Analytica Docs - User contributions [en]

Meta-Inference

2009-07-10T15:36:22Z

Rmorgan: /* Notable attributes */

(TBD: Under construction)
(This is advanced reference that is beyond the scope of the user guide)

= Introduction =

''Meta-Inference'' refers to logic in your model that reasons about (or manipulates) the model itself. For example, an expression that identifies all Chance-node ancestors of variable X is performing meta-inference.

Meta-inference is an advanced topic, appropriate only for the more experienced Analytica modelers. However, the ability to create meta-inferential algorithms opens many doors for expanding the capabilities of Analytica itself. For example, in the past, users of Analytica implemented meta-inferential algorithms including the following:

* Providing an advanced "Find object" form, that locates objects matching rich search criteria.
* Changing the colors or sizes of nodes in influence diagrams to reflect the results of sensitivity analyses.
* Changing the colors of nodes to reflect a special color scheme.
* Implementing specialized forms of sensitivity analyses.
* Running stochastic simulations in batches, so that huge models or huge sample sizes can be utilized within the constraints of available memory.
* Collecting time/memory profiling information after demanding computations.

Other examples of potential meta-inferential algorithms could also include:
* Triangulation and propagation algorithms to compute discrete posterior probabilities in Markov field models such as Bayesian networks.
* Algorithms to automatically re-arrange (layout) variables in an influence diagram.

= Objects and Handles =

Meta-inference involves reasoning about Analytica objects, including the various nodes that appear on diagrams (Variables, indexes, buttons, etc), and the attributes that constitute the properties of those objects. The fundamental unit of representation is a handle to an object, which we refer to as a [[Handle Functions|''handle'']] (or varTerm).

While there is at most one instantiation of any given object, there may be any number of handles that refer to that object. There are many ways in which you might obtain a handle to an object from an Analytica expression. The most straightforward is by using the [[Handle]] function. If Va1 is the identifier of an object, then
Handle(Va1)
returns a handle to that object. This handle unambiguously refers to that particular object. Below several other methods for obtaining handles are identified. You can also obtain a handle for a global object using the [[HandleFromIdentifier]] function.

= Lists and Indexes of Handles =

Often, meta-inference algorithms manipulate lists of handles, or utilize indexes where the index elements are handles.

A global index can be defined as a list of identifiers. You can do this by selecting "List" from the definition type pulldown, and entering identifers of existing objects as the elements of the index. When you do this, the [[IndexValue]] of the index consists of handles to objects. If you define Index In1 in this fashion and evaluate [[IndexValue]](In1), you will obtain a list of handles. Each of the element objects will be evaluated when your index is evaluated, so these must be well-defined variables.

A local index can be defined as a list of handles using the [[MetaIndex..Do]] construct. For example, the following defines an index, I, as the objects contained in Module Mo1, and computes an array based on this index containing all the descriptions of those objects:
[[MetaIndex]] I := [[Contains]] of Mo1;
Description of I

When you are performing meta-inference, you should generally use [[MetaIndex..Do]] rather than [[Index..Do]]. While both can be used, they differ in how the local index behaves when used in a [[Subscript/Slice Operator|Subscript]] operation. [[MetaIndex..Do]] can be used without the elements being evaluated, and hence is what is generally desired.

= The Display of Handles =

When a Handle is displayed in a result table, its title is shown in the table cell, unless ''Show By Identifiers'' is on, in which case its identifier is displayed. ''Show by identifier'' is toggled via the Object menu, or by pressing CTRL-Y.

If you double click on a cell containing a handle, Analytica jumps to the object window for that object.

= Treatment of Handles in Local variables =

When a local variable (defined using [[Var..Do]], [[For..Do]], or declared as a function parameter as [[Function Parameter Qualifiers#Variable|Variable]] or [[Function Parameter Qualifiers#Variable|Variable]]) is assigned a single handle, it becomes an alias to the object pointed to by the handle. When the local variable appears in an expression, it is equivalent to writing the original object identifier. So, for example, the following two expressions are exactly equivalent:

Var x := Handle(Va1) Do x^2

Va1^2

Notice that x does not evaluate to a handle to Va1, it actually serves as an alias of Va1. This is an important subtlety that must be mastered in order to manipulate handles. A local variable is treated differently when it contains a single handle than it is otherwise. This can be quite convenient, since normally when you get to the level of a single handle, you will usually access or manipulate that object in some way, but you must realize that the local evaluates to the object's value, not to a handle to the object. If you really want the handle to the object, use [[Handle]](x).

