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# Security Expected Return and Standard Deviation

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You are planning to form a portfolio with two securities, the details of which are as follows:

Security Expected Return Standard Deviation
1 12% 4%
2 10% 3%

Assume that the returns on these two securities are perfectly negatively correlated. Calculate portfolio expected return and variance for different combinations of these two securities and draw the efficient frontier. If you require an expected return of 11%, calculate the standard deviation of your portfolio.

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To calculate the expected return of a portfolio of two risky assets the following formula is used:
E(R_p) = w_1 + r_1 + w_2 + r_2

To calculate the variance of a portfolio of two risky assets the following formula is used:
omega^2_p = w^2_1 * omega^2_1 + w^2_2 * omega^2_2 + 2*w_1*w_2*omega_1*omega)2*p_12

Where
E(R_p) = expected return of the portfolio
omega = variance of the portfolio
w_1, w_2 = weights of the two assets in the portfolio. They add up to 1 thus
r_1, r_2= expected returns of the two assets. It is given that and
omega_1, omega_2 = standard deviations of the two assets. It is given that omega_1 = 4% and omega_2 = 5%. and
p_12 = correlation between the two assets. It is given that p_12 = -1

The calculations for different combinations of the two securities are shown in the Excel attachment.
The efficient frontier is also shown in the Excel attachment.

For an expected return of 11% the standard deviation will be 0.50% (see calculations in Excel attachment).

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