# What's in your transparent backpack?

In this article, I will discuss a model by which it is possible to disclose information about investment portfolio with a closed-end structure, knowing only the securities that comprise it. This article may be of interest to investors who follow mainly a "buy and hold" strategy.

Despite the simplicity of this approach, many banks and funds offer portfolio products as their main investment opportunities. In particular, the widespread Mutual Funds are based on this. In addition, it is not uncommon for the structure of the portfolio to be known only to those closest to the fund, or, in other words, to the company's clients.

Probably the most famous player on the market of portfolio investment products based on stock indices is Morgan Stanley Bank. This bank has a very wide range of index funds, the composition of which is not disclosed, but periodically some information about the structure of the portfolio still appears in the press. Compilation methods index portfoliosThe bank uses are widespread, so knowing it and having a simple mathematical apparatus, you can accurately enough to form an idea of the composition of the portfolio.

Stock selection in MSCI indices The portfolio is based on the capitalization approach, which means that companies with a high market capitalization have a better chance of being included in the portfolio. Plus, these stocks must meet certain liquidity requirements. Knowing the approximate list of stocks that can get into the index, you can use the regression model to determine their shares in the overall portfolio structure.

As an example, consider MSCI index on shares of major emerging economies. The MSCI BRIC index includes Brazil, Russia, India and China, respectively. We will not determine which specific stocks are included in this index, instead we will simply determine what the aggregate weight of each country's stocks in the index portfolio is.

The factor regression model of daily index returns is determined by the formula:

,

where BRIC (t) - the relative (percentage) change in the model value of the MSCI BRIC index; Braz(t), Rus(t), Ind(t), and Chn(t) - relative (percentage) changes in the real indices of Brazil, Russia, India and China of the MSCI family, respectively; a, b, c, d, e - model parameter, e(t) - model error (i.e., the deviation of the model value of the index from the real value).

To determine the parameters of the model we used the data on the daily changes in the indices. The data for 2007 were used as an interval for determining the parameters of the model. Using the method of least squares, model coefficients were calculated, which were optimal in 2007:

a = -0,0001, b = 0,2752, c = 0,2335, d = 0,1585, e = 0,3353.

The free term a turned out to be insignificantly small. In principle, this is an expected result, as all factors affecting the model index were taken into account. The rest of the model coefficients show the contribution of each index to the overall change in the MSCI BRIC index. Accordingly, Chinese stocks have the greatest weight (and influence on the index). From a logical point of view, this is also an expected result. The smallest share belongs to shares of Indian companies.

The graphs below compare the dynamics of the model index and the actual index.

As can be seen in the graph, the model values almost completely correspond to the real values (on the left axis, the initial value of the indices is taken as 100), while the deviation of the model from the fact does not exceed 0.7% (right scale).

In the interval of determining the parameters of the model there were no cardinal macroeconomic changes, so the high quality of the simulation is quite expected.

Let's check the stability of the model on the interval from 2008 to the present day. The result is shown in the graph below.

Results forward testing show that a stable level of performance was demonstrated up to the beginning of May 2008. After that, the average error of the model increased significantly. Nevertheless, with active growth and high market volatility the maximum deviation of the model from the fact in 4% cannot be called criminal.

In general, the approach has been shown to work, but there are some factors to consider when using it.

1) Index portfolios are periodically reviewed. As a rule, this happens once a quarter. That is why the average model error has risen sharply since the beginning of May 2008 (see figure above). Any dramatic changes in the structure of index portfolios are extremely rare, so past model values can be used until there is enough data to determine new model parameters.

2) Wrongly high weight can be allocated to a component that is highly correlated (the dynamics are very similar) either with the portfolio itself, or with one of the portfolio components that is really important to the portfolio. A model, of course, is a model, but one must also pay close attention to the selection of the components of the portfolio itself.