A portfolio consists of three securities: Treachery (T), Sleazy (S), and Felony (F).The expected returns for Treachery, Sleazy, and Felony are 10.0%, 8.0%, and 16.0%, respectively.The standard deviation is 15.0% for Treachery, 20.0% for Sleazy, and 25.0% for Felony.The covariance of the returns on the three securities is: COVTS = 0.0144, COVTF = 0.0084, and COVSF = 0.03.What is the portfolio standard deviation if 20.0% of the portfolio is in Treachery and 35.0% is in Sleazy?
A)17.73%
B)13.91%
C)3.14%
D)1.93%

Question

Quizplus · Accepted Answer

The correct answer is A because the portfolio standard deviation is 17.73%. This can be calculated using the formula:Portfolio standard deviation = sqrt((w1^2 * s1^2) + (w2^2 * s2^2) + (w3^2 * s3^2) + (2 * w1 * w2 * s1 * s2 * COV12) + (2 * w1 * w3 * s1 * s3 * COV13) + (2 * w2 * w3 * s2 * s3 * COV23))where:w1 = weight of security 1 in the portfolios1 = standard deviation of security 1COV12 = covariance between security 1 and security 2and so on.In this case, we have:w1 = 0.20s1 = 0.15COV12 = 0.0144w2 = 0.35s2 = 0.20COV13 = 0.0084w3 = 0.45s3 = 0.25COV23 = 0.03Plugging these values into the formula, we get:Portfolio standard deviation = sqrt((0.20^2 * 0.15^2) + (0.35^2 * 0.20^2) + (0.45^2 * 0.25^2) + (2 * 0.20 * 0.35 * 0.15 * 0.20 * 0.0144) + (2 * 0.20 * 0.45 * 0.15 * 0.25 * 0.0084) + (2 * 0.35 * 0.45 * 0.20 * 0.25 * 0.03))= sqrt(0.0009 + 0.0049 + 0.0253 + 0.0004 + 0.0002 + 0.0063)= sqrt(0.0314)= 0.1773= 17.73%

A Portfolio Consists of Three Securities: Treachery (T), Sleazy (S)