## Risk Analysis Exercises and Problems

Complete these exercises and problems and then check your work.

### Exercises

#### Question 1

What is Risk? What two factors are important in determining the degree of risk?

#### Question 2

"As long as we can't lose any money, we have a risk-free investment". Discuss this comment.

#### Question 3

Both investing and gambling can be defined as "undertaking risk in order to earn a profit". Explain how these two activities are different and why society generally takes a more favorable view of investing compared to gambling.

#### Question 4

Explain the concept of correlation? If two securities have a high positive correlation what does that mean? Give an example of two securities that might be highly correlated. If two securities have a low positive correlation what does that mean? Give an example of two securities that might have a low positive correlation. If two securities are negatively correlated what does that mean? Give an example of two securities that might be negatively correlated?

#### Question 5

What is diversifiable risk? What is market or non-diversifiable risk? Give an example of each.

#### Question 6

Standard deviation measures what kind of risk? When is this important? When is it not important?

#### Question 7

Beta measures what kind of risk? When is this important? When is it not important?

#### Question 8

Explain why we can use either beta or standard deviation when comparing two well-diversified portfolios. Is this true for any two portfolios?

#### Question 9

If I had a stock with a beta of 1.25 and I thought the stock market was going to climb by 10% over the next 2 months, how much should I expect my stock to move? How about if I thought the stock market was going to drop by 5%? What would happen under each of the previous two cases if my beta was 0.6 instead of 1.25?

#### Question 10

According to the SML, if we purchase only securities with a high beta, we should (on average) earn higher returns. True or False? Explain your answer.

#### Question 11

Stock A has an expected return of 10% and stock B has an expected return of 20%. This means that if we buy stock B, we will be wealthier at the end of the year than if we bought stock A. True or False and explain.

#### Question 12

Due to a recent news announcement, the expected return on XYZ Corp. just went from 13% to 18%. Assuming that the stock was in equilibrium prior to the announcement and the announcement did not affect the required return, explain what will happen to XYZ's stock price (and expected return) in the immediate future to bring the stock back into equilibrium. How long should this process take?

#### Problem 1

Find the expected return and standard deviation of each stock.

Stock A

Probability | Return |

0.20 | -30% |

0.40 | 15% |

0.40 | 30% |

Stock B

Probability | Return |

0.30 | -5% |

0.40 | 10% |

0.30 | 20% |

If you were going to put all of you money into one of these two stocks, which should you pick?

#### Problem 2

2a. Find the expected return and standard deviation of each stock

Probability | Return of Stock C | Return of Stock D |

0.30 | -10% | 25% |

0.50 | 15% | 10% |

0.20 | 40% | 0% |

2b. Calculate the expected return and standard deviation of a portfolio made up of 50% stock C and 50% stock D if the correlation is -0.75.

2c. Would you prefer to put your money in stock C, stock D or the 50/50 portfolio? Explain.

#### Problem 3

Assume you had two stocks. Stock A had an expected return of 20% and a standard deviation of 25%. Stock B had an expected return of 15% and a standard deviation of 20%. You want to create a portfolio made up of 65% stock A and 35% stock B. Find the expected return and standard deviation of this portfolio under the following conditions.

3a. Correlation between stock A and B is 1.0

3b. Correlation between stock A and B is 0.5

3c. Correlation between stock A and B is 0.0

3d. Correlation between stock A and B is -0.5

3e. Correlation between stock A and B is -1.0

#### Problem 4

The stock of Ralph's Restaurants has a standard deviation of 70% and has a correlation with the market of 0.40. The expected return for the market is 13% and it has a standard deviation of 20%. Currently the risk-free rate of return is 5%.

4a. What is the beta for Ralph's Restaurants?

4b. What is the required return for Ralph's Restaurants?

4c. What is the expected return for Ralph's restaurants in equilibrium?

#### Problem 5

We are purchasing a stock that just paid a dividend (D_{0})
of $1.50. The growth rate in dividends for this stock is 4% and it has a
beta of 1.3. The expected return on the market is 12% and the current
Treasury rate is 7%. How much should we pay for this stock?

Source: Kevin Bracker, Fang Lin, Jennifer Pursley, https://businessfinanceessentials.pressbooks.com/chapter/chapter-7-risk-analysis-2/

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 License.