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Math

This page details all math equations in FastTrack products. FastTrack products apply all popular investment calculations to FastTrack’s high quality dividend adjusted database.

Annual Return

The calculation is performed in the following equation:

((TotalReturn + 1 ) ^ ( 252.25 / MarketDays ) – 1

  • Total Return= Calculated as return
  • MarketDays = A count of days over which the TotalReturn was achieved
  • 252.25 = The number of market days in a year.

This calculation is known in the investment industry as Compound Annual Growth Rate (CAGR). There is another calculation called Average Annual Return which takes the return each year and produces and average of the annual return. We think this is a highly misleading number and IS NOT provided or used by FT Cloud or FT4web.

Beta

The calculation used to compute FastTrack’s Beta was published in “Guide to Portfolio Management”, James L. Farrell, Jr., McGraw-Hill – 1983, pages 41-43.

Beta = (correlation of issue and basis x issue’s standard deviation) / Basis standard deviation

There are a number of different ways to compute Beta so do not expect FastTrack’s method to compute exactly the Beta you might see in some publications. Also, for Beta to have ANY validity, the issue’s and the basis MUST be closely correlated (usually a Correlation of 0.95 or higher).

Correlation

FT Cloud’s correlation is the relation of the basis to the relevant fund, etf, stock, or equity curve. It is based on the change of prices, not closing prices.

Correlation length is set using the “correlation length” number box at the lower right of the login page.

Advanced Details:

  • L= The number of days in the period for which correlation is computed
  • Prices = an array of periodic “independent” returns
  • Cor = an array of periodic “dependent” periodic returns
  • I = Starting day; Continue for all days; Each repetition I = I + L
  • Y = the length in days of the period for which correlation is calculated – Start Day + 1

Periodic Calculation

  • XC = [ ( Cor [ I + N ] – Cor [ I ] ) / Cor [ I ] ]
  • XP = [ ( Prices [ I + N ] – Prices [ I ] ) / Prices [ I ] ]
  • Sum Cor = XC + Sum Cor
  • Sum Prices = XP + Sum Prices
  • Sum Cor Squared = Sum Cor Squared + XC * XC
  • Sum Prices Squared = Sum Prices Squared + XP * XP
  • Sum Cor & Prices = (Sum Cor & Prices) + XC * XP

Final Calculation

  • Sum Cor Squared = Sum Cor Squared – (Sum Cor * Sum Cor ) / Y
  • Sum Prices Squared = Sum Prices Squared – (Sum Prices * Sum Prices) / Y
  • Sum Product = Sum Cor & Prices – (Sum Cor * Sum Prices) / Y
  • Correlation Coefficient = Sum Product / Square Root of (Sum Prices Squared
    * Sum Cor Squared)

Dividend Adjustment

Visit the following link to see all details on FastTrack dividend adjustments, including a dividend adjustment worksheet.
http://www.fasttrack.net/newhelp/DistributionWorkSheet.asp

Max Drawdown

Maximum drawdown is the percentage loss from a ticker’s peak value to its lowest value, over a specified time period.

In general, Max Drawdown will be highest for issues whose standard deviation is the highest.

Return

The gain or loss of a security/equity curve for a particular time period.

( Price on last day- price on first day) / price on first day

Standard Deviation

Just like FT4web, FT Rebalance’s SD algorithm is generally described as “The Difference between the Mean and the Square”.

While there are other types of SD calculations which will differ from FastTrack’s and FT Rebalance’s results, FT Rebalance’s standard deviation is calculated on a daily basis and then adjusted to a monthly basis by multiplying by the square root of 21 (the average number of market days in a month.)

FT Rebalance’s statistical values measure the period on shown in the lower left of each tab.

Ulcer Index

To calculate UI:

  • Every day, determine the % amount ‘R’ that a mutual fund is below it’s highest previous value.
  • Calculate a running total of R-squared.
  • Then divide this product by N, the total number of days in the period and take the square root of the quotient to obtain UI.
  • The lower the Ulcer Index the easier an investment will be to live with and the less troubling it will be on the down days.

Ulcer Index = SquareRoot((the sum of all R² values) / N)

Ulcer Performance Index

The Ulcer Performance Index is obtained as follows:

  • Subtract the Annual Return of a Low Risk Base Mutual Fund from the Annual Return of an issue.
  • Divide the result by Ulcer Index to get the UPI.

Ulcer Performance Index = (Annualized Return(Issue) – Annualized Return(Low Risk Base)) / Ulcer Index

The Ulcer Performance Index is a very good measure of the risk adjusted return of an investment. It measures how well an investment outperforms a low risk basis compared with the amount of ulcers it gives you. The higher the value, the better the investment.