Market Dynamics and its Application to Measuring and Forecasting Price Movement and Support Levels

Market Dynamics and its Application to Measuring and Forecasting Price Movement and Support Levels of Traded Investment Instruments1

By Joshua F. Dayanim May 30, 2009

Abstract Market Dynamics presents an approach for measuring and forecasting price movement attributes of traded investment instruments, pursuant to a performance impacting event such as revenue and earnings release, change in industry attractiveness, change in capitalization or liquidity, or a broad market movement. A time derivative method is used to calculate price movement measures such as expected price change, target price, price support level, and event time horizon. Market Dynamics develops and utilizes parallelisms between price attributes and classical and fluid mechanics, and establishes measures such as pressure, kinetic and potential energy, density, velocity, intensity, and viscosity that are used to analyze, forecast, and validate the price movement behavior. Market Dynamics has applicability to a number of fields including investment analysis and decision support through measurement of price appreciation potential, as well as technical chart analysis in areas such as determining support and resistance levels and analyzing and measuring price movements that result in an observed chart pattern.

1

Notices: Copyright Š 2009 Joshua F. Dayanim. All rights reserved.

Patent Pending on methods and measures described in this article.

1

Introduction Price of an investment instrument may vary pursuant to the release of an earnings surprise, attractiveness of the industry or asset class, market liquidity and availability of buyers and sellers, overall market movements based on macroeconomic factors, or other significant news.

Various methods exist for valuing an instrument utilizing fundamental or technical analysis. These methods may consider fundamental factors such as present value of expected future earnings, growth rate, historical and industry performance. Alternative technical analysis methods may leverage chart pattern recognition and attempt to anticipate direction of a price movement through comparison with similar chart patterns.

Several ratios are commonly used when describing investment instruments including Earning per Share (EPS) and Price to Earnings Ratio (PE) to name a few. Daily trading information can be described using various indicators such as trade volume which is the total number of shares bought or sold, up vs. down trade ratio which may be considered an indicator of the overall price direction, money flow rate which is the total value of traded shares, and market capitalization which is a product of share price and total number of issued shares. Terminology can vary across the varying instruments but parallels can be drawn. For example, in case of bonds, share price is the open market value while earnings is the coupon rate multiplied by the par value.

What is needed is a method to forecast the expected price movement behavior pursuant to one or more events that result in a change in EPS and/or PE values of an investment instrument. This includes the expected price change, target price, and time window to reach the target price. Investors also need to measure and validate whether a supported price level has been reached around an observed price point, or whether to expect additional price volatility. A measure of spread between the current and target price points indicates the remaining upside potential or downside risk for an investor. Further, by providing a method for measuring, forecasting, and validating price movements Market Dynamics can be used to explain price movement behavior such as potential, speed, and direction of additional movements, and to analyze and explain observed technical chart patterns.

Dynamics of Price Movement The expected price movement and target price of an investment instrument pursuant to an event can be determined by applying a time derivative to the price equation, as follows: P = EPS ∗ PE

[03]

∆P = ∆EPS ∗ PE + EPS ∗ ∆PE

[04]

where ∆P indicates the expected price change as result of a change in Earnings Per Share (EPS) or Price to Earnings (PE) ratio of the instrument. Another indicator ∆T specifies the event time horizon during which the impact of the event if fully materialized.

Example: Table 1. and Fig. 1. illustrate historical price and trade data for AT&T shares for the time period of Jan – Feb 2006. The covered period includes a stable broad market condition, and a single company specific event, in this case an earnings increase as indicated by the rise in the EPS value on 2

1/25/2006. The target price for AT&T shares following an EPS change event is estimated as follows: EPS0 = 1.16; ∆EPS = 1.42 − 1.16 = 0.26

[05]

PE0 = 21.26; ∆PE = 0

[06]

∆P = 0.26 ∗ 21.26 + 1.16 ∗ 0 = 5.53

[07]

P0 = 24.66; PTarget = P0 + ∆P = 24.66 + 5.53 = 30.19

[08]

where P0 , EPS0 , and PE0 are measured at the starting point of the event, while PTarget is the expected target price. For this calculation the observed drop in PE is ignored as it appears to be a side effect of the EPS adjustment. The expected target price may be compared against the peak price point of $28.65 achieved on 2/16/2006 following a continuous rise triggered by the EPS change event.

