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Sharpe Index Model



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The index model - also known as the single index model or diagonal model - was developed by the economist William F. Sharpe and is based on the portfolio selection theory of Harry M. Markowitz. One of the problems of the Markowitz model is the large amount of data needed to determine the efficient portfolio. The index model reduces this number from 5150 to 302 for 100 investment stocks.

In the index model, Sharpe assumes that the returns of stocks are strongly correlated with each other because certain influences affect (almost) all stocks in a market. These include economic developments, natural disasters, warlike events, changes in key interest rates, etc. A considerable part of the uncertainty factors that exist with regard to future stock returns can be represented by an index.

Usually, a large stock index is used for this purpose. Only part of the uncertainty is due to events that affect only one company individually (e.g. insolvency, takeover, etc.).

Most of the uncertainty can be explained by an index

Practice shows that the general market development exerts the greatest influence on the returns of a stock portfolio: If the DAX falls by 30% in a year, for example, almost all index members show losses. Of course, the decline of the index is not the original cause of the shares' losses, but merely reflects them through its calculation.

However, the index model does not attempt to re-explain the cause of returns, but merely seeks to reduce the amount of input data required to do so. It succeeds in doing so because the index reflects the cause of returns nearly as well as looking at each stock individually, but requires less research.

As a result, the index model assumes that the return of a share is influenced by company-specific variables on the one hand, but that on the other hand a large and often even the larger part of the return is explained by the index. The model also assumes that not all shares react to changes in the index to the same extent.

This observation is also supported by practical experience: so-called "defensive stocks" are preferred in the face of a recession, while "cyclical stocks" are in demand in the early or pre-stage of an economic upswing.

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What data is needed?

In order to determine an efficient portfolio in https://thaiexness20.com/mt5/, the expected index return, the index variance and three other variables are needed for each stock to be included in the portfolio: The sensitivity of each stock to index changes, the variance of each stock and the company-specific returns. Compared to portfolio optimisation according to Markowitz, the number of data required is thus significantly reduced. This is mainly due to the covariances that are not needed, as these are derived from the index.

The simplified approach comes at the price of dispensing with a lot of information. This information is replaced by assumptions that do not necessarily apply in reality. For example, it is by no means certain that the sensitivity of a share with respect to the index is actually constant over time.

The index model also assumes that the company-specific returns have no correlation with each other. This assumption is also unlikely to hold in practice: Industry clusters are found in all major indices. If an event or development affects a company from one industry, it usually also affects other companies from the segment.











































 
 
 
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