1. a) You are provided with the following sample observations relating to historical rate of returns and their corresponding probabilities for individual assets, Brad and Ford: BRAD Obs Return Prob 1 -0.03 0.01 2 0.07 0.09 3 0.10 0.10 4 0.11 0.20 5 0.02 0.05 6 0.15 0.25 7 0.08 0.05 8 0.09 0.10 9 0.12 0.10 10 0.05 0.05 Ford Obs Return Prob 1 -0.01 0.01 2 0.10 0.09 3 0.15 0.10 4 0.20 0.20 5 0.08 0.05 6 0.25 0.25 7 0.13 0.05 8 0.09 0.10 9 0.11 0.10 10 0.06 0.05 Part 2 of question 1 Required: Based on the following information (Note: You can use Microsoft Excel functions to expedite your calculations. Please show answers up to two digits after decimal point): a) Calculate the expected rate of return for each individual asset. b) Calculate the standard deviation of returns for each individual asset. c) Assume that the correlation coefficient between the two assets is -1 (perfectly negatively correlated). Calculate the weighted average rate of returns and standard deviation of returns for the hypothetical portfolios containing the combination of the two assets in varying weights as indicated below. Then, choose a recommended portfolio. Summarize your answers in the following table. For example, for Brad – Ford portfolio: Portfolio Brad Ford Weighted average rate of return Standard deviation of returns Recommended portfolio (please tick √ only one) 1 1.0 0.0 2 0.9 0.1 3 0.8 0.2 4 0.7 0.3 5 0.6 0.4 6 0.5 0.5 7 0.4 0.6 8 0.3 0.7 9 0.2 0.8 10 0.1 0.9 11 0.0 1.0

Managerial Accounting

15th Edition

ISBN:9781337912020

Author:Carl Warren, Ph.d. Cma William B. Tayler

Publisher:Carl Warren, Ph.d. Cma William B. Tayler

Chapter10: Evaluating Decentralized Operations

Section: Chapter Questions

Problem 15E

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a) You are provided with the following sample observations relating to historical rate of returns and their corresponding probabilities for individual assets, Brad and Ford:

BRAD

Obs	Return	Prob
1	-0.03	0.01
2	0.07	0.09
3	0.10	0.10
4	0.11	0.20
5	0.02	0.05
6	0.15	0.25
7	0.08	0.05
8	0.09	0.10
9	0.12	0.10
10	0.05	0.05

Ford

Obs	Return	Prob
1	-0.01	0.01
2	0.10	0.09
3	0.15	0.10
4	0.20	0.20
5	0.08	0.05
6	0.25	0.25
7	0.13	0.05
8	0.09	0.10
9	0.11	0.10
10	0.06	0.05

Part 2 of question 1

Required:

Based on the following information (Note: You can use Microsoft Excel functions to expedite your calculations. Please show answers up to two digits after decimal point):

a) Calculate the expected rate of return for each individual asset.
b) Calculate the standard deviation of returns for each individual asset.
c) Assume that the correlation coefficient between the two assets is -1 (perfectly negatively

correlated).

Calculate the weighted average rate of returns and standard deviation of returns for the hypothetical portfolios containing the combination of the two assets in varying weights as indicated below. Then, choose a recommended portfolio. Summarize your answers in the following table.

For example, for Brad – Ford portfolio:

Portfolio	Brad	Ford	Weighted average rate of return	Standard deviation of returns	Recommended portfolio (please tick √ only one)
1	1.0	0.0
2	0.9	0.1
3	0.8	0.2
4	0.7	0.3
5	0.6	0.4
6	0.5	0.5
7	0.4	0.6
8	0.3	0.7
9	0.2	0.8
10	0.1	0.9
11	0.0	1.0

d) For each of the portfolios in (c) above, plot the risk-return for different weight of
assets (Note: For the risk-return plots, return is on vertical axis and risk is on horizontal axis).
e) Discuss what do you learn from this analysis including factors to be considered in choosing a preferred portfolio.

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what do you learn from this analysis including factors to be considered in choosing a preferred portfolio?

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Can you please elaborate on part c). Which portfolio is the recommended one?

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How do you plot the risk-return for the different weight of
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