An event or condition may alternatively affect the PE value while earnings remain unchanged. For example one may assume that the PE value of an instrument will follow and match that of the industry it competes in given similar growth, profitability and performance characteristics. In a situation where an equity has a materially different starting PE value vs. its industry average, the instrument may be considered under-valued and the expected change in price can be calculated as ∆P = EPS ∗ ∆PE where ∆PE indicates the gap between the equity and its industry average PE values.

Various conditions or events may impact EPS or PE values separately, concurrently, or consecutively, and the impact or change in these values can be used to determine the price movement of the investment instrument from a former stable price point.

Similarly, Market Capitalization of an investment instrument is generally calculated using the following relationship: Market Capitalization (MC) = Total Shares Outstanding ∗ Share Price = STotal ∗ P

[09]

with time derivative method applied to MC as follows: ∆MC = ∆STotal ∗ P + STotal ∗ ∆P

[10]

where ∆STotal indicates change in the total number of outstanding shares. This can be used to calculate the change in price for an event that modifies the number of shares or market capitalization.

Example: the expected price of the instrument upon issuing new shares may be calculated for a scenario where 10% in additional new shares are issued provided that Market Capitalization remains unchanged, as follows: ∆P =

(∆MC −∆S Total ∗P) S Total

=

0−∆S Total ∗P S Total

=

−∆S Total S Total

∗P

[11] 3

∆P = −0.1 P

[12]

A more common scenario is where the number of outstanding shares in an instrument is fixed and the market capitalization changes: ∆MC = 0 ∗ P + STotal ∗ ∆P = STotal ∗ ∆P

[13]

∆MC

∆P = S

[14]

Total

Market Dynamics Formulation The time derivative approach is extended into a more general method which draws parallelism between price movement behavior of investment instruments and classical mechanics and fluid dynamics concepts. It defines and lays out procedures for measuring price movement attributes which can be used to analyze or forecast price targets and price movement behavior. The following relationships are well known in classical mechanics and fluid dynamics: Force = Pressure * Area

[15]

Work = Force * Distance

[16]

Work = Change in Potential Energy (stored energy in a system)

[17]

Energy = Kinetic Energy + Potential Energy

[18]

Kinetic Energy = Pressure =

1 2

1 2

m v 2 ; where m is mass of an object and v is the velocity

ρ v 2 ; where ρ is density and v is velocity of a fluid

[19] [20]

A parallelism is now drawn between price movement of shares in an investment instrument and a fluid under pressure. Such pressure may be exerted by events affecting EPS or PE movements from an initial stable price level. The following equivalencies are defined using “:=” notation: Volume ∶= Number of traded shares = S

[21]

Pressure differential ≔ Price change = ∆P ($/share)

[22]

where Volume is the equivalent fluid volume, and $/share is the unit of measure for price change ∆P. These equivalencies are used to calculate the Work performed during a price movement, as follows: Work = Force * Distance = Pressure * Area * Distance = Pressure * Volume

[23]

Work = S * ∆P ($)

[24]

The latter assumes that all exchanged shares move an equal amount of ∆P. The number of traded shares multiplied by the price change is an indicator of the amount of new money investors have committed to the investment instrument and is represented by Work. As work is performed on a 4

system its potential energy increases in the absence of any frictional forces or extraneous pressures.

Potential Energy of an investment instrument is then the sum of all incremental Work performed on the system, as follows: Potential Energy (Ep ) =

Work =

S ∆P = STotal ∗ P = MC ($)

Ep

Potential Energy Density = Volume = S

Ep Total

= P ($/share)

[25] [26]

which in effect states that the market capitalization or potential energy of an instrument is equal to the total investment in the instrument, and that price is an indicator of the stored energy density in the instrument.

As the full extent of an expected price change may not be realized immediately after an event, the impact may be viewed as an initial impulse force resulting from the pressure differential brought on by the event, which materializes in the form of a Kinetic Energy of movement. This Kinetic Energy subsequently transforms into Potential Energy in the form of a newly established price point.

Applying the conservation of energy, the resultant Kinetic Energy attributed to the event can be equated with the Work performed during the price movement or the change in Potential Energy as follows: Kinetic Energy (Ek ) =

1 2

m v 2 = S ∗ ∆P ($)

[27]

It should be noted that this calculation assumes a positive movement in price. In the event of a price drop due to a lowering EPS value, − S ∆P should be used on the right side of the equation. In such event the negative pressure differential results in a downward oriented movement as energy is transferred out of the investment instrument.

