Financial Management: Quantitative Methods

Question 1

Quantitative Forecasting Methods Types:

Answer 1

There are two types of Quantitative Forecasting Methods:

1. Time Series Models – are based on the premise that data patterns from the past will continue more or less unchanged into some future period.
2. Causal Models – assume the variable being forecasted (dependent variable) is related to one or more other variables (independent variable) and makes forecasts based on those associations.

Question 2

Time Series Methodologies or Models:

Answer 2

Time Series Models: a number of specific models have been developed to predict a future value (or values) from past values, Here are the most significant models, beginning with the simplest method:

1. Naive – Uses the immediate prior period’s actual value as a forecast for the next period.
   
   • “Next year is expected to be just like this year”.
2. Simple Mean (Average) – Uses the average of past values as the forecast for a future period or periods.
   
   • E.g. average the last 2 yrs as the forecast for next year.
3. Simple Moving Average – Uses the average of a specific number of the most recent values as the forecast for future period(s). Values are not adjusted.
4. Weighted Moving Average – Uses the average of a specific number of most recent values with each receiving a different emphasis or weight.
   
   • Average the last 3 months with the last month weight being .5, two months ago weight being .3, and three months ago weighted .2
   • E.g.: Forecasted value = (1 month ago x .5) + (2 months ago x .3) + (3 month ago x .2)
   • Weights must equal 1.0
5. Exponential Smoothing – Uses the average of a specific number of most recent values with weights assigned to each which decline exponentially as data becomes older.
   
   • A weight is assigned to the most recent period; that weight is called “smoothing factor”
   • All other weights for earlier periods are computed asa function of the smoothing factor.
6. Trend-adjusted Exponential Smoothing – An exponential smoothing method which makes adjustments to past data when strong trend patterns are evident in the data.
   
   • This trend can be used when the forecast period is long enough to have a trend.
7. Seasonal Indexes – Adjusts past data to accomodate seasonal patterns in data
8. Linear Trend Line – Uses least squares to fit a straight line to past data and extends trendline to establish forecast.

Question 3

Time Series Patterns:

Answer 3

Over time, actual time series data will relect a pattern. Commom patterns in Time Series Data include:

1. Level or Horizontal – Data are relatively constant or stable over time; little increase or decrease in values.
2. Seasonal -- Data reflects upward or downward swings over a short to intermediate time period, with each swing about same timing and level of change.
3. Cycles – Data reflects upward and downward swings over long period of time.
4. Trend – Data reflects a steady and persistent upward and downward movement over some long time period.
5. Random – Data reflects unpredictable, erratic variations over time.

Question 4

Time Series Decomposition:

Answer 4

Time series data that shows pattern often can be decomposed (i.e., separated into multiple causes).

• Decomposition is the removal of effects of each pattern component from the data.

Decomposition Process:

• 1. Removing the seasonal effects from the data, typically using smoothing;
• 2. Removing the overall trend from the deseasonalized data, typically using regression;
• 3. Removing the cyclic effects from the remaining data values, typically using a cyclic index.

Question 5

Causal Models:

Answer 5

Causal Models: Assume the variable being forecasted (dependent variable) is related to one or more other variables (independent variable) and makes forecasts based on those associations.

Common Causal Model Types:

• Regression Models
• Input-Output Models
• Economic Models

Question 6

Causal Model Types:

Answer 6

1. Regression Models – Uses mathematical equations that relate a dependent variable to one or more independent variables that influence the dependent variable:
   
   • Regression fits a curve to the data points to minimize error
   • Curve may be linear or non-linear
   • Trend analysis uses regression with time as the independent (explanatory) variable.
2. Input-Output Models – Describe the flow from one stage of a process or sector to another stage or sector.
   
   • Outputs of one stage or sector determines inputs to a subsequent stage or sector.
     
     • Crude oil production > refining > gasoline
   • Can be used at macroeconomic level
3. Economic Models – Specify statistical relationship believed to exist between economic quantities.
   
   • Black Scholes model is economic model.