# Performance Calculations

This document outlines the various performance calculation algorithms used by Portfolio mobile for computing returns at equity, portfolio and broker account levels.

## Equity Profit / Performance

Equity positions report profits and performance values. Profits are reported as either realized or unrealized. Realized profits are net gains or losses from executed trades. For example, selling a position of 20 shares for $10 more than the purchase price results in a realized profit of $200. Unrealized profits are theoretical gains or losses that would be recognized from the position if sold at the current last trade price. For example, if a position of 100 shares is trading at $5 below the purchase price, the unrealized loss is -$500.

Percent profit values are calculated based on the investment of the position. Realized profit % is calculated again the total investment in the position. For example, if you purchased a position for $10,000 and later sold half of it, realized profit % would be calculated as realized profit / $10,000 (not $5,000). Unrealized profit % is calculated based on the currently invested basis. In the same example above, unrealized profit % is realized profit / $5,000 (not $10,000). Unrealized profit is always tied to the currently open shares whereas realized profit is tied to the total investment.

Profit and profit % are similarly calculated as the sum of realized and unrealized profit, where profit % is calculated against the total investment (not the basis).

The annualized return of a position represents the performance of that position as if the investment had returned a consistent percentage rate for the year. Calculation of annualized return is performed using XIRR on the actual cashflows in and out of the position. For example, a position purchased with an initial investment of $10,000 with dividend returns of $100 per quarter, and finally sold after 1 year for $12,000 results in a 24.4% annualized return. This value is computed with the cashflows: -$10,000 (initial investment), $100 x 4 (quarterly), and $12,000 (value at position sale).

## Equity Performance Charts

Equity performance charts are not tied to a specific position history. In other words, the performance chart is the normalized change in price from 1 year ago (or the first historical price available if the equity does not have 1 year of price history). This representation you to view the performance of equities as potential investments, not just those that you have owned. Charts can also be directly compared against market indexes on an apples-to-apples basis.

## Portfolio Profit / Performance

Portfolio profit is shown in realized and unrealized components similarly to equities. Portfolio profits are the sum of all of the equities in the portfolio. Profit % calculations are tied to total investment and basis values as described above.

Portfolio performance figures are calculated using the True Return method by first building a complete value history of the equities in the portfolio. This value history includes current market value net of cash investments / withdrawals, and basis points. (The daily valuation is arrived at by taking the market value of a position net its cost basis and adding any profit from trading activity. For example, a position purchased for $1000 that is currently valued at $1100 and has received $200 in dividends has an adjusted value of $300.) **Positions with missing price history are not included in this accounting and therefore will skew performance numbers.**

To calculate the performance of the portfolio, Portfolio mobile creates windows in the value history for each basis point, takes the change in value during each window to calculate a performance for that time period, and multiplies all performances together as a geometric series. For example, if you purchased shares Jan 1, Feb 1, and Dec 1, there would be 3 windows for the year – the invested cost basis changed at 2 points during the year (assuming we treat the Jan 1 investment as our initial value / cost basis). For each of these windows, the ending and beginning values are subtracted to find a net profit during the period. By dividing the profit by the invested basis we arrive at a performance value. The resulting performances for each window (time period) are multiplied together as follows: (1 + P0)(1 + P1)(1 + P2) – 1. This method of performance calculation is used to compute YTD, 1 Year, 2 Year, 3 Year, and 5 Year values.

Portfolio annualized return is calculated using XIRR and the combined cash flows from all equity positions as described above in Equity Profit / Performance.

## Portfolio Performance Charts

Charted versions of portfolio performance are derived by calculations similar to the portfolio performance. To build a chartable representation, the daily performance of the portfolio is calculated for every day over the past year (every day that price history is available). The performance for each day is calculated as the market value net of cash investments / withdrawals divided by the invested basis. The performance values are then normalized for the year by subtracting the first day’s performance from all performance values. Performance charts always start at zero on their first day and therefore comparable to market indexes performance changes which are also normalized for the year. **The charted performance may differ from the displayed YTD, 1 Year performance figures due to the fact that charted performances are a daily representation of performance whereas YTD, 1 Year values are the cumulative performance over the target time period.**

## Broker Account Profit / Performance

Broker account profit, performance and charted performance are calculated using the same methods described above for portfolios.

## Category Profit / Performance

Category profit, performance and charted performance are calculated using the same methods described above for portfolios with the exception that market values and profits are converted to the category’s currency.