This subtlety does have some ramifications. For example, if no element of array A contains a handle, then the following expression copies the value of A:

[[For..Do|For]] x := A do x

However, if an element of A is a handle, then the value of the object will be substituted for that element when the above is executed. This could increase the dimensionality of the result. To make a true copy, where handles remain handles, you would need to use:

[[For..Do|For]] x := A do
if [[TypeOf]](x,shallow:true)="Object" Then Handle(x) Else x

= Evaluation =

= Subscripting =

= Accessing attributes =

== Notable attributes ==

[[Contains]], [[IsIn]], [[Outputs]], [[Inputs]], [[DisplayOutputs]], [[DisplayInputs]], [[Identifier]], [[Class]], [[nodeSize]], [[nodeLocation]], [[nodeColor]], [[nodeFontColor]].

= Manipulating Local Indexes =

[[IndexesOf]].

= Parameters and Local Variables holding varTerms =

= Assignment =

= Looping over Handles =

= See Also =

* [[:category:Meta-Inference Functions]]
* [[Handle]] function
* [[HandleFromIdentifier]]
* [[IndexesOf]]
* [[Function Parameter Qualifiers#VariableType|Variable]] parameter qualifier
* [[MetaIndex..Do]]
* [[Attrib of Obj]]

File:TUTORIAL 2007 07 24.pdf

2007-07-24T22:08:22Z

Rmorgan:

File:ADE User Guide 2007 06 26.pdf

2007-07-23T16:20:36Z

Rmorgan:

File:Analytica Tutorial 2007 07 04.pdf

2007-07-12T17:31:53Z

Rmorgan:

Index Position Operator::@

2007-07-06T21:12:39Z

Rmorgan: Fixed two typos that invalidated the example

[[category:Operators]]
[[Category:Doc Status C]] 

(new to 4.0)

The '''''position''''' of value x in an index i is the integer n where x is the nth element of i. n is a number between 1 and Size(i). The first element of i is at position 1; the last element of i is at position Size(i). The position operator "@" offers three ways to work with positions:

:'''@i''' --> an array of integers from 1 to Size('''i''') indexed by '''i'''.
:'''@[i=x]''' --> the position of value '''x''' in index '''i''' -- or 0 if '''x''' is not an element of '''i'''
:'''e[@i=n]''' --> the '''n'''th [[Slice]] of the value of expression '''e''' over index '''i'''.

These turn out to make many array operations much simpler than prior to release 4.0.

= Examples =
[[Media:At_Example_Model.ANA|Click here to download example model]]

We'll use the following indexes for illustration:
Index Car_type := ['VW','Honda','BMW']
Index Time := [0,1,2,3,4]
Index Years := Time+2007

{| border="0"
| @CarType -->
|
{| border="1"
! colspan="3" text-align="left" | Car_Type >>
|-
! 'VW' !! 'Honda' !! 'BMW'
|-
| 1 || 2 || 3
|}
|}

@[Car_type='Honda'] --> 2

Car_type[@Car_type=2] --> 'Honda'

{| border="0"
| @Time -->
|
{| border="1"
! colspan="5" text-align="left" | Time >>
|-
! 0 !! 1 !! 2 !! 3 !! 4
|-
| 1 || 2 || 3 || 4 || 5
|}
|}

@[Time=2] --> 3

Time[@Time=3] --> 2

(Time+2007)[@Time=3] --> 2009

You can use the slice variation to re-index an array by another array having the same length but different elements. Suppose Revenue is indexed by Time, then this returns the same array indexed by Years:

Revenue[Time=@Years]

= Notes =

@I is equivalent to Cumulate(1,I)

If an index has duplicate elements, then subscripting (associative indexing) is ambiguous. For example,
Index In1 := [ 'a','b','a','c' ]
Index In2 := [ 'a','b','a','c' ]
Variable A := Array(In1,[7,4,5,9])
If you were to re-index using A[In1=In2], you would obtain:
{| border="0"
| A[In1=In2] -->
|
{| border="1"
! colspan="4" | In2 >>
|-
! 'a' !! 'b' !! 'a' !! 'c'
|-
| 7 || 4 || 7 || 9
|}
|}
Since A[In1='a'] returns 7. Because of the duplicate in the index values, an array value was lost. When duplicates are possible, accessing elements by position removes the ambiguity:
{| border="0"
| A[@In1=@In2] -->
|
{| border="1"
! colspan="4" | In2 >>
|-
! 'a' !! 'b' !! 'a' !! 'c'
|-
| 7 || 4 || 5 || 9
|}
|}

