## Unit 4 Activities

##### Time Advisory

This unit should take you 19.75 hours to complete

- Subunit 4.1: 4.7 hours
- Reading: 4.5 hours
- Web Media: 0.2 hours
- Subunit 4.2: 1 hour
- Reading: 1 hour
- Subunit 4.3: 2 hours
- Reading: 2 hours
- Subunit 4.4: 2 hours
- Reading: 2 hours
- Subunit 4.5: 4 hours
- Reading: 4 hours
- Subunit 4.6: 6 hours
- Reading: 6 hours

##### Learning Outcomes

Upon successful completion of this unit, the student will be able to:

- Compute expected values when risk issues need to be considered in finance.
- Explain why the standard deviation is used in finance as a measure of risk.
- Explain how the financial manager makes financial investment decisions when confronted with issues of risk and uncertainty while considering different risk preferences.
- Analyze an investment portfolio and apply market betas to the analysis.

**4.1 Statistical Concepts in Finance: Probabilities, Expected Value, Standard Deviation, and Risk-Return Tradeoff**

**Reading:** Dr. Ivo Welch's *Corporate Finance (3rd Edition)*: Chapter 6: Uncertainty, Default, and Risk: "Section 6.1: An Introduction to Statistics” (HTML) and "Section 6.2: Interest Rates and Credit Risk (Default Risk)” (HTML)

Instructions: Read Sections 6.1 and 6.2 from Chapter 6 in the textbook. Section 6.1 introduces you to statistical concepts in finance such as the "expected value” (an average) and the "standard deviation.” The sections also introduce the different types of investors commonly found in the real-world: 1) individuals who like to take on risky investment projects, known as "risk-seekers,” 2) individuals who do not like to take on risky investment projects, known as "risk-averters,” and 3) individuals who are neutral concerning risky propositions, known as "risk-neutrals.” Section 6.2 explains several real-world credit instruments used today. Also, make sure to answer the questions given at the end of Sections 6.1 and 6.2 and compare your answers to the answers given at the end of Chapter 6 under the heading titled "Answers.” This resource covers the topics outlined in sub-subunits 4.1.1 to 4.1.3.

This reading should take you approximately 4 hours to complete.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**Reading:** University of West Florida: Dr. Richard Constand's FIN 4424 - *Problems in Financial Management*: Risk and Return: "Overview of Risk and Return” (HTML) and "Types of Risk” (HTML)

Instructions: Read the two resources from Dr. Constand's site as they explain the risk-return tradeoff and the different types of risk commonly faced by investors. This resource covers the topics outlined in sub-subunit 4.1.3.

This reading should take you approximately 0.5 hours to complete.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**Web Media:** Khan Academy's *Finance*: "Risk and Reward Introduction” (YouTube)

Instructions: This video explains an example of the relationship between risk and reward. This resource covers the topics outlined in sub-subunit 4.1.3.

Watching this video should take approximately 15 minutes.

Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 United States License. It is attributed to the Khan Academy.

**4.1.1 Expected Value**

*Note: This topic is covered by the resources in subunit 4.1. The expected value is simply an average but with probabilities attached. For example, suppose that you have these three possible investment outcomes with their respective probabilities of occurring:*

Investment Outcome | Probability |

Profit $100,000 | 0.30 |

Profit$50,000 | 0.40 |

No profit and no loss | 0.30 |

*Notice that the sum of these probabilities needs to add up to 1.00 (or 100%). To compute your "average” profits, you need to consider their probabilities. This average is normally called the "expected value” in statistics. Using this example, the expected value is computed as follows: (100,000x0.30) + (50,000x0.40) + (0x0.30) = 30,000 + 20,000 + 0 = 50,000. Therefore, you expect to receive $50,000 from this investment project. In general, the expected value formula is:*

*Expected Value = (outcome A x probability of A) + (outcome B x probability of B) + ... + (outcome of Z x probability of Z)*

*where the sum of the probabilities add up to 1.00.*

**4.1.2 Standard Deviation**

*Note: This topic is covered by the resources in subunit 4.1. The standard deviation does not have an intuitive meaning, but it is a measure of risk in finance. When you are facing an investment project with several possible outcomes and you know their respective probabilities, you learned from sub-subunit 4.1.1 that you can compute the expected value of an investment project. But when you also need to know the level of risk, you can compute the standard deviation as follows:** *

