A stock has a beta of 1.56 and an expected return of 17.3 percent. A risk-free asset currently earns 5.1 percent. If a portfolio of the two assets has a beta of 1.06, what are the portfolio weights?

Question

BlackTom AI · Accepted Answer

To determine the portfolio weights, we use the portfolio beta formula: Beta_p = w_stock * Beta_stock + w_rf * Beta_rf.
Since the risk-free asset has a beta of 0, Beta_p = w_stock * Beta_stock.
Given Beta_p = 1.06 and Beta_stock = 1.56, we solve for w_stock: w_stock = 1.06 / 1.56 ≈ 0.6795.
The remaining weight goes to the risk-free asset, so w_rf = 1 - w_stock ≈ 1 - 0.6795 = 0.3205.
Now evaluate the options:
Option 1: Stock weight 0.28; risk-free 0.72. This would yield a portfolio beta of 0.28 * 1.56 ≈ 0.4368, far from 1.06, so it’s incorrect.
Option 2: Stock weight 0.032; risk-free 0.68. This gives Beta_p ≈ 0.032 * 1.56 ≈ 0.0499, which is far too low; clearly incorrect.
Option 3: Stock weight 0.44; risk-free 0.56. Beta_p ≈ 0.44 * 1.56 ≈ 0.6864, still short of 1.06; not correct.
Option 4: Stock weight 0.68; risk-free 0.32. Beta_p ≈ 0.68 * 1.56 ≈ 1.0608, which matches the given portfolio beta very closely; this aligns with the calculation and rounding, so this is the correct construction.
Option 5: Stock weight 0.72; risk-free 0.28. Beta_p ≈ 0.72 * 1.56 ≈ 1.1232, which is higher than 1.06, so this is not correct.
In summary, only the fourth option yields a portfolio beta that closely equals the target 1.06 when using the given stock beta and the zero beta of the risk-free asset, and the weights sum to 1 as required.

FNBSLW 344-23 Chapter 11 Practice Quiz (not graded)

A stock has a beta of 1.56 and an expected return of 17.3 percent. A risk-free asset currently earns 5.1 percent. If a portfolio of the two assets has a beta of 1.06, what are the portfolio weights?

查看解析

登录即可查看完整答案

类似问题

Question 1 of 2 What is the portfolio beta? Round your final answer to a number with two decimal places, i.e. if the answer is 1.2311 then write 1.23

Which one of the following statements is accurate?

You have a portfolio that is invested 20 percent in Stock R, 38 percent in Stock S, and the remainder in Stock T. The beta of Stock R is .75, and the beta of Stock S is 1.30. The beta of your portfolio is 1.18. What is the beta of the Stock T?

You have a portfolio that is invested 20 percent in Stock R, 38 percent in Stock S, and the remainder in Stock T. The beta of Stock R is .75, and the beta of Stock S is 1.30. The beta of your portfolio is 1.18. What is the beta of the Stock T?

See the attached spreadsheet for a table of various monthly returns Download attached spreadsheet for a table of various monthly returns over the past five years. Create a portfolio of the three stocks that consists of 10% Stock A, 70% Stock B, and 20% Stock C. What is the beta of the portfolio?

You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.04 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio?

You would like to create a portfolio that is equally invested in a risk-free asset and two stocks. One stock has a beta of 1.14. What does the beta of the second stock have to be if you want the portfolio to be equally as risky as the overall market?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单