In variable definitions, it is more often the case that associative access (subscripting, non-positional) is preferred. Associative access is more robust when elements are added to indexes. For example, Revenue[Region='Europe'] doesn't break when a new region is inserted, while Revenue[@Region=5] would change. However, in [[User-Defined Functions]], positional indexing (i.e., is of the @ operator) is often more robust than associative indexing. For example, when a function uses two equal-length indexes (e.g., for a square matrix), with positional indexing the expression does not have to assume the indexes have identical elements or no duplicate elements.

= See Also =

* [[Slice]]
* [[Subscript]]
* [[PositionInIndex]]
* [[Subscript/Slice Operator]]

Index Position Operator::@

2007-07-06T21:06:10Z

Rmorgan: /* Notes */

[[category:Operators]]
[[Category:Doc Status C]] 

(new to 4.0)

The '''''position''''' of value x in an index i is the integer n where x is the nth element of i. n is a number between 1 and Size(i). The first element of i is at position 1; the last element of i is at position Size(i). The position operator "@" offers three ways to work with positions:

:'''@i''' --> an array of integers from 1 to Size('''i''') indexed by '''i'''.
:'''@[i=x]''' --> the position of value '''x''' in index '''i''' -- or 0 if '''x''' is not an element of '''i'''
:'''e[@i=n]''' --> the '''n'''th [[Slice]] of the value of expression '''e''' over index '''i'''.

These turn out to make many array operations much simpler than prior to release 4.0.

= Examples =
[[Media:At_Example_Model.ANA|Click here to download example model]]

We'll use the following indexes for illustration:
Index Car_type := ['VW','Honda','BMW']
Index Time := [0,1,2,3,4]
Index Years := Time+2007

{| border="0"
| @CarType -->
|
{| border="1"
! colspan="3" text-align="left" | Car_Type >>
|-
! 'VW' !! 'Honda' !! 'BMW'
|-
| 1 || 2 || 3
|}
|}

@[Car_type='Honda'] --> 2

Car_type[@Car_type=2] --> 'Honda'

{| border="0"
| @Time -->
|
{| border="1"
! colspan="5" text-align="left" | Time >>
|-
! 0 !! 1 !! 2 !! 3 !! 4
|-
| 1 || 2 || 3 || 4 || 5
|}
|}

@[Time=2] --> 3

Time[@Time=3] --> 2

(Time+2007)[@Time=3] --> 2009

You can use the slice variation to re-index an array by another array having the same length but different elements. Suppose Revenue is indexed by Time, then this returns the same array indexed by Years:

Revenue[@Year=@Time]

= Notes =

@I is equivalent to Cumulate(1,I)

If an index has duplicate elements, then subscripting (associative indexing) is ambiguous. For example,
Index In1 := [ 'a','b','a','c' ]
Index In2 := [ 'a','b','a','c' ]
Variable A := Array(In1,[7,4,5,9])
If you were to re-index using A[In1=In2], you would obtain:
{| border="0"
| A[In1=In2] -->
|
{| border="1"
! colspan="4" | In2 >>
|-
! 'a' !! 'b' !! 'a' !! 'c'
|-
| 7 || 4 || 7 || 9
|}
|}
Since A[In1='a'] returns 7. Because of the duplicate in the index values, an array value was lost. When duplicates are possible, accessing elements by position removes the ambiguity:
{| border="0"
| A[@In1=@In2] -->
|
{| border="1"
! colspan="4" | In2 >>
|-
! 'a' !! 'b' !! 'a' !! 'c'
|-
| 7 || 4 || 5 || 9
|}
|}

In variable definitions, it is more often the case that associative access (subscripting, non-positional) is preferred. Associative access is more robust when elements are added to indexes. For example, Revenue[Region='Europe'] doesn't break when a new region is inserted, while Revenue[@Region=5] would change. However, in [[User-Defined Functions]], positional indexing (i.e., is of the @ operator) is often more robust than associative indexing. For example, when a function uses two equal-length indexes (e.g., for a square matrix), with positional indexing the expression does not have to assume the indexes have identical elements or no duplicate elements.

