**Last update on September 23, 2013**

One differentiating feature of the Income Discovery tool is the ability to create and store multiple capital market assumption sets, each representing different future expectations of inflation and returns. You can analyze your client cases under those varying assumptions and compare the performance of an income strategy side-by-side against different market expectations.

Capital market assumptions present themselves in several main areas of the Income Discovery tool. While in the *Income Parameters* tab, you select the assumption set that best reflects your future return expectations. The chosen capital market assumption will drive the Monte Carlo simulation based analysis. When using the custom income plan feature to choose a specific income strategy or optimizing across multiple strategies, the tool will ask you to choose from Systematic Withdrawal Portfolio allocation models. These model allocations are configured for each capital market assumption scenario set separately.

The tool comes preloaded with a number of capital market assumptions for convenience, but you are expected to change these, or create new ones, to reflect your market outlook. The first part of this article describes the underlying methodology of capital market assumptions within the Income Discovery tool. Next, the article explains how to understand the capital market assumptions tab, followed by a guide for altering the existing assumptions and creating new ones.

**Scenario Set Methodology**

The inflation and asset return sequences that make up a scenario set can be constructed in two ways: Historical Sequence and Forward Looking Expectations.

**Historical Sequence**

If we assume that past market data is a good representation of future outcomes, we can use historical sequences of inflation and asset class returns to generate a scenario set. The scenario sets whose name begins with Ibbotson are sets of 30 year paths of annual real total returns and inflation. They are built using *rolling *30 year windows from historical monthly total returns and inflation for the asset classes available in Ibbotson's Classic Yearbook. A rolling window means that for any given month in the historical data, the 30 year period is calculating by going forward 30 years from that month. Although historical scenarios are based on rolling periods, the statistics (mean, standard deviation and correlation) are reported for annual independent periods of Jan-Dec every year from 1926 onwards. Similarly, for tax based analysis, mean real capital appreciation and mean income return are also calculated based on independent periods. Total return based set is used for all analysis that ignores taxes and also for Tax Deferred Account (TDA) and Tax Free Account (TFA) simulation. For tax based analysis, capital appreciation and income return are also calculated for Intermediate Term Government Bonds (ITGB) and US Large Caps (ULC), only asset classes with the return breakup in Ibbotson's yearbook. Capital appreciation and income return are used in Taxable account simulation. Calculation formulas for annual inflation and returns and converting them to real returns are described in the Methodology document available in the tool.

**Forward Looking Expectations**

You can create a scenario set based on your expectations of the future, which allows you to create your own categories of asset classes. The scenarios are generated using random walk assumption, which means that the returns/inflation are normally distributed (statistical bell shaped curve) and the returns/inflation in successive periods are independent. A scenario set consists of 1000 scenario paths, each containing a 60 year series of inflation and real returns. These scenario paths are used in Monte Carlo Simulation based analysis.

**Navigating the Capital Market Assumptions Tab**

The capital market assumptions tab contains four sections. All the scenario sets are listed in the upper left section, and the data corresponding to the selected scenario set - Asset Classes, Model Allocations and Correlations - are in the other three sections. Each scenario set is completely independent of the other; the data altered under one scenario set will not be applied to the others. Each set can contain its own asset class definitions - for example, one set may define an asset class at large cap level while another set may define large cap growth and large cap value as separate asset classes. Each set also has its own model allocations across the asset classes, which can be changed as described below. The latter part of this article describes how to alter existing scenario sets and create custom ones.

**Model Allocations Section**

This section shows the percent of the SWP that would be invested in each asset class for a given allocation model. Each column represents an asset class and each allocation model (row) must total 100. The tool will alert you if there is a discrepancy.

**Modifying Existing Sets**

Within each Random Walk scenario set, you may choose to modify the asset classes, model allocations and/or asset class correlations. There are two ways to edit the existing data; by double-clicking the row to edit the data in-line, or by clicking the button, which will result in a pop-up window to edit the data. You may create new model allocations and asset classes by clicking on the button in the upper right corner of their respective sections.

Creating a new asset class will automatically add a row to the correlations and a column to the model allocation section. Remember that when entering correlation data, the matrix must be internally consistent, which in mathematical terms is referred to as positive definite. This property of internal consistency is best explained through an example:

-Suppose you say that large cap and mid cap stocks are 90% correlated

-And that large cap stocks have a 40% correlation with bonds

-At the same time you say that mid-cap stocks have a -60% correlation with bonds

The data above appears to be intuitively inconsistent because a very high positive correlation between large and mid-cap stocks implies that these asset classes will have similar correlation with bonds (we have not verified the above simple example for mathematical consistency, but are simply using it to make a point). If the correlation matrix is not internally consistent, the tool will provide a warning prior to running plan analysis. Also, you cannot edit asset class or correlation data under the Ibbotson Historical Sequence scenario set, but you can create new model allocations based off this data.

**Creating Assumption Sets**

Not only can you customize the preloaded scenario data, but you can also create your own, completely unique capital market assumptions based scenario set. The first step in doing this is to select an existing scenario set that you wish to use as a starting point for your own data. Clicking the button will produce a clone of the scenario, which you may then rename and completely customize. Follow the steps in the “modifying existing scenarios” section to transform the cloned scenario into your own capital market assumptions. To analyze an income plan using the newly created scenario, simply click back to the main screen of the tool and select your capital market assumption under the *Income Parameters *tab.

Asset class returns and inflation expectations are configured in Asset Classes section. The fields for defining expectations, which are explained below, are different in the tax and non-tax mode.

**Asset Classes Section (Non-Tax Mode)**

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* Mean Compounded Real Return*: The long term compounded real (net of inflation) return for the asset class or inflation.

* Standard Deviation: *The standard deviation of real returns. Please view the Methodology document for a detailed explanation of the mathematical principles underlying the capital market assumptions and tool as a whole.

**Asset Classes Section (Tax Mode)**

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* Mean Real Capital Appreciation: *The long term compounded real (net of inflation) capital appreciation for the asset class or long term compounded inflation.

* Income Return: *The return from dividends on stocks or interest payments on bonds. The percentage income return is kept constant across scenario paths and for each year on every scenario path; only the capital appreciation varies as per the standard deviation described below.

* Standard Deviation: *The standard deviation of real capital appreciation.

* Capital Gains Distribution: *The percentage of the asset class capital appreciation that is assumed to be distributed by the underlying mutual fund or ETF. For example, if stocks have 10% capital appreciation, 50% of which is distributed, it implies a 5% capital gain distribution rate. Stock index funds will typically have low distribution rates as they have lesser churn and, subsequently, smaller realized capital gains. An active fund manager will have a higher distribution rate for capital gains because of the higher turnover rate in his holdings. This distribution percentage does not apply in case of capital loss.

**Reuse of Scenario Paths**

To effectively compare multiple income strategies, they must be analyzed against the same scenario set of inflation and asset return data. Therefore, the multiple inflation and asset return 30 year paths that are generated for a scenario set are stored for reuse in subsequent analyses. A change in asset class returns and correlations will lead to recreation of the return series next time that specific capital market assumption is chosen for income plan analysis.

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