Bob Has a $50,000 Stock Portfolio with a Beta of 1.2,an

question 81

Multiple Choice

Bob has a $50,000 stock portfolio with a beta of 1.2,an expected return of 10.8%,and a standard deviation of 25%.Becky also has a $50,000 portfolio,but it has a beta of 0.8,an expected return of 9.2%,and a standard deviation that is also 25%.The correlation coefficient,r,between Bob's and Becky's portfolios is zero.If Bob and Becky marry and combine their portfolios,which statement about their combined $100,000 portfolio is true?

• A)The combined portfolio's expected return will be less than the simple weighted average of the expected returns of the two individual portfolios, 10.0%.
• B)The combined portfolio's beta will be equal to a simple average of the betas of the two individual portfolios, 1.0; its expected return will be equal to a simple weighted average of the expected returns of the two individual portfolios, 10.0%; and its standard deviation will be less than the simple average of the two portfolios' standard deviations, 25%.
• C)The combined portfolio's expected return will be greater than the simple weighted average of the expected returns of the two individual portfolios, 10.0%.
• D)The combined portfolio's standard deviation will be greater than the simple average of the two portfolios' standard deviations, 25%.

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Definitions:

Lagrangian

Function to be maximized or minimized, plus a variable (the Lagrange multiplier) multiplied by the constraint.

Lagrange Multiplier

A technique used in constrained optimization problems to find the maximum or minimum of a function subject to constraints.

Lambda

A symbol commonly used in mathematics and physics to represent wavelengths, eigenvalues, and decay constants, among other concepts.

Lagrange Multipliers

A strategy used in mathematical optimization to find the local maxima and minima of a function subject to equality constraints.