= See Also =

* [[Slice]]
* [[Subscript]]
* [[PositionInIndex]]
* [[Subscript/Slice Operator]]

Analytica 4.0 PDF docs

2007-06-26T20:44:24Z

Rmorgan:

[[Media:TUTORIAL.pdf]]

[[media:ADE_User_Guide.pdf]]

Analytica 4.0 PDF docs

2007-06-26T20:43:57Z

Rmorgan:

[[Image:TUTORIAL.pdf]]
[[Image:ADE_User_Guide.pdf]]

File:ADE User Guide.pdf

2007-06-26T20:39:11Z

Rmorgan: ADE User Guide

ADE User Guide

File:TUTORIAL.pdf

2007-06-26T20:37:51Z

Rmorgan: Analytica Tutorial in PDF format

Analytica Tutorial in PDF format

Putoption

2007-06-25T20:33:20Z

Rmorgan: Created page and initial function documentation

[[Category:Doc Status C]] 

===Function Putoption(s,x,t,r,theta)===
Calculates the value of a put option using the Black-Scholes formula.

;Example
Putoption(50, 50, 0.25, 0.05, 0.3) → 2.67

; Expects: '''s''', '''x''', '''t''', '''r''', and '''theta''', all to be numeric.

; Parameters: '''s''' is the current price of the security; '''x''' is the exercise price; '''t''' is the time in years to exercise; '''r''' is the risk-free interest rate; '''theta''' is the volatility of the security
; Function definition: USING d1 := (ln(S/X) + (t * (r + (0.5 * theta^2))))/(theta * t^0.5) DO (x * exp(-r * t) * Cumnormal(-d1 + (theta * t^0.5)) - (s * Cumnormal(-d1))
; [[Syntax]]: Putoption(s,x,t,r,theta:Numeric)
; Library: [[Financial library functions]]
; More Examples and Tips: ''None yet.''

Capm

2007-06-25T20:22:23Z

Rmorgan: /* Function Capm(rf,rm,beta:Numeric) */

[[Category:Doc Status C]] 

===Function Capm(rf,rm,beta:Numeric) ===
Calculates the expected stock return under the Capital Asset Pricing Model on a stock or list of stocks.
; Example:
Capm(0.08, 0.12, 1.5) → 0.14
; Expects: '''rf''' (risk free rate), '''rm''' (market return), and '''beta''' (beta of individual stock) all as numbers. Beta is the relative marginal contribution of the stock to the market return, defined as the ratio of the covariance between the stock return and market return, to the variance in the market return.
; Function definition: rf + beta * (rm - rf)
;[[Syntax]]: Capm(rf,rm,beta:Numeric)
;Library: [[Financial library functions]]
;More Examples and Tips: ''None yet.''

Calloption

2007-06-25T20:21:54Z

Rmorgan: /* Function Calloption(s,x,t,r,theta) */

[[Category:Doc Status C]] 

===Function Calloption(s,x,t,r,theta)===
Calculates the value of a call option using the Black-Scholes formula.

; Example
Calloption(50,50,0.25,0.05,0.3) → 3.292

; Expects: '''s''', '''x''', '''t''', '''r''', and '''theta''' all as numeric.

; Parameters: '''s''' is the price of the security now; '''s''' is the exercise price; '''t''' is the time in years to exercise; '''r''' is the risk-free interest rate; '''theta''' is the volatility of the security.
; Function definition: USING d1 := (ln(s/x) + t * (r+ (0.5 * theta^2))) / (theta * t^0.5) DO s * Cumnormal(d1) - (x * exp(-r * t) * Cumnormal(d1 - (theta * t^0.5)))

; [[Syntax]]: Calloption(s,x,t,r,theta : Numeric)

; Library: [[Financial library functions]]

; More Examples and Tips: ''None yet.''

CostCapme

2007-06-25T20:21:12Z

Rmorgan: /* Function Costcapme(rOpp,rD,nTx,dvr) */

[[Category:Doc Status C]] 

===Function Costcapme(rOpp,rD,nTx,dvr) ===
Calculates Miles and Ezzell's formula for adjusting the weighted average cost of capital for financial leverage. The Miles and Ezzell formula works when the firm adjusts its future borrowing to keep debt proportions constant.
; Example:
Costcapme(0.14,0.08,0.35,0.5) → 0.1252
; Expects: '''rOpp''', '''rD''', '''nTx''', and '''dvr''', all as numbers.

