Expected Rate Of Return And Risk For Bj Gautney Enter 103026

Expected Rate Of Return And Risk Bj Gautney Enterprises Is Evaluati

In this analysis, we evaluate the expected returns and risks associated with two investment opportunities: a security evaluated by B.J Gautney Enterprises and a mortgage securities fund considered by James Fromholtz. The assessment includes calculating the expected rate of return and the standard deviation for each investment, providing insights into their potential profitability and risk levels. Such measurements are vital in investment decision-making, enabling investors to balance risk and return effectively.

Paper For Above instruction

Analysis of B.J Gautney Enterprises Security

The first part of this evaluation encompasses the security that B.J Gautney Enterprises is assessing. The data provided includes possible returns with associated probabilities: a 5% chance of losing 5%, a 40% chance of gaining 1%, a 50% chance of gaining 5%, and a 5% chance of earning 8%. The risk-free rate, represented by one-year Treasury bills, is 3.8%, but our focus will be on the risk-related to this security.

To compute the expected return, each outcome’s return is multiplied by its probability, then summed up:

Expected Return = (0.05)(-5%) + (0.40)(1%) + (0.50)(5%) + (0.05)(8%)

Calculating these components:

• 0.05 × (-5%) = -0.25%
• 0.40 × 1% = 0.40%
• 0.50 × 5% = 2.50%
• 0.05 × 8% = 0.40%

Summing these gives:

Expected Return = -0.25% + 0.40% + 2.50% + 0.40% = 3.05%

Therefore, the expected return on the security is approximately 3.05%.

Next, to determine the risk of this investment, we calculate its standard deviation. First, we find the variance, which involves summing the squared deviations of each return from the expected return, weighted by their respective probabilities.

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

Calculations step-by-step:

• For -5%: 0.05 × (-5% - 3.05%)^2 = 0.05 × (-8.05%)^2 = 0.05 × 0.00648 = 0.000324
• For 1%: 0.40 × (1% - 3.05%)^2 = 0.40 × (-2.05%)^2 = 0.40 × 0.000420 = 0.000168
• For 5%: 0.50 × (5% - 3.05%)^2 = 0.50 × 1.95%^2 = 0.50 × 0.000380 = 0.000190
• For 8%: 0.05 × (8% - 3.05%)^2 = 0.05 × 4.95%^2 = 0.05 × 0.00245 = 0.000122

Summing variances:

Variance = 0.000324 + 0.000168 + 0.000190 + 0.000122 = 0.000804

Standard deviation is the square root of the variance:

Standard deviation = √0.000804 ≈ 0.0283 or 2.83%

Thus, the security has an expected return of approximately 3.05% with a standard deviation of about 2.83%, indicating its risk level.

Evaluation of James Fromholtz’s Mortgage Securities Investment

The second part considers an investment fund focused on home mortgage securities dependent on economic outcomes. The potential future states, their probabilities, and corresponding returns are as follows:

State of Economy	Probability	Fund Returns
Rapid expansion and recovery	5%	100%
Modest growth	50%	30%
Continued recession	40%	10%
Falls into depression	5%	-100%

To compute the expected return, multiply each return by its probability and sum the results:

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

Calculations:

- 0.05 × 100% = 5%

- 0.50 × 30% = 15%

- 0.40 × 10% = 4%

- 0.05 × (-100%) = -5%

Summing:

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

Hence, the expected rate of return for this mortgage securities investment is approximately 19%.

Next, the risk or volatility is measured through the standard deviation. We compute the variance by summing the squared deviations of each possible return from the expected return, weighted by their probabilities:

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

Calculations:

- For 100%: 0.05 × (100% – 19%)^2 = 0.05 × (81%)^2 = 0.05 × 0.6561 = 0.032805

- For 30%: 0.50 × (30% – 19%)^2 = 0.50 × (11%)^2 = 0.50 × 0.0121 = 0.00605

- For 10%: 0.40 × (10% – 19%)^2 = 0.40 × (-9%)^2 = 0.40 × 0.0081 = 0.00324

- For -100%: 0.05 × (-100% – 19%)^2 = 0.05 × (-119%)^2 = 0.05 × 0.14161 = 0.0070805

Total variance:

0.032805 + 0.00605 + 0.00324 + 0.0070805 ≈ 0.0491755

Standard deviation:

√0.0491755 ≈ 0.2218 or 22.18%

This indicates a relatively high level of risk, reflecting the significant potential loss in the worst-case scenario and the sizeable volatility associated with the project.

Investment Decision:

Given the expected return of approximately 19%, the high expected profitability is attractive, but the high risk revealed by a 22.18% standard deviation makes this investment highly volatile. An investor's willingness to proceed would depend on their risk appetite. Conservative investors might shy away from such high volatility despite the attractive expected return, whereas risk-tolerant investors might find it appealing, especially considering the potential for high gains during economic expansions.

Conclusion:

The analysis demonstrates that both investments offer differing risk-return profiles. The security evaluated by B.J Gautney Enterprises presents a modest expected return of about 3.05% with relatively low risk. In contrast, the mortgage securities fund exhibits a high expected return of 19%, but with significant volatility, reflecting substantial risk. Such assessments highlight the importance of aligning investment choices with individual risk tolerance and financial goals.

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