Kinetic energy density and velocity at an observation time t can then be determined as follows: Kinetic Energy Density = : ρk = v2 2

=

v=

Ek m

S

= m ∆PT =

2 ∆P T P

=

∆P T ρ

2 (P T −P) P

=

∆P T

Ek S

= ∆PT = PT − P ($/share)

(no unit)

P P

= 2( PT − 1)

1

2

[28] [29]

(no unit)

[30]

where PT is the target price and P is the observed price at time t. More accurately, velocity can be stated as v± = ±

2∗ |∆P T | P

in order to account for the direction of movement or velocity. The above

uses the relationship that mass density ρ is mass divided by volume, and utilizes other equivalencies: ρ ≔ P , Potential Energy Density or Mass Density ($/share)

[31]

m ≔ S ∗ ρ = S ∗ P = MF ($)

[32] 5

and establishes that mass is the total trade value of the investment instrument or Money Flow (MF) over the event time horizon ∆T. The ratio of Market Capitalization to Money Flow can be viewed as Investment Leverage and is described in the following manner: MC

Leverage (L) ∶= MF =

S Total P SP

=

S Total

[33]

S

indicating that leverage is the ratio of market capitalization, or the total amount of investment in the instrument, divided by the amount of trading activity in the aftermath of the event. The higher the leverage the more volatile the price level and subject to sudden swings.

The MF derivation can be further fine tuned for the special case of a linear price movement where ∆P P = P0 + β t, with β = ∆T , and ∆P = PT − P0 or the expected change in price, using a constant S

trade volume of σ = ∆T as shown below: MF =

∆T s 0

∗ P dt =

∆T S 0 ∆T

S

P0 + β t dt = ∆T P0 t +

β 2

t2

∆T 0

= S(P0 +

∆P 2

= S Pavg

[34]

where s is the trade volume at time t, with S the total trade volume and Pavg is the average price value over the event time horizon ∆T. However, as the instrument’s trade volume is unlikely to remain at a constant level, and the price is likely to fluctuate over time, a measure of support for the target price is defined as the sum of incremental new investments divided by the change in market capitalization value, as follows: Support =

N n =1

{s n ∗∆P n }

[35]

S Total ∗ ∆P

where N is the number of trade transactions during an observation time period starting at the event onset, while n is an individual trade transaction involving s n shares, and ∆Pn = Psell − Pbuy indicates the incremental new investment or the difference of the sale price Psell and the seller’s cost basis Pbuy . As consecutive trades transactions are undertaken, the incremental new investment is the contribution of each buyer in terms of price appreciation or discount relative to the seller’s original purchase price or cost basis. As the Support ratio for the change event moves towards the value of 1, there is increased support for the target price level as the change in capitalization is fully funded through new investment, in effect resulting in a newly established price support level. Once at this new support level, a continuing price climb would indicate an over-investment condition and may trigger a price reversal, barring any additional events.

For a special case of constant daily trade volume sd , the share turnover rate or turnover frequency may be defined as, Turnover Rate (f) = S

sd

[36]

Total

6

1

which is the portion of outstanding shares exchanging hands each day. The inverse value τ = f represents the turnover cycle time or the number of days required for all shares to exchange hands ∆T once and τ is the number of turnover cycles within the event horizon. As Fig. 4 depicts, the cost basis and incremental investment vary after each turnover cycle by the following amounts: δP = β ∗ τ

[37]

δMF = STotal ∗ δP

[38]

where δP indicates incremental price movement, and δMF incremental money flow. During each turnover cycle all shares or an equivalent number exchange hands for an average price movement of δP, which establishes a new cost basis. The incremental money flow per outstanding share per day δP is then simply τ or β, that is the net change in daily price, assuming a high turnover rate and a relatively short cycle time. The support ratio and leverage can be rewritten, on a per share basis, and for observation time t and observed price P as follows: Support =

β ∗t

Leverage ∶=

S Total

∆P

=

sd ∗ t

∆P 0 ∆P

t

= ∆T

[39]

1

= f∗t

[40]

where t is the observation time measured from the onset of the event, ∆P0 = P − P0 , and ∆P = β ∗ ∆T. At t = ∆T the support level equals 1.

