Risk Analysis. å To change Benchmark tickers:

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1 Property Sheet will appear. The Return/Statistics page will be displayed. 2. Use the five boxes in the Benchmark section of this page to enter or change the tickers that will appear on the Performance Analysis page. 3. Click OK to confirm changes and close the Property Sheet. Risk Analysis page Risk Analysis This Portfolio Manager page is mainly designed to show you the level of risk involved with an account. Based on all of the securities and cash held in the account, a number of statistical parameters measuring investment performance and risk are computed. For comparison, these same parameters are computed for as many as five different benchmark tickers. å To display Risk Analysis for an account: 1. Select the account in the Account List panel. 2. Display the Risk Analysis page by clicking on its tab. 3. Click the button labeled Calculate. å To change Benchmark tickers: 1. Right click on the Risk Analysis page and a window titled Property Sheet will appear. The Return/Statistics page will be displayed. 2. Use the five boxes in the Benchmark section of this page to change the tickers that will appear on the Risk Analysis page. 3. Click OK to confirm changes and close the Property Sheet. New Features 17

2 Parameters listed on Risk Analysis page Internal Rate of Return (IRR) The internal rate of return (IRR) is a useful measure of the performance of an investment (1 + r) portfolio. ((t t )/365) i n For investments such as a stock portfolio that produce varying cash flows over time, the IRR is defined as the discount rate that when applied to all cash flows results in a net present value of zero. The formula for the computation of annualized IRR is: n P i PV = å i = 1 where: t i = time of the ith payment P i = the ith payment amount PV = Present Value r = rate n = number of payments The iterative technique used to solve for IRR involves calculating PV for different interest rates. The program cycles through the calculation until it finds the rate (accurate to four decimal places) that results in a Return/Statistics page of Property Sheet 18 AIQ TradingExpert Pro Vers. 7.0

3 PV value equal to zero. The formula for non-annualized IRR is the same except that the time difference (t i - t n ) is not divided by 365. Note The Time Period selected from the Return/Statistics tab also determines the period used for computing returns shown on the Performance Analysis tab. å To change the IRR figures shown on the Risk Analysis page to annualized returns: 1. Right click on the Risk Analysis page. A window titled Property Sheet will appear. 2. The tab labeled Return/Statistics will be displayed. 3. The option box located between the Time Period section and the Risk Free Rate section is titled Annualize Returns. Check this box to specify annualized returns. 4. Click OK to confirm the change and close the Property Sheet. Two factors needed for the computation of IRR are the periodicity (time period) and the total time interval. Both of these can be changed. Time Period is selected from the Return Statistics tab of the Property Sheet. Time interval is taken from the value specified for the graph time interval which is entered on the Graph tab of the Property Sheet. å To specify the time period used for computing IRR: 1. Open the Return/Statistics tab of the Property Sheet. 2. From Time Period section, select one of the four options: Weekly Monthly Quarterly Annually 3. Click OK. å To specify the time interval used for computing IRR: 1. Right click on the Risk Analysis page to display the Property Sheet window. 2. Select the Graph tab from the top of the window. New Features 19

