An Investor Considers Investing $10,000 In The Stock Market
1an Investor Considers Investing 10000 In The Stock Market He Beli
1) An investor considers investing $10,000 in the stock market. He believes that the probability is 0.30 that the economy will improve, 0.40 that it will stay the same, and 0.30 that it will deteriorate. Further, if the economy improves, he expects his investment to grow to $15,000, but it can also go down to $8,000 if the economy deteriorates. If the economy stays the same, his investment will stay at $10,000.
a. What is the expected value of his investment?
b. Should he invest the $10,000 in the stock market if he is risk neutral?
c. Is the decision clear-cut if he is risk averse? Explain.
Paper For Above instruction
The decision to invest in the stock market involves analyzing various economic scenarios and understanding the investor's risk preferences. This paper evaluates the expected value of the investment, discusses investment choices under risk neutrality, and examines the implications for a risk-averse investor.
Expected Value Calculation
The expected value (EV) of an investment is calculated by summing the products of each outcome's value and its probability. Given the scenarios:
- Economy improves (probability 0.30): Investment grows to $15,000
- Economy remains the same (probability 0.40): Investment stays at $10,000
- Economy deteriorates (probability 0.30): Investment drops to $8,000
The EV is computed as:
EV = (0.30 $15,000) + (0.40 $10,000) + (0.30 * $8,000) = $4,500 + $4,000 + $2,400 = $10,900
This expected value suggests that, on average, the investor can expect to gain $900 above the initial investment ($10,000).
Decision for a Risk-Neutral Investor
A risk-neutral investor focuses solely on maximizing expected monetary value. Since the EV of investing ($10,900) exceeds the initial investment ($10,000), a risk-neutral investor would choose to invest, expecting a positive return.
Implications for a Risk-Averse Investor
However, risk-averse investors prioritize minimizing uncertainty and potential losses. Although the EV is favorable, the potential decline to $8,000 in a deteriorating economy poses a risk. The investor might prefer investments with less volatility or higher certainty, even if the expected return is lower.
In this scenario, the risk-averse investor might opt against investing because of the possibility of losing $2,000, which could be uncomfortable relative to the potential gain, especially if they weigh losses more heavily than gains (Kahneman & Tversky, 1979).
Conclusion
For a risk-neutral investor, the positive expected value makes investing financially justifiable. Conversely, for a risk-averse individual, the decision depends on their personal risk tolerance. The possibility of substantial loss might deter investment, highlighting the importance of individual risk preferences in financial decision-making.
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