Example: In the AT&T example, for the period of rise immediately following the EPS change from 1/25/06 to 2/16/06, leverage and support ratios can be calculated using Table 1 data in the following manner using an estimated 3.4B in outstanding shares: L =

3,400M 276M

≈ 12.3, on 2/16/2006 $3.79

Support = $5.53 = 0.685, on 2/16/2006 1

Turnover Rate = Leverage

1

∗t

= 12.3 ∗ 16 = 0.0051

[41] [42] [43]

using a 16 day observation period, resulting in a 200 day or roughly 10 month turnover cycle time, assuming 20 business days per month.

Example: An extended inspection of the price movement as displayed in Fig. 3 reveals a halt in price momentum, followed by a drop, before a continuation of the rise in price and a continued increase in money flow supporting multiple consecutive upwards EPS adjustments. The EPS value reached a high of 1.98 near October 2007 as observed in Fig. 3. The expected price adjustment for this elongated period can be estimated assuming a stable PE environment (∆PE = 0) and ignoring any market or industry movements during this time period, as follows: ∆P = ∆EPS ∗ PE = (1.98 – 1.16) * 21.26 = $17.43 7

[44]

PTarget = 24.66 + 17.43 = $42.09

[45]

which compares closely to an observed peak value of $42.27 reached on 9/24/2007. The contribution is primarily from EPS changes as the PE was restored to its original value following the initial drop and in the absence of any material events affecting a change to PE. Using a rough estimate of 16M for daily trade volume, 20 business days per month, and a linear price increase from 1/25/06 through 9/28/07, the Support ratio may be estimated as follows: Support =

∆P observed

=

∆P

$42.097−$24.66 $17.43

$17.61

= $17.43 = 1.01

[46]

where ∆Pobserved = Pobserved − P0 , and Pobserved the observed price on 9/28/07. As the support ratio approaches the value of 1 it indicates full support for the observed price level. The time period to reach the expected target price may be estimated by dividing the observation time t by the observed Support ratio and is evaluated using: t

∆T = Support

[47]

and the results are provided in Table 2 at each event point. The final value as of 9/24/2007 is around 426 days or roughly 21 months, counting only business days when market is open, to achieve full Support which sets the estimated event time horizon at around 10/25/2007. As noted, multiple consecutive EPS increases resulted in a sustained price movement over this time period. Future expectations of EPS adjustment may also serve to prolong the price movement; however, if not backed by actual events such forecasted price movements will likely reverse.

As vT = 0 due to full transfer of kinetic energy to potential at time ∆T, and since previously established, we may define a new attribute of Divergence, as follows: Divergence D ≔

∆P T P

=

PT P

−1

v2 2

=

∆P T P

as

[48]

which provides an indicator of the gap or spread between the current price level and the target price point. As the price moves towards the target level, the divergence approaches 0. A negative divergence value indicates an expected price drop, while a positive value indicates an expected rise.

The higher the absolute value of the divergence the bigger the gap between the current price and the target level, and the larger the corresponding opportunity for price movement. Divergence also indicates what portion of the initial kinetic energy has transferred to potential energy.

Technical Analysis among other factors relies on the concept of Support and Resistance levels in explaining the movement of stock charts. In Market Dynamics price movements are attributed to changes in EPS or PE, where the response to an event will result in a new price point or potential energy level. As the associated Support ratio nears 1, a new Support level is established which acts as a stable price level and reflects new investment flow into (for a price rise) or out of (for a price drop) the instrument that fully accounts for the change in price level and the adjusted market capitalization. Such stable price level represents a wave of new investment into or out of the instrument triggered by the underlying events. As investors in each wave react to a common event and expect a return on their investment, they appear to act in unison to changes in the underlying 8

instrument price and to each new event. In the case of multiple consecutive events with overlapping time horizons the price movements are superimposed or combined and an aggregate Support level may be established.

Example: Table 2 details six distinct EPS events during the Jan 2006 through Mar 2007. It uses the Market Dynamics methods to calculate the expected price movement ∆P, event duration or time horizon ∆T, along with the target price point for each individual event. The table also lists the superposed or combined valuation for the six closely spaced events with overlapping event time horizons. Table 3 details the anticipated monthly price movements attributed to each successive event by adding each upcoming event’s contribution to the price point resulted from the preceding event. The results are shown graphically in Fig. 5 with the solid black line indicating the aggregate or superimposed performance. Table 4 details the Support ratios over time for each event and the aggregate Support level. The results are shown graphically in Fig. 6. As calculations demonstrate a Support level of 1 is attained around March 1, 2007 at a price point near $39.44, close to the anticipated target price of $42.27. Fig. 2 details actual historical performance of AT&T stock. For the period after March 1, 2007 the price continued to hover in the range of $39 and $43 until January 2008 where it dropped. However, a rebound is observed in April 2008 where the price climbed back to the established $39 Support level and stayed near that level until June 2008, after which the drop began a downward spiral due to the deteriorating market and economic conditions.

