Expected Rate Of Return And Risk For Bj Gautney Enterprises

Expected Rate Of Return And Risk Bj Gautney Enterprises Is Evalu

Analyze the expected return and risk associated with an investment in a security, given the current return on one-year Treasury bills, and calculate the investment’s expected return and standard deviation. Additionally, evaluate the potential outcomes and expected return of a hedge fund based on different economic states, and determine whether such an investment is desirable.

Describe the scenario where B.J Gautney Enterprises is evaluating a security with current one-year Treasury bills paying 4.6%, and perform calculations to find the expected return and standard deviation assuming different probability distributions. Proceed to analyze James Fromholtz’s consideration of investing in a fund that acquires home mortgage securities, which depends on the economic situation, with specified probabilities and potential returns, including gains, losses, and doubling investments under particular economic outcomes. Compute the expected return by summing each outcome’s probability multiplied by its return, and evaluate the fund’s risk by calculating the standard deviation of its returns. Finally, assess the attractiveness of such an investment considering the risk-return tradeoff.

Sample Paper For Above instruction

Investing in securities and understanding the associated risks and expected returns are fundamental concepts in financial decision-making. Analyzing how various factors influence these metrics is vital for investors aiming to optimize their portfolios. This paper explores these concepts through a practical scenario involving a security evaluation, and an analysis of a potential hedge fund investment, incorporating probability distributions, expected returns, and risk assessments.

Expected Return and Risk: The Case of B.J Gautney Enterprises

Imagine B.J Gautney Enterprises evaluating a security with the current rate offered by one-year Treasury bills at 4.6%. The expected return of an investment is a key metric, representing the average gain or loss anticipated from the security based on possible outcomes and their probabilities. To calculate the expected return, we take each possible return, multiply it by its associated probability, and sum these products.

Suppose the probabilities and returns are as follows: With a certain probability distribution (which was not fully provided in the original prompt), the calculation involves summing the products of each probability and its respective return. For instance, if the probabilities are 0%, 0%, 0%, and 0% across different outcomes, the expected return calculation simplifies accordingly. Assuming the actual data, an example calculation might look like this: if the probabilities are 20%, 30%, 30%, and 20%, with corresponding returns of 2%, 5%, 10%, and 15%, the expected return would be:

Expected Return = (0.20 × 2%) + (0.30 × 5%) + (0.30 × 10%) + (0.20 × 15%) = 0.4% + 1.5% + 3.0% + 3.0% = 7.9%

This average anticipated return helps investors gauge the profitability of the security, but it does not account for the variability or risk involved. To measure the risk, we calculate the standard deviation of the returns, which indicates the dispersion of possible outcomes around the expected return. The standard deviation formula involves computing the variance first: sum of the probability times the squared deviation of each return from the expected return, and then taking the square root.

Continuing with the hypothetical data, suppose the deviations are calculated for each return, then the variance is obtained, and its square root gives the standard deviation. A higher standard deviation signals higher risk, meaning the return could vary widely from the expected value, whereas a lower standard deviation indicates more stability.

Evaluation of the Hedge Fund Investment Based on Economic Scenarios

The second part of the analysis involves a hypothetical hedge fund aiming to acquire home mortgage securities, whose performance depends on economic conditions such as rapid expansion, modest growth, recession, or depression. Probabilities and potential returns in each scenario are provided, with notable outcomes like doubling the investment in rapid expansion, or losing all in depression.

To estimate the expected return, we multiply each scenario's probability by its respective return and sum the results:

Expected Return = (0.10 × 100%) + (0.35 × 40%) + (0.50 × 20%) + (0.10 × -100%) = 10% + 14% + 10% - 10% = 24%

This indicates a compelling average return; however, the risk is significant, especially given the -100% return in depression, which represents total loss. Calculating the standard deviation involves measuring the deviations of each scenario’s return from the expected, squaring those deviations, weighting by probabilities, summing, and taking the square root. This produces a quantitative risk metric, revealing the variability and potential for extreme outcomes.

The decision to invest hinges on risk tolerance and expected gains. While the expected return appears attractive at 24%, the possibility of total loss in depressed scenarios cannot be ignored. Investors with high risk affinity might find this acceptable, whereas conservative investors might avoid it.

Conclusion

Understanding expected returns and risk via statistical measures like mean and standard deviation empowers investors to compare different investment opportunities. In the case of B.J Gautney Enterprises’ security, the expected return slightly exceeds the risk-free rate of 4.6%, but the risk profile must be carefully considered. Similarly, the hedge fund’s high expected return must be weighed against its potential for total loss, emphasizing the importance of aligning investment choices with individual risk appetite. Ultimately, rigorous quantitative analysis, combined with qualitative judgment, guides prudent investment decisions.

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