Expected Rate Of Return And Risk For Bj Gautney Enter 163525

Expected Rate Of Return And Risk Bj Gautney Enterprises Is Evalu

Analyze the expected rate of return and risk associated with different investment opportunities, including Treasury bills and a new investment fund, by calculating the expected returns and standard deviations based on provided probabilities and outcomes. Evaluate whether these investments are appealing based on computed risk and return metrics.

Paper For Above instruction

Investors constantly seek to evaluate the potential profitability and risk associated with different investment opportunities. One common approach involves calculating the expected rate of return and the variability of returns, measured by standard deviation, to gauge the attractiveness of these investments under uncertain economic conditions. This paper applies these principles to three scenarios: investing in one-year Treasury bills, a new mortgage securities fund, and a hypothetical investment opportunity with distinct economic states.

Expected Rate of Return and Risk Analysis

BJ Gautney Enterprises is assessing a security with a current one-year Treasury bill rate of 3.8%. To determine whether investing in this security is advisable, it is essential to calculate its expected return and its risk measured by standard deviation. Treasury bills are generally considered risk-free benchmarks due to their backing by the government, but for illustrative purposes, we will compute these metrics assuming the potential for deviations or for more volatile securities with similar returns.

The expected return of an investment is calculated as the sum of the products of each possible return and its associated probability. Since Treasury bills are quoting a 3.8% yield with a probability distribution not provided explicitly in detail, the simplest assumption is that the expected return closely approximates this risk-free rate, given the absence of alternative return scenarios.

However, if we hypothesize a range of possible returns based on market fluctuations, the calculation would involve assigning probabilities to each return and using the formula:

Expected Return = Σ (Probability of Return × Return)

Similarly, the standard deviation measures the dispersion of potential returns around the expected return, capturing investment risk. It is calculated as the square root of the variance, which is the weighted average of squared deviations from the expected return:

Standard Deviation = √Σ [Probability of Return × (Return - Expected Return)²]

In the context of Treasury bills, given their low-risk profile, the expected return will approximately equal the current rate of 3.8%, and the standard deviation will be minimal, reflecting the low volatility.

Analysis of the Investment Fund Based on Economic Outcomes

James Fromholtz considers investing in a new mortgage securities fund, with its performance tied to the state of the economy. The fund's potential outcomes, along with their probabilities and returns, provide a clear example to evaluate expected return and risk. The given economic states are rapid expansion and recovery, modest growth, continued recession, and depression, with respective probabilities of 5%, 50%, 40%, and 5%. The corresponding returns are 100%, 30%, 10%, and -100%.

To compute the expected rate of return, multiply each state’s probability by its return, then sum these products:

Expected Return = (0.05 × 100%) + (0.50 × 30%) + (0.40 × 10%) + (0.05 × -100%)

= 5% + 15% + 4% - 5% = 19%

The calculated expected return indicates a favorable average outcome; however, risk evaluation requires calculating the standard deviation, which involves the variance — the weighted squared deviations of each return from the expected return:

Variance = Σ [Probability × (Return - Expected Return)²]

Calculating each term:

  • Rapid expansion: 0.05 × (100% - 19%)² = 0.05 × (81%)² = 0.05 × 6561 = 328.05
  • Modest growth: 0.50 × (30% - 19%)² = 0.50 × (11%)² = 0.50 × 121 = 60.5
  • Recession: 0.40 × (10% - 19%)² = 0.40 × (-9%)² = 0.40 × 81 = 32.4
  • Depression: 0.05 × (-100% - 19%)² = 0.05 × (-119%)² = 0.05 × 14161 = 708.05

Total variance = 328.05 + 60.5 + 32.4 + 708.05 = 1129

Standard deviation = √1129 ≈ 33.6%

This high standard deviation displays considerable risk, as the investment outcomes are highly dispersed around the mean. The possibility of losing all investment money in a depression state is significant, reflecting a high-risk, high-return scenario.

Investment Decision and Risk-Return Tradeoff

Based on the calculations, the expected return of approximately 19% suggests a potentially profitable opportunity. However, the substantial risk indicated by the standard deviation of about 33.6% necessitates careful consideration. Risk-averse investors may hesitate, given the sizable probability of severe loss, especially in the depression scenario. Conversely, risk-tolerant investors seeking high returns might find this investment attractive despite its volatility.

Personal investment decisions depend on the risk appetite and the investor's capacity to withstand potential losses. Given the high standard deviation, only investors with a high risk tolerance and capacity to absorb losses are likely to pursue this opportunity.

Conclusion

Calculating the expected return and standard deviation provides vital insights into the risk-reward profile of investment opportunities. The Treasury bill scenario exhibits low risk and modest returns, aligning with conservative investment strategies. Conversely, the mortgage securities fund shows a high expected return accompanied by substantial risk, reflecting the inherent volatility of economic-dependent investments. Ultimately, investment choices should align with individual risk preferences and financial goals, supported by quantitative risk-return analysis as demonstrated.

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