Additional classical attributes related to price movement are derived next and measured. The acceleration or change in velocity is determined as follows: ∆v a= = ∆T =

−1

2 PT −1 2 P

P

( ) 2 ∆P

1

2

T

PT P2

=

−1

2

−PT −1 ∆PT = P2 2 P

−P T

−1

2

PT P2

; with the unit of (1/$)

2∆P T P 3 2

[49]

where a sign adjustment is also required here in the event of a drop in price and the formulation changed to a = ∓

PT

.

2|∆P T | P3 2

The distance travelled is measured as follows: ∆r = r − r0 =

t v 0

dt

[50]

where t is in the range of 0 and ∆T. For the special case of a linear price movement, price is calculated as follows: P(t) = P0 + β t; where β =

∆P ∆T

=

PT − P0

[51]

∆T

∆PT = PT − P = P0 + ∆P − P0 + βt = ∆P − βt

[52]

∆P T

[53]

P

∆P−βt

=P

0 +β

t

9

and the distance travelled can be calculated as follows: ∆r =

∆r =

∆r =

∆r =

∆r = ∆r = ∆r =

t v 0

dt =

2β

2β

2β

t 0

t 0

2 ∆P T

∆T−t P0 β +t

∆T − t (

P0

2β

∆T−t P

2 β 2 β

β

β

P 0 +β t

dt

[54]

[55]

∆T − t (

∆T∗P 0

2 (∆P−βt)

dt

P0

2β

t 0

dt =

P

1

P0

1

P0

β + t) – 2 ∆T +

β + t) – 2 ∆T +

1

– 2 ∆T +

P0

β tan

−1

P ∆T− 0 β −2t ( ) P 2 ∆T−t ( 0 β +t)

| 0t

β tan

−1

P ∆T− 0 β −2t ( ) P 2 ∆T−t ( 0 β +t)

−

P ∆T− 0 β

−1 β tan ( 2

1

– 2β PT tan−1 (

∆P−P 0 −2βt

2 β ∆T−t P

∆T∗P 0 β

∆P−P 0 −2βt

2

2

1

∆PT ∗ P – 2 PT tan−1 (

∆P−βt P

∆P T −P 2 ∆P T ∗P

) −

)

[57]

) − 2β

1

∆P − βt P – PT tan−1 (

) − 2 β

[56]

2 β

∆T∗P 0 β

1

– 2β PT tan−1 (

∆P−P 0

2 β ∆T∗P 0

1

∆P−P 0

2

2 ∆P∗P 0

∆P ∗ P0 – PT tan−1 ( 1

)

∆P ∗ P0 – 2 PT tan−1 (

∆P−P 0

2 ∆P∗P 0

)

[58] )

[59] [60]

with unit of ( $ Day ).

The momentum and momentum density can be determined as follows: Momentum = m v Momentum Density =

[61] Momentum Volume

=

m S

v = ρ v = ±P 2

|∆P T | P

= ± 2 P |∆PT | ($)

[62]

Intensity is defined as the power per unit of time, or equivalently as the product of energy density and velocity: Intensity I = P ∗ v = ±P ∗

2 |∆P T | P

= ± 2 P |∆PT | = Momentum Density ($)

10

[63]

Volume Flow Rate (VFR) is defined as a product of area A by the effective velocity across the area.

On the other hand, Viscosity (R), also known as fluidity, or resistance to flow of a fluid, is an indicator of how fast a fluid may move under a pressure differential. R is defined as the ratio of pressure differential to VFR. These two relationships can be expressed together as follows, wherein the trade volume s(t) represents the volume flow rate: Volume Flow Rate ∶= s t = A v = A=

s t

s(t)

=±

v

2 |∆P T | P

=±

sP 2 P |∆P T |

=

∆P

[64]

R sP

[65]

(Share)

I

or equivalently, Energy Flow Rate = A ∗ I = s ∗ P

[66]

with the latter indicating that Energy flow rate, a product of intensity and area, equals the value of traded shares. Additionally, viscosity at an observation time t and observed price P is measured as: R=

∆P T Av

∆P T

=± A

1

2| ∆P T | P

= ±A

P |∆P T | 2

I

= 2A

[67]

($/share)

and for the special case of a constant volume flow rate, that is a constant trade volume over time period ∆T, the effective viscosity is calculated as follows: R=

∆P S

∆P

β

= σ ∆T = σ

[68]

which indicates viscosity represents share price change per trade.

