Question

You have \(\$ 1,000\) that you can invest. If you buy General Motors stock, then, in one year's time: with a probability of 0.4 you will get \(\$ 1,600\); with a probability of 0.4 you will get \(\$ 1,100\); and with a probability of 0.2 you will get \(\$ 800\). If you put the money into the bank, in one year's time you will get \(\$ 1,100\) for certain. a. What is the expected value of your earnings from investing in General Motors stock? b. Suppose you prefer putting your money into the bank to investing it in General Motors stock. What does that tell us about your attitude to risk?

Short answer

Answer: The expected value of earnings from investing in General Motors stock is $1,240. If the student prefers putting their money in the bank to investing it in General Motors stock (despite the higher expected value), it indicates that they have a risk-averse attitude.

Step-by-step solution

List the possible outcomes and their probabilities

We have 3 possible outcomes from investing in General Motors stock: 1. With a probability of 0.4, you will get \(\$ 1,600\). 2. With a probability of 0.4, you will get \(\$ 1,100\). 3. With a probability of 0.2, you will get \(\$ 800\).

Calculate the expected value

To find the expected value of your earnings from investing in General Motors stock, we will multiply the amount of each outcome by its respective probability and add them together: Expected value = (0.4 * 1,600) + (0.4 * 1,100) + (0.2 * 800)

Simplify the expression

Now, let's simplify the expression to find the expected value: Expected value = (640) + (440) + (160) Expected value = \(\$ 1,240\) The expected value of your earnings from investing in General Motors stock is \(\$ 1,240\). #b. Analyzing your attitude towards risk#

Compare the expected value with the guaranteed return

We will now compare the expected value from investing in General Motors stock (\(\$ 1,240\)) with the guaranteed return from putting the money in the bank (\(\$ 1,100\)).

Analyze the decision-making process

If you prefer putting your money into the bank instead of investing it in General Motors stock, even though the expected value from the stock is higher, it means that you are risk-averse. To conclude, the expected value of your earnings from investing in General Motors stock is \(\$ 1,240\), and if you prefer putting your money in the bank to investing it in General Motors stock, it suggests that you have a risk-averse attitude.

Key concepts

Risk Aversion

Risk aversion is an important concept in investment and finance that describes a preference for certainty over uncertainty. When someone is risk-averse, they prefer to avoid risk and are more likely to choose options with lower potential returns if those options also come with less risk. In our investment scenario, a risk-averse individual would choose the guaranteed return from the bank over the potentially higher, yet uncertain, returns from the stock market.

In this exercise, even though the expected value of investing in General Motors stock is higher at $1,240 compared to the $1,100 from the bank, a risk-averse person chooses the bank. This choice demonstrates their preference for security over the chance of gaining more. Some reasons for risk aversion might include:

• Fear of potential loss. Choosing the safe option avoids the negative outcome of an investment loss.
• Personal financial circumstances. A person might not be able to afford any potential losses.
• Lack of investment experience. New investors may not feel comfortable taking risks.

Overall, risk aversion plays a crucial role in how individuals make investment decisions.

Probability

Probability plays a central role in determining the likely outcomes of different investment choices. In the context of our exercise, probability helps in calculating the expected value of returns from the potential outcomes of investing in General Motors stock.

Each outcome of the investment has an assigned probability that sums up how likely each result is to happen:

• 0.4 probability for earning $1,600
• 0.4 probability for earning $1,100
• 0.2 probability for earning $800

To find the expected value, we multiply each outcome by its probability and sum these products. This method allows investors to forecast potential returns while accounting for the uncertainty of each outcome. Understanding probability helps investors to make more informed decisions by evaluating both risks and rewards.

In investing, acknowledging the probability of various outcomes lets one weigh rewards against potential risks, ultimately guiding sounder financial decisions and identifying the nature of their risk tolerance.

Investment Analysis

Investment analysis involves evaluating the potential returns and risks associated with different investment choices. This process is crucial for making well-informed financial decisions. In our scenario, it involves analyzing the expected value and comparing it with the guaranteed return from a bank investment.

The expected value calculation for General Motors stock is a key part of investment analysis. By considering probabilities and possible returns, investors can estimate a single average outcome, which in our case, was $1,240. This expected value is then compared to the certain return from a bank to decide which is preferable.

Investment analysis doesn't only consider potential payoffs but also involves assessing risk levels. Calculated expected values and risk assessments help investors develop strategies such as diversification, where investments are spread across different assets to mitigate risk. With tools like probability assessments, investors can gauge their risk tolerance and choose investments aligning with their financial goals.

Effectively conducting an investment analysis can differentiate between a successful financial decision and a poorly judged one, making it an essential skill for any investor.