Asked by Rukhna Chaudhry on Jun 18, 2024
Verified
Suppose that Fenner Smith must divide his portfolio between two assets, one of which gives him an expected rate of return of 15% with zero standard deviation and one of which gives him an expected rate of return of 45% and has a standard deviation of 10.He can alter the expected rate of return and the variance of his portfolio by changing the proportions in which he holds the two assets.If we draw a "budget line" with expected return on the vertical axis and standard deviation on the horizontal axis, depicting the combination that Smith can obtain, the slope of this budget line is
A) 1.50.
B) 1.50.
C) 3.
D) 3.
E) 4.50.
Standard Deviation
A measure of the amount of variation or dispersion in a set of values, commonly used in statistics to quantify the degree to which values differ from the average value.
Budget Line
An illustration showing all the different pairs of two items that a buyer can afford, considering their financial resources and the pricing of such goods.
Expected Rate
In finance, it refers to the return anticipated on an investment or the interest rate at which money is borrowed or lent.
- Analyze and compute the gradient of a budget line when examining combinations of portfolios on a risk-return diagram.
- Examine the effects of changing asset allocations within a portfolio on the anticipated rate of return and standard deviation.
Verified Answer
MV
Maria VillalobosJun 20, 2024
Final Answer :
D
Explanation :
The slope of the budget line between two assets in a portfolio is calculated by the difference in their expected returns divided by the difference in their standard deviations. Since one asset has a standard deviation of zero, the slope is simply the difference in returns (45% - 15%) divided by the standard deviation of the risky asset (10%), which equals 3.
Learning Objectives
- Analyze and compute the gradient of a budget line when examining combinations of portfolios on a risk-return diagram.
- Examine the effects of changing asset allocations within a portfolio on the anticipated rate of return and standard deviation.