Impulse is a product of force and impact duration or equivalently a product of mass and change in velocity, and can be measured for the applied force resulting in the onset of the event: Impluse = Force ∗ Time = m ∆v Impluse Density =

m ∆v S

[69]

= ρ ∆v

[70]

Impluse Density|t=0 = ρ0 v0 − 0 = ρ0 v0 = P0 v0 =

2 P0 ∆P0 ≔ I0

[71]

Example: Figures 7-10 depict velocity, intensity, acceleration, and divergence as a function of price (x-axis) for AT&T during the period of 1/25/2006 through 9/24/2007. Sample values are calculated below: D0 =

∆P 0 P0

=

17.43 24.66

= 0.70681

[72]

∆T ≈ 426 business days, estimated at 21 months from Table 2 11

[73]

β=

∆P ∆T

426

2 ∆P

v0 = a0 =

17.43

=

P0

= 0.040915 ($/day) 2∗17.43

=

24.66

−P T 2∆P P 0 3 2

=

[74]

= 1.18896

−42.27 2∗17.43 ∗ 24.66 3 2

[75] = -0.058463 (1/day)

[76]

∆rT = 231.12-170.35=60.77 ( $ Day )

[77]

I0 =

2 P0 ∆PT0 = 2 ∗ 24.66 ∗ 17.43 = 29.32 ($)

[78]

IT =

2 PT ∆PTT = 2 ∗ 42.27 ∗ 0 = 0

[79]

where subscript T indicates value at time t = ∆T, and the area is calculated as: A0 =

s P0

AT =

s PT

I0

I ∆T

=

16M

shares day

∗24.66

29.32

= 13.457M (Share)

[80]

→ ∞

[81]

and the effective value of R can be estimated as follows: I

29.32

R 0 = 2 A0 = 2∗13.457M = 1.089 ∗ 10−6 ($/Share) 0

I

R T = 2 AT → 0

[82] [83]

T

which indicates a lesser viscosity or change in price per traded share as the target price nears. For a linear price movement and constant trade volume, the effective viscosity over the time period is: R Effective =

∆P S

=

17.43 sha res 16M day

∗426 day

= 2.557 ∗ 10−9 ($/Share)

[84]

and while this is a reasonable approximation a more accurate treatment would utilize the actual daily trade volumes over the period.

Example: Market Dynamics can be applied to a variety of situations. For example, certain investment instruments may lack adequate liquidity or flow such as lightly traded stocks or closed end funds. This situation may be paralleled to a “choked flow” condition observed in fluid dynamics. The restriction imposed by the lack of liquidity is similar to a flow through a small orifice where the velocity reaches a maximum and the flow becomes choked. The restriction results in a decrease in the downstream pressure which is the trade value of shares. This explains why such closed end funds or other low liquidity instruments are typically priced below their underlying equities or peer group valuation levels. In a classic choked flow, Mass Flow Rate is proportional to the upstream Pressure or open market price, as well as the Area of the hole, as follows: 12

Mass Flow Rate MFR ∝ Popen ∗ Aorifice

[85]

while MFR can also be written as: s

MFR = Density ∗ Area ∗ Velocity = ρ A v = P A v = P v v = P s

[86]

which is an equivalent expression to Money Flow rate. In the case of a constrained flow, such as a closed fund, MFR may be recasted as: MFR = Popen ∗ Aorifice ∗ vmax = Pclosed ∗ sclosed

[87]

where the left side represents the flow within the orifice where the velocity is capped and pressure matches the open market pressure, while the right side represents the downstream flow. As mass is conserved during the flow, in the area past the orifice the investment rate which is a product of price and trade volume is reduced when compared to an open market. This is a result of the choked flow where vmax is lower than the velocity within the orifice for a non-choked or open market flow of similar pressure and area. The reduction in investment rate can present itself as a reduction in price, trade volume, or both.

