Question

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?

Answer 1

Answer:

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:

$\sigma_{P}=\sqrt{w^{2}_{1}\sigma_{1}^{2}+w^{2}_{2}\sigma_{2}^{2}+2\times r\times w_{1}\sigma_{1}w_{2}\sigma_{2}}$

(1)

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

$\sigma_{P}=\sqrt{w^{2}_{1}\sigma_{1}^{2}+w^{2}_{2}\sigma_{2}^{2}+2\times r\times w_{1}\sigma_{1}w_{2}\sigma_{2}}\\=\sqrt{(0.30^{2}\times 0.51^{2})+(0.70^{2}\times 0.40^{2})+(2\times1\times0.30\times 0.51\times0.70\times 0.40)}\\=\sqrt{0.187489}\\=0.433$

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

(2)

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

$\sigma_{P}=\sqrt{w^{2}_{1}\sigma_{1}^{2}+w^{2}_{2}\sigma_{2}^{2}+2\times r\times w_{1}\sigma_{1}w_{2}\sigma_{2}}\\=\sqrt{(0.30^{2}\times 0.51^{2})+(0.70^{2}\times 0.40^{2})+(2\times0\times0.30\times 0.51\times0.70\times 0.40)}\\=\sqrt{0.101809}\\=0.3191$

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

(3)

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

$\sigma_{P}=\sqrt{w^{2}_{1}\sigma_{1}^{2}+w^{2}_{2}\sigma_{2}^{2}+2\times r\times w_{1}\sigma_{1}w_{2}\sigma_{2}}\\=\sqrt{(0.30^{2}\times 0.51^{2})+(0.70^{2}\times 0.40^{2})+(2\times-1\times0.30\times 0.51\times0.70\times 0.40)}\\=\sqrt{0.016129}\\=0.127$

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