; Parameters: '''rOpp''' is the opportunity cost of capital; '''rD''' is the expected return on debt; '''nTx''' is the net tax saving per dollar of interest paid. This is difficult to pin down in practice and is usually taken as the corporate tax rate; '''dvr''' is the debt-to-value ratio
; Function definition: rOpp - (L * rD * Tc * (1 + rOpp)/(1 + rD))
;[[Syntax]]: Costcapme(rOpp,rD,nTx,dvr:Numeric)
;Library: [[Financial library functions]]
;More Examples and Tips: ''None yet.''

CostCapmm

2007-06-25T20:20:29Z

Rmorgan: /* Function Costcapmm(rAllEq, nTx, dvr) */

[[Category:Doc Status C]] 

===Function Costcapmm(rAllEq, nTx, dvr)===
Calculates Modigliani and Miller's formula for adjusting the weighted average cost of capital for financial leverage. Modigliani and Miller's formula works for any project that is expected to:
#generate a level, perpetual cash-flow and
#support fixed permanent debt

;Example
costcapmm(0.2,0.35,0.4) → 0.172

;Expects: '''rAllEq''', '''nTx''', '''dvr''' all to be numeric

;Parameters: '''rAllEq''' is the cost of capital under all-equity financing; '''nTx''' is the net tax saving per dollar of interest paid. This is difficult to pin down in practice and is usually taken as the corporate tax rate; '''dvr''' is the debt-to-value ratio

;Function definition: rAllEq * (1 - (nTx * dvr))

;[[Syntax]]: Costcapmm(rAllEq, nTx, dvr : Numeric)

;Library: [[Financial library functions]]

;More Examples and Tips: ''None yet.''

Wacc

2007-06-25T20:19:32Z

Rmorgan: Created page and initial function documentation

[[Category:Doc Status C]] 

===Function Wacc(debt,equity,rD,rE,tC) ===
Calculates the after-tax weighted average cost of capital, based on the expected return on a portfolio of all the firm's securities. Used as a hurdle rate for capital investment.

; Example
wacc(1000000, 3000000, 0.08, 0.16, 0.35) → 0.133

; Expects: '''debt''', '''equity''', '''rD''', '''rE''', and '''tC''' all as numeric

; Parameters: '''debt''' is the market value of debt; '''equity''' is the market value of equity; '''rD''' is the expected return on debt; '''rE''' is the expected return on equity; '''tC''' is the corporate tax rate.
Definition: (((1 - tC) * debt * rD)/(debt + equity)) + ((equity * rE)/(debt + equity))
; [[Syntax]]: Wacc(debt, equity, rD, rE, tC : Numeric)
; Library: [[Financial library functions]]
; More Examples and Tips: ''None yet.''

Pvgperp

2007-06-25T20:17:53Z

Rmorgan: /* Function Pvgperp(c1, rate, growth) */

[[Category:Doc Status C]] 

===Function Pvgperp(c1, rate, growth)===
Calculates the present value of a ''growing'' perpetuity (a bond that pays an amount ''growing'' at a constant rate in perpetuity). '''Note:''' To calculate the present value of a non-growing perpetuity use [[Pvperp]].

; Example
Pvgperp(200, 0.08, 0.06) → 10,000

; Expects: '''c1''', '''rate''', and '''growth''' all as numeric.

; Parameters: '''c1''' is the coupon payment amount in year 1; '''rate''' is the interest rate per time period; '''growth''' is the growth rate per time period.

; Function definition: c1/(rate - growth)

; [[Syntax]]: Pvgperp(c1, rate, growth : Numeric)

; Library: [[Financial library functions]]

; More Examples and Tips: ''None yet.''

Pvperp

2007-06-25T20:17:17Z

Rmorgan: /* Function Pvperp(c,rate) */

[[Category:Doc Status C]] 

===Function Pvperp(c,rate)===
Description: Calculates the present value of a perpetuity (a bond that pays a constant amount in perpetuity). '''Note:''' To calculate the present value of a ''growing'' perpetuity use [[Pvgperp]].

;Example
Pvperp(200,0.06) → 3333

; Expects: '''c''' and '''rate''' as numeric.

; Parameters: '''c''' is the constant payment amount; '''rate''' is the interest rate per time period.

