Portfolio Management in Investment Partners Bank

Note: We suggest using the electronic Excel File instead of the printed version due to printing difficulties.

Part One

The following is an explanation for the calculations shown in the Excel file: we will only refer to the calculations for annual data as they are in the format required by the questions. The monthly data serves as an error proofing tool. All the references made in this section apply to the Excel book called "Q1 ANNUAL".

It is known that by combining different assets into one portfolio it is possible to carry out a risk reduction by eliminating the idiosyncratic risk of an individual asset through the diversification effect. By creating efficient portfolios we can not only reduce the risk of an investment, but we can also have higher returns. The purpose of this part of the case study is to give evidence and to apply this methodology on the given data.

The first step is to calculate the historical returns of the different stocks (table 1) and for the Market (IGBM). This is done by using the formula Rt = (Pt-Pt-1)/Pt-1 (topic 4, slide 20).

As it has been taught in this course, when dealing with historical data, a good measure of the expected return is the mean of the historic returns (topic 4, slide 16).

E[R i]Σ Rt

In the same manner, we measure risk with the standard deviation (ex-post) of such historical returns applying the following formula:

The standard deviation (also defined as "risk" in this course) is the square root of this term.

As explained in class, we know that to obtain the annual average return/variance of a stock we have to multiply the corresponding monthly figure by 12. In the case of the standard deviation, this must be multiplied by the squared root of 12.

By obtaining the correlation coefficients between sets of data (using the Excel formula) and then multiplying this coefficient by the standard deviations of both sets of data (using the definition σxy=rxyσxσy) we obtain the Covariance. This data is reflected in table 3 and 4, the covariance matrix.

Thus we can use the covariance between an asset and the IGBM and divide by the term for market variance (the Variance of IGBM) to obtain this asset´s Beta. According to the formula from the slides:

The results of these computations (expected return, variance, standard deviation and the Beta) can be found in table 2.

From these computations we obtain all the necessary information to evaluate the assets individually.

We plot the assets in a mean-variance graph (Figure 1). This is a graph that relates expected return

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