Conclusion Market Dynamics presents a method for measuring the expected price, price movement, support level, and related movement attributes of an investment instrument pursuant to a material event that affects the initial price level. Additional measures are provided for calculating price stability and support level, dispersion or spread from the expected target price, event time horizon, and related price movement behavior. These measures can inform investors of the potential, direction, and speed of additional price movements.

By drawing parallels to classical mechanics and fluid dynamics, various measures describing the price movement are defined and calculated. Such measures include pressure resulting from the onset of an event, potential and kinetic energy associated with an investment instrument and its price movement, velocity of price movement, density, momentum, intensity, and resistance to movement among others. These measures are used to calculate, forecast, validate and analyze performance of traded investment instruments.

The presented methods and measures assist investors with forecasting and validating whether a supported price level has been reached around an observed price point, or whether to expect additional price volatility. A measure of spread between the current and target price points indicates the remaining upside potential or downside risk for an investor. Further, by providing a method for measuring, forecasting, and validating price movements Market Dynamics can be used to explain price movement behavior such as potential, speed, and direction of additional movements, and to analyze and explain observed technical chart patterns.

About the Author Joshua F. Dayanim holds several graduate and undergraduate degrees including MBA from Villanova University, MS in Electrical Engineering from the University of Pennsylvania, and BS in 13

Physics and Electrical Engineering from the University of Maryland. Currently, he works as a Sr. Director of IT Operations for a healthcare company. The motivation behind the research presented in this article has been a lack of fundamental understanding of why technical analysis works. He can be reached at jdayanim@gmail.com. *****

14

Fig. 1. Historical Price Chart for AT&T, Jan–Feb 2006

Fig. 2. Historical Price Chart for AT&T, Apr 2007 – Jul 2008

15

Fig. 3. Historical Price, EPS, PE, and Volume Charts for AT&T, Jan 2006 – Sep 2007

16

Fig. 4.Turnover Cycle Time and Moving Cost Basis

Fig. 5. Price Movement for Superimposed EPS Events, AT&T Jan 2006 – Sep 2007 45 40

Event 1

35

Event 2

30

Event 3 Event 4

25

Event 5

May-07

Mar-07

Jan-07

Nov-06

Sep-06

Jul-06

May-06

Mar-06

Jan-06

20

Event 6

Fig. 6. Support Ratio for Superimposed EPS Events, AT&T Jan 2006 – Jun 2007 1.6 1.4 1.2

Support 1

1

Support 2

0.8

Support 3

0.6

Support 4

0.4

Support 5

0.2

Support 6

0

Aggregate

17

Fig. 7-8. Velocity and Intensity for AT&T, Jan 2006 – Sep 2007 Fig. 7: v t = ± 2

Fig. 8: Intensity = ± 2 P |∆P|

|∆P| P

Fig. 9-10. Acceleration and Divergence for AT&T, Jan 2006 – Sep 2007 Fig 9.: a = ∓

P ∆T

Fig. 10: D =

2|∆P| P 3 2

18

∆P P

Table 1. Historical Data for AT&T, Jan-Feb 2006 Date 1/17/2006 1/18/2009 1/24/2006 1/25/2006 1/26/2006 1/27/2006 1/30/2006 1/31/2006 2/1/2006 2/2/2006 2/3/2006 2/6/2006 2/7/2006 2/8/2006 2/9/2006 2/10/2006 2/13/2006 2/14/2006 2/15/2006 2/16/2006

Price 24.82 24.82 24.66 25.21 25.51 25.89 26.05 25.95 26.55 26.52 26.79 27.05 26.92 27.13 27.13 27.48 27.65 28.29 28.32 28.45

Price Change

0.55 0.85 1.23 1.39 1.29 1.89 1.86 2.13 2.39 2.26 2.47 2.47 2.82 2.99 3.63 3.66 3.79

EPS 1.16 1.16 1.16 1.42 1.42 1.42 1.42 1.42 1.42 1.42 1.42 1.42 1.42 1.42 1.42 1.42 1.42 1.42 1.42 1.42

Trade Up/Down Money PE Volume (M) Ratio Flow ($M) 21.414 9.103 21.397 12.445 21.26 10 1.888 -268 17.75 15.592 0.837 98 17.96 15.638 2.337 199 18.23 16.099 1.941 424 18.35 13.101 1.035 523 18.27 16.168 0.737 301 18.70 18.627 1.456 710 18.68 14.939 0.3 693 18.87 21.797 0.533 967 19.05 17.963 1.541 1273 18.96 14.168 0.332 1152 19.11 13.628 1.679 1504 19.11 14.174 0.834 1347 19.35 16.478 0.86 1591 19.47 16.691 0.512 1629 19.92 23.06 2.725 1685 19.94 14.124 1.658 1962 20.04 14.128 4.111 1988

