Suppose The Percentage Annual Return You Obtain

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 national economy as indicated below. For example, the probability that the economy will be in "boom" state is 0.15. In this case, if you invest in the stock market your return is assumed to be 25%; on the other hand if you invest in gold when the economy is in a "boom" state your return will be minus 30%. Likewise for the other possible states of the economy. Note that the sum of the probabilities has to be 1—and is.

State of economy | Probability | Market Return | Gold Return

Boom | 0.15 | 25% | -30%

Moderate Growth | 0.40 | 10% | -9%

Weak Growth | 0.25 | 5% | 35%

No Growth | 0.20 | 0% | 50%

Based on the expected return, would you rather invest your money in the stock market or in gold? Why?

Paper For Above instruction

Investment decisions are inherently probabilistic, especially when considering the fluctuating nature of economic conditions. Understanding the expected returns associated with different investment options under various economic states provides vital insights into making rational investment choices. This paper evaluates whether, based on the expected return calculations, investing in the stock market or in gold is more advantageous given the probabilities of economic states and their corresponding returns.

The problem presents four distinct states of the economy—boom, moderate growth, weak growth, and no growth—with assigned probabilities and corresponding returns for both the stock market and gold. The goal is to compute the expected return for each investment option and determine which one offers a higher expected value, thus indicating a preferable investment choice according to expected return criterion.

Let's proceed by calculating the expected returns. The expected return is the weighted average of possible returns, with weights corresponding to the probability of each state. Formally, the expected return (E) for each investment can be expressed as:

E = Σ (Probability of state × Return in that state)

Starting with the stock market:

  • Boom: 0.15 × 25% = 0.15 × 0.25 = 0.0375 or 3.75%
  • Moderate Growth: 0.40 × 10% = 0.40 × 0.10 = 0.04 or 4%
  • Weak Growth: 0.25 × 5% = 0.25 × 0.05 = 0.0125 or 1.25%
  • No Growth: 0.20 × 0% = 0.20 × 0 = 0

Adding these up, the expected return for the stock market is:

Expected Market Return = 3.75% + 4% + 1.25% + 0% = 9%

Now, calculating for gold:

  • Boom: 0.15 × -30% = 0.15 × -0.30 = -0.045 or -4.5%
  • Moderate Growth: 0.40 × -9% = 0.40 × -0.09 = -0.036 or -3.6%
  • Weak Growth: 0.25 × 35% = 0.25 × 0.35 = 0.0875 or 8.75%
  • No Growth: 0.20 × 50% = 0.20 × 0.50 = 0.10 or 10%

Adding these, the expected return for gold is:

Expected Gold Return = -4.5% + (-3.6%) + 8.75% + 10% = 10.65%

Comparing the expected returns, the gold investment offers an expected return of approximately 10.65%, which exceeds the stock market's expected return of 9%. According to the expected return criterion, investing in gold appears to be more advantageous. It offers a higher average return across the range of economic states, indicating a better risk-adjusted expectation in this scenario.

However, it is essential to consider other factors such as risk, volatility, and personal risk tolerance. The expected return does not capture the variability or potential extremes of returns—the gold investment shows two highly volatile points with significant positive and negative returns, which could imply higher risk. The stock market, while generally offering a lower expected return, might have a more consistent return profile with less volatility. Diversification strategies often combine assets to balance these considerations.

In conclusion, purely based on expected return calculations derived from given probabilities and returns, investing in gold is the more attractive option financially. Nonetheless, investors should weigh the risk profile, liquidity preferences, and potential for variability before making a final decision. Optimal investment strategies often involve balancing expected return against risk, aligning with personal investment objectives and risk tolerance.

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