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.