Question

You have \(\$ 1,000\) that you can invest. If you buy Ford stock, you face the following returns and probabilities from holding the stock for one year: with a probability of 0.2 you will get \(\$ 1,500\); with a probability of 0.4 you will get \(\$ 1,100\); and with a probability of 0.4 you will get \(\$ 900 .\) 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 Ford stock? b. Suppose you are risk-averse. Can we say for sure whether you will invest in Ford stock or put your money into the bank?

Short answer

Answer: For a risk-averse individual, they will prefer to put their money in the bank rather than investing in Ford stock. This is because the bank option provides a certain outcome of $1,100 while the investment has potential outcomes ranging from $900 to $1,500, despite the equal expected values for both options.

Step-by-step solution

Calculate the expected value of the earnings from investing in Ford stock

To calculate the expected value, multiply the potential outcomes by their corresponding probabilities and sum the results. The expected value of the earnings from investing in Ford stock is: $$ E(Ford)=0.2(\$1,500)+0.4(\$1,100)+0.4(\$900) $$

Solve for the expected value

Calculate the expected value: $$ E(Ford)=0.2(\$1,500)+0.4(\$1,100)+0.4(\$900)=\$300+\$440+\$360=\$1,100 $$ So, the expected value of investing in Ford stock for one year is \(\$1,100\).

Compare the options

The expected value of investing in Ford stock (\$1,100) is the same as the certain outcome of putting the money in the bank (\$1,100). However, given risk aversion, an individual will generally prefer the option with a certain outcome over the one with uncertainty, even if expected values are equal.

Conclusion

For a risk-averse individual, we can say for sure that they will prefer to put their money in the bank rather than investing in Ford stock, because the bank option provides a certain outcome of \$1,100 while the expected value of investing in Ford stock is also \$1,100 but with potential outcomes ranging from \$900 to \$1,500.

Key concepts

Investment Risk

Investment risk refers to the possibility of achieving a different outcome from the expected one when investing. In the example of investing in Ford stock, there are various scenarios: making a return of $1,500, $1,100, or $900. Each scenario has a specific probability attached to it, highlighting the uncertain nature of investing in stocks. This variability in potential outcomes constitutes the investment risk.

• Higher potential returns usually come with greater risk.
• Investments with certain returns carry lower risk.

When evaluating investment opportunities, understanding the level of risk involved is crucial. It helps decide whether the potential rewards justify the uncertainty involved. In contrast, putting money in the bank typically represents low risk due to guaranteed returns.

Probability

Probability plays a significant role in calculating expected values and understanding potential outcomes of investments. In the given exercise, each potential outcome from investing in Ford stock has an associated probability:

• 20% chance of earning $1,500
• 40% chance of earning $1,100
• 40% chance of earning $900

These probabilities help investors in computing the expected value of their investments. By multiplying each possible outcome by its probability and then summing those values, investors obtain a predicted average return, indicating what they might expect over many similar investments. Probability doesn't guarantee a particular outcome, but it helps gauge the likelihood of various results, allowing investors to make more informed decisions.

Risk Aversion

Risk aversion is a concept describing the preference for certainty over uncertainty. Individuals who are risk-averse prefer a certain gain over a gamble with a potentially higher payoff but with uncertainty. In this exercise, even though the expected value of investing in Ford stock matches the bank's guaranteed return of $1,100, a risk-averse person would likely choose the bank option.

• Risk-averse individuals value predictability and security.
• Ensuring a specific outcome can be more appealing than the potential for higher gains.

For a risk-averse individual, the possibility of lower returns (e.g., $900 from the stock investment) outweighs the opportunity for higher returns (e.g., $1,500). Therefore, despite the same expected value, the guarantee with the bank deposit is often more attractive to those who value stability and risk reduction.