Mapping stocks to an index means aggregating more than one stock to an index. This index is then examined in risk analysis evaluations instead of individual stocks. The following two reasons explain the advantages of mapping stocks to an index.

1. In capital market theory, according to the Capital Asset Pricing Model (CAPM) the risk of each share can be split in to a systematic part (general risk) and an unsystematic part (specific risk). When setting up portfolios, you can eliminate the unsystematic part of the risk by the effects of diversification. However, the general risk remains. Only the beta factor is relevant as a measure of risk for an individual security in the portfolio. This is because it represents a fluctuation of the security relative to the market.

The ß-factor of a stock in relation to the market (= index) is calculated as follows:



2. When mapping stocks to an index, less market data is need for value at risk analysis. If mapping is not used, for a historical simulation using one historical time period of n days and one portfolio containing x stocks, you would need n times x stock prices. If you use mapping, for each stock you would need exactly one ß factor and n historical index positions, therefore x+n market parameters.

You need to have carried out the following steps to enable the SAP System to display the risk of stocks mapped to an index:

1. Definition of the index
2. Assignment of individual classes to the index for the evaluation type you want to use
3. Creation of beta factors for the individual classes
4. Creation of the index position (for net present value analysis) and its history (for value at risk evaluations)
5. Only for value at risk evaluations: Inclusion of the index in the risk hierarchy as a risk factor

The calculation of the risk of individual stocks takes place using the valuation of the index and of the retrograde calculation using beta factors.

Stock 1: 10 units in the portfolio, rate as at the day of evaluation EUR 80, beta factor 0.5

Stock 2: 20 units in the portfolio, rate as at the day of evaluation EUR 120, beta factor 1.5

Index position at the date of evaluation EUR 2000

If mapping is not used:

If mapping is used:

All single value analyses ignore mapping when calculating risk but still mark the individual risk items with the name of the index.

Note that in the case of sensitivity analyses and grid analysis, a risk analysis of mapped items only takes place when the index position of the risk factor changes. Changes to the individual stock prices have no effect.

You can store a simple mapping in the evaluation type for stocks that have not explicitly been assigned to an index in Customizing. Defined there is the index, and a standard beta factor that can be used for all stocks.