;Function definition: c/rate

; [[Syntax]]: Pvperp(c, rate : Numeric)

; Library: [[Financial library functions]]

; More Examples and Tips: ''None yet.''

Pvperp

2007-06-25T20:03:36Z

Rmorgan: /* Function Pvperp(c,rate) */

[[Category:Doc Status C]] 

===Function Pvperp(c,rate)===
Description: Calculates the present value of a perpetuity (a bond that pays a constant amount in perpetuity). '''Note:''' To calculate the present value of a ''growing'' perpetuity use [[Pvgperp]].

;Example
Pvperp(200,0.06) → 3333

; Expects: '''c''' and '''rate''' as numeric.

; Parameters: '''c''' is the constant payment amount; '''rate''' is the interest rate per time period.

;Function definition: c/rate

; [[Syntax]]: Pvperp(c, rate : Numeric)

; Library: [[Financial functions]]

; More Examples and Tips: ''None yet.''

Pvperp

2007-06-25T20:03:11Z

Rmorgan: Created page and initial function documentation

[[Category:Doc Status C]] 

===Function Pvperp(c,rate)===
Description: Calculates the present value of a perpetuity (a bond that pays a constant amount in perpetuity). '''Note:''' To calculate the present value of a ''growing'' perpetuity use [[Pvgperp]].

;Example
Pvperp(200,0.06) → 3333

; Expects '''c''' and '''rate''' as numeric.

; Parameters: '''c''' is the constant payment amount; '''rate''' is the interest rate per time period.

;Function definition: c/rate

; [[Syntax]]: Pvperp(c, rate : Numeric)

; Library: [[Financial functions]]

; More Examples and Tips: ''None yet.''

Pvgperp

2007-06-25T19:57:38Z

Rmorgan: /* Function Pvgperp(c1, rate, growth) */

[[Category:Doc Status C]] 

===Function Pvgperp(c1, rate, growth)===
Calculates the present value of a ''growing'' perpetuity (a bond that pays an amount ''growing'' at a constant rate in perpetuity). '''Note:''' To calculate the present value of a non-growing perpetuity use [[Pvperp]].

; Example
Pvgperp(200, 0.08, 0.06) → 10,000

; Expects: '''c1''', '''rate''', and '''growth''' all as numeric.

; Parameters: '''c1''' is the coupon payment amount in year 1; '''rate''' is the interest rate per time period; '''growth''' is the growth rate per time period.

; Function definition: c1/(rate - growth)

; [[Syntax]]: Pvgperp(c1, rate, growth : Numeric)

; Library: [[Financial functions]]

; More Examples and Tips: ''None yet.''

Pvgperp

2007-06-25T19:57:04Z

Rmorgan: /* Function Pvgperp(c1, rate, growth) */

[[Category:Doc Status C]] 

===Function Pvgperp(c1, rate, growth)===
Calculates the present value of a ''growing'' perpetuity (a bond that pays an amount ''growing'' at a constant rate in perpetuity). Note: To calculate the present value of a non-growing perpetuity use [[Pvperp]].

; Example
Pvgperp(200, 0.08, 0.06) → 10,000

; Expects: '''c1''', '''rate''', and '''growth''' all as numeric.

; Parameters: '''c1''' is the coupon payment amount in year 1; '''rate''' is the interest rate per time period; '''growth''' is the growth rate per time period.

; Function definition: c1/(rate - growth)

; [[Syntax]]: Pvgperp(c1, rate, growth : Numeric)

; Library: [[Financial functions]]

; More Examples and Tips: ''None yet.''

CostCapmm

2007-06-25T19:53:33Z

Rmorgan: Created page and initial function documentation

[[Category:Doc Status C]] 

===Function Costcapmm(rAllEq, nTx, dvr)===
Calculates Modigliani and Miller's formula for adjusting the weighted average cost of capital for financial leverage. Modigliani and Miller's formula works for any project that is expected to:
#generate a level, perpetual cash-flow and
#support fixed permanent debt

;Example
costcapmm(0.2,0.35,0.4) → 0.172

;Expects: '''rAllEq''', '''nTx''', '''dvr''' all to be numeric

;Parameters: '''rAllEq''' is the cost of capital under all-equity financing; '''nTx''' is the net tax saving per dollar of interest paid. This is difficult to pin down in practice and is usually taken as the corporate tax rate; '''dvr''' is the debt-to-value ratio

;Function definition: rAllEq * (1 - (nTx * dvr))

;[[Syntax]]: Costcapmm(rAllEq, nTx, dvr : Numeric)

;Library: [[Financial functions]]

;More Examples and Tips: ''None yet.''