4 Note For the purpose of computing IRR and Sigma, the interval of time specified for evaluation is divided into equal recurring time periods. These periods can be weeks, months, quarters, or years. The length of the time period specified is referred to as the periodicity. Note If, instead of a numerical value, a row of asterisks (*****) appears in a data field, the value could not be calculated because of insufficient (less than 3) data points. You need to open the Property Sheet and either increase the time interval (Max. days or Date range on Graph tab) or decrease the periodicity (Time Period on Return/Statistics tab). 3. At the top of the page, choose one of the following options: Maximum days In the adjacent text box, enter the number of days you want plotted. Date Range In the two adjacent text boxes, enter start and end dates for the data plotted. 4. Click OK to close the Property Sheet. Sigma This parameter is a measure of the amount of total risk for a portfolio evaluated for a specific interval of time. It is derived as the standard deviation of IRR for the periodicity specified. The user specifies periodicity by selecting one of four time period options: weekly, monthly, quarterly, or annually. The factors used for the computation of Sigma are the same as those used for the computation of IRR. To change the values used for periodicity or time interval, see IRR. Alpha, Beta, and R-Squared These parameters are simple linear regression terms as defined in classical statistical analysis. The values are generated from a statistical analysis that compares excess return for a portfolio against excess return for a benchmark ticker. Excess return is computed as IRR less a risk free rate. The computational procedure involves linear correlation and regression analysis to define the straight line that best fits the distribution of data points. This line is spoken of as the regression line, or line of regression, and the criterion for best fit is that the sum of the squared vertical distances between the data points and the regression line must be as small as possible. The regression analysis yields the following parameters: Alpha (x-axis intercept) - No practical significance. Beta (slope) The portfolio s market (or systematic) risk. It is a measure of the volatility of a portfolio of securities in comparison with the market as a whole. A beta of 1 indicates that the portfolio s value moves with the market. A beta greater than 1 indicates that it will be more volatile than the market and a beta less than 1 means that 20 AIQ TradingExpert Pro Vers. 7.0

5 it will be less volatile. R-Squared Also known as the coefficient of determination or the square of the correlation coefficient, it is an indication of how closely the excess returns of the portfolio were associated with the excess returns of the benchmark ticker. That is, it shows how much of the movement in the portfolio s excess returns can be explained by movement in the excess returns of the benchmark ticker. R-squared values range from 0 to 100; an R-squared of 100 means that all movements of a fund are completely explained by movements in the index. Note If, instead of a numerical value, a row of asterisks (*****) appears in a data field, the value could not be calculated because of insufficient (less than 3) data points. You need to open the Property Sheet and either increase the time interval (Max. days or Date range on Graph tab) or decrease the periodicity (Time Period on Return/Statistics tab). Sharpe Ratio The Sharpe Ratio is a measure of the risk-adjusted return of an investment. It measures the return earned in excess of the risk free rate (normally Treasury instruments) relative to the total risk as measured by the standard deviation of the returns over the measurement period. It answers the question, How much better did you do for the risk assumed? The ratio is calculated by first determining the excess return for a portfolio (portfolio rate of return less risk free rate) and then dividing the excess return by the standard deviation of the portfolio returns. Sharpe Ratio formula: Excess Return = Annualized Annual Return Risk Free Return Sharpe Ratio = Excess Return Annualized Standard Deviation of Returns The Risk Free Rate is the rate specified on the Return/Statistics tab of the Property Sheet, or a symbol may be entered and the rate is New Features 21

6 computed as the average of the data from the specified symbol. å To specify the risk free interest rate: 1. Right click on the Risk Analysis page to select the Property Sheet with the Return/Statistics page displayed. 2. From the Risk Free Rate section, select one of the following: Symbol Enter the ticker for the security you want to use for this rate. Value Enter a numerical value for the rate. 3. Click OK to confirm your changes and close the Property Sheet. Treynor Ratio This ratio, also known as the Reward to Volatility Ratio, is the ratio of a portfolio s average excess return to the portfolio s beta. It measures 22 AIQ TradingExpert Pro Vers. 7.0

7 the returns earned in excess of those that could have been earned on a riskless investment per unit of market risk assumed. Treynor Ratio formula: Excess Return = Annualized Annual Return Risk Free Return Treynor Ratio = Excess Return Beta of Portfolio Right click menu for graph å To specify the risk free interest rate: See Sharpe Ratio previous page. New Features 23

8 Property Sheet Graph page Enhancements to Portfolio Graph You can now control the period of time shown on the graph. The date range or the number of days of history can be specified. You can also change the graph colors. å To change the period of time plotted on the graph: 24 AIQ TradingExpert Pro Vers. 7.0