Table 2. Historical Data for AT&T, Jan 2006 - Mar 2007 Measurement Date EPS

Description Event Date EPS value after event EPS change for the dEPS event P_Observed Observed price P_target Target price Expected price movement due to dP_event event Expected cumulative dP_total price movement dT_start Days from the start Support_Aggreg Support ratio for ate preceding events Time horizon for dT_Aggregate preceding events

Start Event 1 Event 2 Event 3 Event 4 Event 5 Event 6 End 1/24/2006 1/25/2006 4/20/2006 7/18/2006 10/18/2006 1/20/2007 3/1/2007 9/24/2007 1.16 1.42 1.5 1.65 1.8 1.9 2 2

24.66 24.66

0.26 25.21 30.19

0.08 25.34 31.89

0.15 26.99 35.08

0.15 32.94 38.27

0.1 35.24 40.39

0.1 36.71 42.52

5.53

1.70

3.19

3.19

2.13

2.13

5.53 1

7.23 57

10.42 116

13.61 156

15.73 218

17.86 244

17.86 420

0.123

0.322

0.795

0.778

0.766

0.986

463

360

196

280

319

426

19

42.27 42.52

Table 3. Price Movement for Superimposed EPS Events, AT&T Jan 2006 - Jun 2007 Date Event 1 Event 2 Event 3 Event 4 Event 5 Event 6

Jan-06 Feb-06 24.66 24.79 24.66 24.79 24.66 24.79 24.66 24.79 24.66 24.79 24.66 24.79

Mar-06 25.66 25.66 25.66 25.66 25.66 25.66

Apr-06 26.53 26.53 26.53 26.53 26.53 26.53

May-06 27.41 27.71 27.71 27.71 27.71 27.71

Jun-06 28.28 29.45 29.45 29.45 29.45 29.45

Jul-06 29.15 30.85 30.85 30.85 30.85 30.85

Aug-06 Sep-06 Oct-06 30.02 30.19 30.19 31.72 31.89 31.89 32.07 33.11 33.98 32.07 33.11 33.98 32.07 33.11 33.98 32.07 33.11 33.98

Nov-06 Dec-06 30.19 30.19 31.89 31.89 34.85 35.08 35.20 36.30 35.20 36.30 35.20 36.30

Jan-07 Feb-07 30.19 30.19 31.89 31.89 35.08 35.08 37.17 38.04 37.17 38.35 37.17 38.35

Mar-07 30.19 31.89 35.08 38.27 39.44 39.44

Apr-07 30.19 31.89 35.08 38.27 40.31 41.19

May-07 30.19 31.89 35.08 38.27 40.39 42.14

Jun-07 30.19 31.89 35.08 38.27 40.39 42.52

Table 4. Support Level for Superimposed EPS Events, AT&T Jan 2006 - Mar 2007 Date Jan-06 Support 1 Support 2 Support 3 Support 4 Support 5 Support 6 Aggregate

Feb-06 0.00

Mar-06 0.02

Apr-06 0.07

0.00

0.01

0.02

May-06 0.15 0.01

0.05

Jun-06 0.26 0.09

Jul-06 0.39 0.22

Aug-06 0.56 0.32 0.00

0.10

0.17

0.24

Sep-06 0.67 0.41 0.05

0.32

20

Oct-06 0.77 0.50 0.15

Nov-06 0.86 0.60 0.30 0.00

0.40

0.51

Dec-06 0.96 0.69 0.41 0.05

0.62

Jan-07 1.05 0.79 0.51 0.15

Feb-07 1.14 0.88 0.60 0.30 0.00

Mar-07 1.24 0.97 0.70 0.41 0.07

0.74

0.88

1.02

Apr-07 1.33 1.07 0.79 0.51 0.21 0.04 1.23

May-07 1.43 1.16 0.88 0.60 0.32 0.15 1.40

Jun-07 1.52 1.26 0.98 0.70 0.41 0.28 1.52