Pvgperp

2007-06-25T19:34:36Z

Rmorgan: /* Function Pvgperp(c1, rate, growth) */

[[Category:Doc Status C]] 

===Function Pvgperp(c1, rate, growth)===
Calculates the present value of a growing perpetuity (a bond that pays an amount growing at a constant rate in perpetuity).

; Example
Pvgperp(200, 0.08, 0.06) → 10,000

; Expects: '''c1''', '''rate''', and '''growth''' all as numeric.

; Parameters: '''c1''' is the coupon payment amount in year 1; '''rate''' is the interest rate per time period; '''growth''' is the growth rate per time period.

; Function definition: c1/(rate - growth)

; [[Syntax]]: Pvgperp(c1, rate, growth : Numeric)

; Library: [[Financial functions]]

; More Examples and Tips: ''None yet.''

Calloption

2007-06-25T19:33:06Z

Rmorgan: /* Function Calloption(s,x,t,r,theta) */

[[Category:Doc Status C]] 

===Function Calloption(s,x,t,r,theta)===
Calculates the value of a call option using the Black-Scholes formula.

; Example
Calloption(50,50,0.25,0.05,0.3) → 3.292

; Expects: '''s''', '''x''', '''t''', '''r''', and '''theta''' all as numeric.

; Parameters: '''s''' is the price of the security now; '''s''' is the exercise price; '''t''' is the time in years to exercise; '''r''' is the risk-free interest rate; '''theta''' is the volatility of the security.
; Function definition: USING d1 := (ln(s/x) + t * (r+ (0.5 * theta^2))) / (theta * t^0.5) DO s * Cumnormal(d1) - (x * exp(-r * t) * Cumnormal(d1 - (theta * t^0.5)))

; [[Syntax]]: Calloption(s,x,t,r,theta : Numeric)

; Library: [[Financial functions]]

; More Examples and Tips: ''None yet.''

Calloption

2007-06-25T19:32:27Z

Rmorgan: Created page and initial function documentation

[[Category:Doc Status C]] 

===Function Calloption(s,x,t,r,theta)===
Calculates the value of a call option using the Black-Scholes formula.

; Example
Calloption(50,50,0.25,0.05,0.3) ==> 3.292

; Expects: '''s''', '''x''', '''t''', '''r''', and '''theta''' all as numeric.

; Parameters: '''s''' is the price of the security now; '''s''' is the exercise price; '''t''' is the time in years to exercise; '''r''' is the risk-free interest rate; and '''theta''' is the volatility of the security.
; Function definition: USING d1 := (ln(s/x) + t * (r+ (0.5 * theta^2))) / (theta * t^0.5) DO s * Cumnormal(d1) - (x * exp(-r * t) * Cumnormal(d1 - (theta * t^0.5)))

; [[Syntax]]: Calloption(s,x,t,r,theta : Numeric)

; Library: [[Financial functions]]

; More Examples and Tips: ''None yet.''

Pvgperp

2007-06-25T19:22:50Z

Rmorgan: Created page and initial function documentation

[[Category:Doc Status C]] 

===Function Pvgperp(c1, rate, growth)===
Calculates the present value of a growing perpetuity (a bond that pays an amount growing at a constant rate in perpetuity).

; Example
Pvgperp(200, 0.08, 0.06) → 10,000

; Expects: '''c1''', '''rate''', and '''growth''' all as numeric.

; Parameters: '''c1''' is the coupon payment amount in year 1; '''rate''' is the interest rate per time period; '''growth''' is the growth rate per time period.

; Function definition: c1/(rate - growth)

; [[Syntax]]: Costcapme(rOpp,rD,nTx,dvr:Numeric)

; Library: [[Financial functions]]

; More Examples and Tips: ''None yet.''