* Standard Deviation = square root of *

* (outcome A - expected value) ^{2 }x probability of A*

* + (outcome B - expected value) ^{2 }x probability of B*

* + ... *

* + (outcome Z - expected value) ^{2 }x probability of Z*

*where the sum of the probabilities add up to 1.00.*

**4.1.3 Risk-Return Tradeoff**

*Note: This topic is covered by the resources in subunit 4.1. In finance, an investor will take on more risk only if the return is higher, or vice versa. This is what we call in finance the "risk-return tradeoff.*

**4.2 Uncertainty in Capital Budgeting**

**Reading:** Dr. Ivo Welch's *Corporate Finance (3rd Edition)*: Chapter 6: Uncertainty, Default, and Risk: "Section 6.3: Uncertainty in Capital Budgeting”

Instructions: Read Section 6.3 from Chapter 6 in the textbook as it shows how to apply risk in capital budgeting. Also, make sure to answer the questions given at the end of Section 6.3 and compare your answers to the answers given at the end of Chapter 6 under the heading titled "Answers.”

This reading should take you approximately 1 hour to complete.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**4.3 Risk and Reward in a Portfolio**

**Reading:** Dr. Ivo Welch's *Corporate Finance (3rd Edition)*: Chapter 8: Investor Choice: Risk and Reward: "Section 8.1: Measuring Risk and Reward” (HTML)

Instructions: Read Section 8.1 from Chapter 8 in the textbook. Section 8.1 shows you how to compute the expected value and the standard deviation for a group of investment projects. This group with several investment projects is oftentimes called a "portfolio.” Also, make sure to answer the questions given at the end of Section 8.1 and compare your answers to the answers given at the end of Chapter 8 under the heading titled "Answers.” This reading should take you approximately 2 hours to complete.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**4.4 Risk Diversification in a Portfolio**

**Reading** Dr. Ivo Welch's *Corporate Finance (3rd Edition)*: Chapter 8: Investor Choice: Risk and Reward: "Section 8.2: Diversification” (HTML)

Instructions: Read Section 8.2 from Chapter 8 in the textbook. Section 8.2 shows you how to adjust a portfolio's composition to lower its risk. Also, make sure to answer the questions given at the end of Section 8.2 and compare your answers to the answers given at the end of Chapter 8 under the heading titled "Answers.” This reading should take you approximately 2 hours to complete.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**4.5 Risk of Stock Investments and Market Betas**

Link: Dr. Ivo Welch's *Corporate Finance (3rd Edition)*: Chapter 8: Investor Choice: Risk and Reward: "Section 8.3: Investor Preferences and Risk Contribution,” (HTML) "Section 8.4: Interpreting Some Typical Stock Market Betas,” (HTML) and "Section 8.5: Market Betas for Portfolios and Conglomerate Firms” (HTML)

nstructions: Read Sections 8.3, 8.4, and 8.5 from Chapter 8 in the textbook. Section 8.3 introduces you to the concepts of "market betas.” Make sure to pay special attention to the statistical model behind an asset's expected return calculated from a market's beta. The market beta effect is simply the relationship between the stock performance of the overall stock market and an individual stock's performance. If the market beta has a positive value, it means that the individual stock's performance will move in the same direction as the market's performance. And if the market beta is negative, it means that the individual stock's performance will move in opposite direction. Sections 8.4 and 8.5 give you several real-world examples of market betas. Also, make sure to answer the questions given at the end of Sections 8.3, 8.4, and 8.5 and compare your answers to the answers given at the end of Chapter 8 under the heading titled "Answers.”

This reading should take you approximately 4 hours to complete.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**4.6 Using Excel in Applications of Risk**

**Activity:** The Wharton School at the University of Pennsylvania: Dr. Michael R. Roberts' Finance 100: Corporate Finance: "Topic 3: Portfolio Analysis and Diversification” (PDF and Excel)

Instructions: In Dr. Roberts' webpage titled "Topic 3: Portfolio Analysis and Diversification,” scroll down to the section titled "Downloadable Files” and access the three problem set files with these titles: "Problem Set (PDF File),” "Problem Set Solutions (Excel File),” and "Alternative Problem Set Solutions (PDF File).” Make sure to solve the problems on your own and then take a look at the solutions.

These assignments should take you approximately 6 hours to complete.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.