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Risk and Return in a Portfolio Context



Risk and Return in a Portfolio Context            

Portfolio
It is combination of two or more securities or assets

Portfolio Return
The expected return of a portfolio is a weighted average of the expected returns of the securities constituting the portfolio.

For Example,
We have two securities, i.e. Security A and Security B and we have also their corresponding expected returns and standard deviation
                                       

Security A
Security B
Expected Return
10%
12%
Standard Deviation
8%
5%


If equal amounts of money are invested in the two securities, the expected return of the portfolio is
(0.5)10% + (0.5)12% = 11%

Portfolio Risk
From the previous example our portfolio risk will be:
(0.5)8% + (0.5)5% = 5.25%
Portfolio risk is not so simple. To understand portfolio risk we must understand covariance

Covariance
It is a statistical measure of the degree to which two variables move together.
There are three different kinds of covariance directions.

Positive Covariance
It implies that the two variables move in the same direction.

Negative Covariance
It implies that the two variables move in the opposite direction.

Zero Covariance
It implies that the two variables show no tendency to vary together in either a positive or negative direction.

Conclusion
The riskiness of a portfolio depends much more on the paired security covariance than on the riskiness of the separate security covariance.

High covariance lead to high portfolio risk and
Low covariance lead to low portfolio risk

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