CostCapme

2007-06-25T19:14:26Z

Rmorgan: /* Function Costcapme(rOpp,rD,nTx,dvr) */

Capm

2007-06-25T19:13:16Z

Rmorgan: /* Function Capm(rf,rm,beta:Numeric) */

CostCapme

2007-06-25T19:12:22Z

Rmorgan: Created page and initial function documentation

[[Category:Doc Status C]] 

===Function Costcapme(rOpp,rD,nTx,dvr) ===
Calculates Miles and Ezzell's formula for adjusting the weighted average cost of capital for financial leverage. The Miles and Ezzell formula works when the firm adjusts its future borrowing to keep debt proportions constant.
; Example:
Costcapme(0.14,0.08,0.35,0.5) → 0.1252
; Expects: '''rOpp''', '''rD''', '''nTx''', and '''dvr''', all as numbers.

; Parameters: '''rOpp''' is the opportunity cost of capital; '''rD''' is the expected return on debt; '''nTx''' is the net tax saving per dollar of interest paid. This is difficult to pin down in practice and is usually taken as the corporate tax rate; '''dvr''' is the debt-to-value ratio
; Function definition: rOpp - (L * rD * Tc * (1+rOpp)/(1+rD))
;[[Syntax]]: Costcapme(rOpp,rD,nTx,dvr:Numeric)
;Library: [[Financial functions]]
;More Examples and Tips: ''None yet.''

Capm

2007-06-25T18:44:32Z

Rmorgan:

[[Category:Doc Status C]] 

===Function Capm(rf,rm,beta:Numeric) ===
Calculates the expected stock return under the Capital Asset Pricing Model on a stock or list of stocks.
; Example:
Capm(0.08, 0.12, 1.5) → 0.14
; Expects: '''rf''' (risk free rate), '''rm''' (market return), and '''beta''' (beta of individual stock) all as numbers. Beta is the relative marginal contribution of the stock to the market return, defined as the ratio of the covariance between the stock return and market return, to the variance in the market return.
; Function definition: rf + beta*(rm-rf)
;[[Syntax]]: Capm(rf,rm,beta:Numeric)
;Library: [[Financial functions]]
;More Examples and Tips: ''None yet.''

Capm

2007-06-25T18:41:23Z

Rmorgan: Created page and initial function documentation

[[Category:Doc Status D]] 

===Function Capm(rf,rm,beta:Numeric) ===
Calculates the expected stock return under the Capital Asset Pricing Model on a stock or list of stocks.
; Example:
Capm(0.08, 0.12, 1.5) → 0.14
; Expects: '''rf''' (risk free rate), '''rm''' (market return), and '''beta''' (beta of individual stock) all as numbers. Beta is the relative marginal contribution of the stock to the market return, defined as the ratio of the covariance between the stock return and market return, to the variance in the market return.
; Function definition: rf + beta*(rm-rf)
;[[Syntax]]: Capm(rf,rm,beta:Numeric)
;Library: [[Financial functions]]
;More Examples and Tips:

File:Stuff for Max.ZIP

2007-06-01T01:13:13Z

Rmorgan:

This is a zip file with some things I've promised you:

1) A new version of chapter 11 of the user Guide on which you are going to be working. This has the following:
A comment paragraph type. Use this when embedding comments into the chapters.

You can import this paragraph tag into all the other chapters on which you will be working as follows:

- Replace chapter 11 that you have with this new version.

- Open the book file (Ugbook.book) in FrameMaker

- Open this new chapter 11 in FrameMaker

- With the book file select all the chapters and click on File -> Import -> Formats

- When the Import Formats window comes up select Import from Document = ArraysIndexes.fm (i.e., chap 11), Import and Update = Paragraph Formats *and* Reference Pages (see the screen shot of this window that is in the zip file)

2) A screenshot of the Import Formats window with the correct settings.

3) The ADE Scripting Guide in Word

File:Stuff for Max.ZIP

2007-06-01T01:10:51Z

Rmorgan:

This is a zip file with some things I've promised you:

1) A new version of chapter 11 of the user Guide on which you are
going to be working. This has the following:
A comment paragraph type. Use this when embedding comments
into the chapters.
You can import this paragraph tag into all the other
chapters on which you will be working as follows:
- Replace chapter 11 that you have with this
new version.
- Open the book file (Ugbook.book) in FrameMaker
- Open this new chapter 11 in FrameMaker
- With the book file select all the chapters and
click on File -> Import -> Formats
- When the Import Formats window comes up select
Import from Document = ArraysIndexes.fm (i.e., chap 11)
Import and Update = Paragraph Formats *and* Reference Pages
(see the screen shot of this window that is in the zip file)

2) A screenshot of the Import Formats window with the correct settings.

3) The ADE Scripting Guide in Word