 then 0 else delta; # Don't count this if it is down

def Up = ExpAverage(U,Length); # Take the Exponential average of the up moves

def Dn = ExpAverage(D,Length); # Take the Exponential average of the down moves

def RS = Up/Dn; Plot RSI =100-(100/1+RS); # This just makes it pleasant to view.

Here is the expression which ThinkOrSwim uses. Even though it's more simple, it's probably the better algorithm.

input Length = 14;

def NetChgAvg = ExpAverage(price - price[1], length);

def TotChgAvg = ExpAverage(AbsValue(price - price[1]), length);

def ChgRatio = if TotChgAvg != 0 then NetChgAvg / TotChgAvg else 0;

plot RSI_EMA = 50 * (ChgRatio + 1);

Either way, Strength is basically a comparison of the overall movement compared to the sum of movement over that same time.

It's the conviction of the market. In other words if the market is making large swings, but trading within a range then the Strength would be low. It would demonstrate bouncing momentum and low overall strength. You could also think about it as commitment. How committed is the market to a trend? A Strong market is committed to a trend.

As a side note I think we have all notice how a market will shift quickly from an uncommitted move to a market with conviction.

My take on this is that the market must make up for lost time. Generally we will see the market break out in the direction of the previous move, but occasionally the weakness is a period of change of direction.

So now we have these indicators. Momentum and Strength. How can they help us understand the market? If Momentum is increasing or decreasing, we can assume it will continue to move in the same direction, but we often we see the market abruptly turn. How does this relate to a ball being tossed?

Here's the answer. We can generally find the relationship in market patterns. Where did the market turn before? Think of this turning point as a brick wall that the market (the ball) will bounce off of.

What about strength? Strength is weak when the market moves sideways. Knowing when strength will resume is the key. Can you guess how we can determine this point?

It's through symmetric patterns which we can draw with channels and Andrews Pitchforks. Now you see how indicators and pattern analysis work together to predict the markets moves.

Notice the symmetry in the fork drawn below. The next time Price tests the upper tine it will most likely break through.

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