# Understanding Return

A general rule of investing is that risk is linked to total return, or what you get back in terms of price appreciation and dividends on your investment. The greater the risk you take, the greater your return should be. The less risk you take, the less return you can expect.

For example, an investor whose primary objective is the preservation of capital, would consider building portfolios weighted towards bonds and limited stock exposure. The expected overall return on the portfolio will be lower, but so would the expected risk associated with the loss of principal.

There are various ways to perform return calculations. WebPortfolio uses two types of calculations depending on which transaction or cash activity is reflected for the period.

Dollar Weighted Return (DWR) is computed to reflect the inflow and outflow of capital. The Modified Dietz method, is a widely used industry methodology for dollar weighted returns and the one used by WebPortfolio. Modified Dietz is similar to IRR in methodology and application. Modified Dietz is recognized as an appropriate method for performance presentation for Association of Investment Management and Research (AIMR).

Modified Dietz is computed by adjusting the change in market value over a period for transaction activity. Transaction activity is weighted over the period, and therefore transactions occurring toward the beginning of the period have more impact on the computation than those occurring nearer the period's end. Modified Dietz is used in WebPortfolio to calculate DWR.

Time Weighted Return (TWR) is computed to reflect the performance of underlying assets. It is used to represent a manager's performance for an actively managed portfolio, and shows the return on the underlying assets under management.

The following is an example illustrating the difference between DWR and TWR:

Investor A owns 100 shares of ABC worth \$50 per share. During the period, the value of ABC appreciates to \$75 per share. Believing that increase to be the sign of further appreciation, the investor buys an additional 100 shares at \$75 per share, three quarters through the period. At the end of the period, shares of ABC are priced at \$50.

TWR Return = Zero

DWR Return = Negative

The TWR return on ABC shares is zero (\$50 beginning and \$50 ending values). However, the return that the investor has actually earned for the period is negative. The negative return is explained by breaking down the period into several parts. First, the initial investment in ABC at the beginning of the period, which has no change in value at the period end. Second, investment in ABC three quarters through the period represents a loss of \$25 per share, weighted to reflect its inclusion in the last quarter of the period the result is an accurate measure of return earned by the investor.

The following example illustrates the utilization of the Modified Dietz Methodology for computing a dollar weighted return:

Given asset XYZ, the following data is available for computing a 3-month return:

• Day 0: You hold 100 shares XYZ @ \$90; Value = \$9,000

• Day 21: You receive a dividend of \$0.10 / share on XYZ; Value = \$10

• Day 37: You buy an additional 100 shares XYZ @ \$100; Value = \$10,000

• Day 64: You sell 100 shares XYZ @ \$110; Value = \$11,000

• Day 87: You sell 50 shares XYZ @ \$120; Value = \$6,000

• Day 90: Your remaining 50 shares XYZ closed at \$110; Value = \$5,500

XYZ asset is treated like a portfolio of one holding, where the transaction data represents inflow and outflow activity from the asset. The information above is applied to the The Modified Dietz formula:

Return = [Ending Market Value - Beginning Market Value - S (Transaction Activity)]

divided by

[Beginning Market Value + S (Transaction Activity * Weight)]

Where:

• Ending Market Value = \$5,500

• Beginning Market Value = \$9,000

• Net Transaction Activity = \$10 + \$10,000 - \$11,000 - \$6,000

• Transaction Weight = Days Included/Days In Period

The equation simplifies to:

Return = [5500-9000+6990] / [9000+(10)(.77) + (10000)(.59) + (11000)(.29) + (6000)(.03)

Return =  / [9000+9277.7]

Return =  / [18277.7]

Return = [.19094]

Return = 19.094%

WebPortfolio uses Modified Dietz to calculate Dollar Weighted Returns. WebPortfolio returns are calculated on a 3/6/12 month rolling, year-to-date and lifetime, and 1/3/5 year calendar bases.

IMPORTANT: The calculations performed in WebPortfolio provide you with aggregate information based on the data available to WebPortfolio. The performance measures and underlying calculations used in WebPortfolio, as with any computations offered in WebPortfolio, should be fully understood, researched and results confirmed by the investor; these computations are not designed to serve as the impetus for an investment decision such as a trade, but rather facilitate the investor's research process.