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

The expected value of the earnings from investing in General Motors stock is \( $1200 \. Choosing the bank over investing in the stock indicates a risk-averse attitude.

Step-by-step solution

Calculate expected earnings from each outcome

To find the expected value from investing in General Motors stock, multiply each possible outcome by the probability of that outcome occurring. Three possible outcomes are given, with three different probabilities.

Sum the products of outcomes and probabilities

Add the results of all three products to determine the total expected value of the stock investment.

Interpretation of preference for bank over stock

If investing in the bank is preferred despite its lower potential returns compared to the stock's expected value, it suggests a risk-averse attitude towards investment.

Key concepts

Investment Decision Making

When faced with an investment choice, such as whether to place money in stocks or in a bank account, decision-making often comes down to comparing potential gains and the risks involved. To illustrate, let's consider an example where you have \$1000\ to invest. With General Motors (GM) stock, there are different outcomes based on the stock's performance after one year.
Within this scenario, you need to assess the probable gains or losses and determine what's the best avenue for your investment. Calculating the expected value of your potential earnings from investing in GM stock is crucial; it gives you an estimated average of what you can expect to gain, taking into account the varying outcomes and their probabilities.
Here's where you bring in a mathematical approach to aid your decision. By calculating the expected value, which in this exercise would represent the earnings from the stock, you'd multiply each possible outcome (\(\$1600\), \(\$1100\), and \(\$800\)) by the likelihood of each outcome occurring (probability of 0.4, 0.4, and 0.2 respectively) and adding them up to get one number – the expected value. If this value is higher than the certain \(\$1100\) from the bank, the math suggests GM stock might be the better option; however, that's not the sole factor you should consider.

Probability and Outcomes

The concept of probability is fundamental when contemplating future scenarios in investments. It quantifies the chance of an event happening, such as the appreciation or depreciation of stock, and is expressed as a number between 0 and 1, with 1 representing certainty.
In our example with GM stock, the outcomes have associated probabilities indicating how likely each scenario is. For instance, there's a 40% chance (\(0.4\) probability) the stock will yield \(\$1600\), another 40% chance for \(\$1100\), and a 20% chance for \(\$800\). To get a clear picture of what you're potentially diving into, it's crucial to look at both the probabilities and the outcomes they're attached to.

Calculating the Expected Value

To do this, multiply each outcome with its probability and sum these up, which goes as follows: Expected Value = (\(0.4 \times \$1600\)) + (\(0.4 \times \$1100\)) + (\(0.2 \times \$800\)). This formula yields a result that, when compared to the guaranteed \(\$1100\) from a bank deposit, can guide you through the murky waters of investment decisions.

Attitude to Risk

Your attitude towards risk is often the final and most personal piece of the investment puzzle. In simple terms, it's your individual comfort level with the possibility that an investment might not turn out as expected. Someone with a low tolerance for risk, known as being risk-averse, might prefer more predictable, lower-return investments - favoring security over the chance at higher profits.
If, given our exercise's context, you would rather put your money into the bank than risk it on GM stock, this signals a risk-averse attitude. You are opting for the certainty of receiving \(\$1100\) instead of dealing with the uncertain outcomes of the stock, despite the higher expected value of the stock investment. Your preference leans towards stability and away from the variability of returns, even if it means potentially missing out on greater earnings.
Understanding one's risk tolerance is critical because it influences not only the types of investments you might choose but also how you react to market fluctuations – sticking with your investment strategy during downturns can be just as important as the initial decision of where to invest.