Suppose That The Percentage Annual Return You Obtain 970016 ✓ Solved

Suppose That The Percentage Annual Return You Obtain When You Invest A

Suppose that the percentage annual return you obtain when you invest a dollar in gold or the stock market is dependent on the general state of the economic environment. The possible states include "boom," "moderate growth," "weak growth," and "no growth," each with associated probabilities and returns for both investment options. The probability that the economy is in a "boom" state is 0.15, with a stock market return of 25% and a gold return of -30%. In the "moderate growth" state (probability 0.35), the stock market yields a 20% return, while gold yields -9%. During "weak growth" (probability 0.25), stock returns are 5%, and gold yields 35%. In the "no growth" state (probability 0.25), the returns are 0% for the stock market and 50% for gold. The sum of all probabilities equals 1. Based on these expected returns, an analysis of whether to invest in the stock market or gold will be conducted.

Sample Paper For Above instruction

Investors constantly face the challenge of deciding where to allocate their resources to maximize returns while considering the risks associated with these investments. A common approach to making such decisions involves analyzing the expected returns based on different economic scenarios. In this case, the decision-maker must compare the expected returns of investing in the stock market versus gold, considering various states of the economy and their probabilities.

The expected return of an investment is calculated by summing the products of the returns in each state by the probability of that state occurring. For the stock market, the expected return (ER)

is computed as follows:

ER_stock = (Probability of Boom × Return in Boom) + (Probability of Moderate Growth × Return in Moderate Growth) + (Probability of Weak Growth × Return in Weak Growth) + (Probability of No Growth × Return in No Growth)

= (0.15 × 25%) + (0.35 × 20%) + (0.25 × 5%) + (0.25 × 0%)

= (0.15 × 0.25) + (0.35 × 0.20) + (0.25 × 0.05) + (0.25 × 0)

= 0.0375 + 0.07 + 0.0125 + 0

= 0.12 or 12%

Similarly, the expected return for gold (ER_gold) is:

ER_gold = (0.15 × -30%) + (0.35 × -9%) + (0.25 × 35%) + (0.25 × 50%)

= (0.15 × -0.30) + (0.35 × -0.09) + (0.25 × 0.35) + (0.25 × 0.50)

= -0.045 + -0.0315 + 0.0875 + 0.125

= 0.136 or 13.6%

Based on the expected returns, gold has an expected return of approximately 13.6%, slightly higher than the 12% expected return for the stock market. This suggests that, purely from an expected return perspective, investing in gold might seem more advantageous.

However, decision-making should also consider risk factors, such as the variability of returns and potential losses. The stock market's negative return in the "boom" state indicates high variability and the possibility of losses in certain states. Conversely, gold offers a higher return in the "no growth" state, but also exhibits significant losses during the "boom" that could impact the investment's risk profile.

Additionally, investors need to consider their risk tolerance. The higher expected return of gold is accompanied by the possibility of large losses (e.g., -30%), which might be unacceptable for risk-averse investors. The stock market's returns are more balanced but also come with volatility. Real-world investment decisions should incorporate risk measures such as standard deviation, VaR (Value at Risk), and other risk-adjusted performance metrics to determine the preferable investment.

In conclusion, based solely on the expected return calculations, investing in gold appears slightly more advantageous than the stock market. Nevertheless, a comprehensive investment decision must incorporate risk preferences, market volatility, and portfolio diversification strategies.

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