The expected return and standard deviation of a portfolio that is 30 percent invested in 3 Doors, Inc., and 70 percent invested in Down Co. are the following: 3 Doors, Inc. Down Co. Expected return, E(R) 18 % 11 % Standard deviation, σ 51 40 What is the standard deviation if the correlation is +1? 0? −1?

For correlation 1 the standard deviation of portfolio is 0.433.

For correlation 0 the standard deviation of portfolio is 0.3191.

For correlation -1 the standard deviation of portfolio is 0.127.

Explanation:

The standard deviation of a portfolio is computed using the formula:

(1)

For r = + 1 compute the standard deviation of portfolio as follows:

Thus, for correlation 1 the standard deviation of portfolio is 0.433.

(2)

For r = 0 compute the standard deviation of portfolio as follows:

Thus, for correlation 0 the standard deviation of portfolio is 0.3191.

(3)

For r = -1 compute the standard deviation of portfolio as follows:

Thus, for correlation -1 the standard deviation of portfolio is 0.127.

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