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# Investment management strategies - Essay Example

## Extract of sample Investment management strategies

The correlation coefficient between the daily stock return in each portfolio is also calculated and combined with the standard deviations in a covariance matrix to calculate the variance and standard deviation for each portfolio. Sensitivity analysis is also carried out by changing the weights of each stock in the portfolio to see how the performance changes.
The variance and thus the standard deviation are far more difficult to calculate because the variance of a portfolio is not simply a weighted average of the individual variances of the stocks included in the portfolio except for the special case where the individual stock returns are uncorrelated with one another. The variance for a two stock portfolio is given by:
We need to set up a covariance matrix to bordered covariance matrix to be able to calculate the 1variance and standard deviation for a portfolio of more than two stocks. For a three stock portfolio the bordered covariance matrix can be written as follows (Bodie et al., 2002):
The portfolio variance is calculated from the above nine terms by multiplying the bordered weights by the corresponding covariance and then summing the different terms. The standard deviation is calculated by taking the square root of the variance. From the table above, the variance is given by:
(3) and the standard deviation of the portfolio is given by:
(4)
The covariance matrix in table 1 above can be extended to any number of stocks.
Haven discussed how to calculate the expected return on portfolio, the variance and standard deviation; we now apply the above models to the U.S and Australian portfolios.

Std. Dev (%)
Ave Ret (%)
Citi Group Inc.

3.58
-0.03
American Express

2.99
0.26
Motorola Inc

2.25
-0.30
Boeing Co.

1.85
-0.38
McDonalds Corp

1.45
-0.44
Coca Cola

0.91
-0.34

Table two above show the standard deviation and average return of each of the stocks included in the U.S portfolio over the period under study (details of the calculations are found in the attached excel file). To be able to calculate the covariance between the different stocks, we need to know the correlation coefficients between the different stocks. We use the correlation function in Excel to calculate the correlation coefficient between the different stocks. Doing this we obtain the following correlation matrix for the different stocks:
Table 2: Correlation matrix (U.S Portfolio)

Citigroup Inc.
American Express
Motorola Inc
Boeing Co.
McDonalds Corp
Coca Cola
Citi Group Inc.
1.00
0.90
0.54
0.74
0.78
0.25
American Express
0.90
1.00
0.64
0.78
0.87
0.34
Motorola Inc
0.54
0.64
1.00
0.37
0.53
0.23
Boeing Co.
0.74
0.78
0.37
1.00
0.72
0.16
McDonalds Corp
0.78
0.87
0.53
0.72
1.00
0.31
Coca Cola Co.
0.25
0.34
0.23
0.16
0.31
1.00

To obtain the covariance matrix we use the following formula formula to calculate the ...Show more

## Summary

The objective of this paper is to compare the performance of two portfolios: A U.S portfolio consisting of six Stocks (Citigroup Inc., American Express Company, Motorola Inc., Boeing Co., McDonalds Corp., and Coca-Cola Co.); and an Australian Portfolio consisting of Westpac Banking Corp, ANZ Banking Group Ltd., Rio Tinto Ltd., BHP Billiton Ltd., QBE Insurance Group Ltd, and Qantas Airways Ltd.
Author : zgreenholt
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