Question

Suppose you have \(\$ 1,000\) that you can invest in Ted and Larry's Ice Cream Parlor and/or Ethel's House of Cocoa. The price of a share of stock in either company is \(\$ 100\). The fortunes of each company are closely linked to the weather. When it is warm, the value of Ted and Larry's stock rises to \(\$ 150\) but the value of \(\underline{\text { Ethel's stock falls to }}\) \(\$ 60\). When it is cold, the value of Ethel's stock rises to \(\$ 150\) but the value of Ted and Larry's stock falls to \(\$ 60\). There is an equal chance of the weather being warm or cold. a. If you invest all your money in Ted and Larry's, what is your expected stock value? What if you invest all your money in Ethel's? b. Suppose you diversify and invest half of your \(\$ 1,000\) in each company. How much will your total stock be worth if the weather is warm? What if it is cold? c. Suppose you are risk-averse. Would you prefer to put all your money in Ted and Larry's, as in part a? Or would you prefer to diversify, as in part b? Explain your reasoning.

Short answer

a. Ted and Larry's expected value: \((\$150 + \$60) / 2 = \$105\). Ethel's expected value: same calculation, so also \$105. b. Warm weather diversified value: \((5 \times \$150) + (5 \times \$60)) = \$1050. Cold weather diversified value: \((5 \times \$60) + (5 \times \$150)) = \$1050. c. A risk-averse investor would prefer to diversify, as the stock value would be \$1050 regardless of weather, compared to the fluctuating potential values of \$1000 or \$600 when investing solely in one company.

Step-by-step solution

Calculate Expected Value for Ted and Larry's

To calculate the expected stock value of investing all in Ted and Larry's, multiply each possible outcome by its probability and sum the results. The probability of each outcome is 0.5. The possible values are \(\$150\) for warm weather and \(\$60\) for cold weather.

Calculate Expected Value for Ethel's

Repeat the calculation for Ethel's. The stock value possibilities are also \(\$150\) for favorable cold weather and \(\$60\) for unfavorable warm weather, with a 0.5 probability for each outcome.

Calculate Stock Value when Diversified During Warm Weather

When investing half in each company and it's warm, you would own 5 shares of Ted and Larry's valued at \(\$150\) each and 5 shares of Ethel's valued at \(\$60\) each.

Calculate Stock Value when Diversified During Cold Weather

Conduct a similar calculation for cold weather. Each share would now be worth \(\$60\) for Ted and Larry's and \(\$150\) for Ethel's.

Analyze Risk-Averse Investment Choices

To make a decision as a risk-averse investor, compare the volatility of the investment value in Ted and Larry's versus the diversified investment. A risk-averse investor typically prefers the investment with the least amount of fluctuation in value.

Key concepts

Expected Value Calculation

Understanding the expected value is essential when making informed economic decisions, particularly in investments. It helps to predict the average outcome when the future holds multiple possibilities each with their own probabilities.

In the exercise's context, to find the expected stock value of investing solely in Ted and Larry's or Ethel's, one must consider two potential outcomes based on the weather. In either scenario, there's a 50% chance of warm weather, boosting Ted and Larry's stock value to \(150, and a 50% chance of cold weather, which would lower it to \)60. Using the formula for expected value, we calculate \( EV = (0.5 \times 150) + (0.5 \times 60) \), which simplifies to \( EV = 75 + 30 = 105 \). This means, on average, each share of stock in Ted and Larry's would be worth \(105 over time, assuming an even chance of warm or cold weather.

Similarly, the expected value for Ethel's stock is calculated with the same probabilities but reversed weather outcomes. The formula remains \( EV = (0.5 \times 150) + (0.5 \times 60) \), and the result is also \)105 per share.

Investment Diversification

Diversification is a risk management strategy employed in investing that involves spreading investments across various financial assets to reduce exposure to any single asset or risk. It's akin to the adage 'don't put all your eggs in one basket'.

By investing in both Ted and Larry's Ice Cream Parlor and Ethel's House of Cocoa, as proposed in the exercise with \(500 in each, you balance the risk posed by fluctuating weather conditions. If the weather is warm, the total value of the stock would be \( 5 \times 150 + 5 \times 60 = 750 + 300 = 1050 \). Conversely, in cold weather, the outcome would also be \)1050, resulting from \( 5 \times 60 + 5 \times 150 \). This non-variable result showcases the primary benefit of diversification; it stabilizes your investment's value irrespective of external, unpredictable factors like weather.

Risk Aversion in Microeconomics

Risk aversion is a concept in microeconomics that reflects the preference for a sure thing over a gamble with potentially higher, but uncertain, gains. Risk-averse investors prefer to minimize uncertainty and protect their investments from extreme variations.

In the scenario given, a risk-averse individual would likely choose diversification over investing everything in a single company. By spreading their investment between Ted and Larry's and Ethel's, the investor guarantees an even outcome (\(1050) regardless of the weather. On the other hand, investing solely in one company would result in either a \)1500 or $600 return, a decision that is too unpredictable for someone with a risk-averse disposition.

These tendencies are crucial to financial markets and personal investment strategies. They influence decisions on asset allocation, portfolio management and can help investors in aligning their financial strategies with their personal risk tolerance.