Historical Realized Rates Of Return For Stocks A And B ✓ Solved

Historical Realized Rates Of Returnstocks A And B Have The

Historical realized rates of return for Stocks A and B have the following historical returns:

Calculate the average rate of return for each stock during the 5-year period. Round your answers to two decimal places. Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would have been the realized rate of return on the portfolio in each year? What would have been the average return on the portfolio during this period? Round your answers to two decimal places. Calculate the standard deviation of returns for each stock and for the portfolio. Round your answers to two decimal places. If you are a risk-averse investor, then, assuming these are your only choices, would you prefer to hold Stock A, Stock B, or the portfolio?

Paper For Above Instructions

Investing in stocks consistently requires a thorough understanding of the historical realized rates of return for different stocks and the overall performance of a portfolio. In this analysis, we will evaluate Stocks A and B based on given historical rates of return over a 5-year period. The objective is to calculate the average rates of return for both stocks, assess the overall performance of a 50/50 portfolio between Stocks A and B, compute the standard deviations of the returns for each stock, and determine which investment option would best suit a risk-averse investor.

Average Rate of Return for Stocks A and B

Given the historical rates of return for Stocks A and B, the first step is to calculate the average rate of return for each stock over the 5-year period. Let's assume the respective rates of return for Stocks A and B over the years are as follows:

• Year 1: Stock A = 30% | Stock B = -14.60%
• Year 2: Stock A = 10% | Stock B = 20%
• Year 3: Stock A = -5% | Stock B = 15%
• Year 4: Stock A = 25% | Stock B = 10%
• Year 5: Stock A = 20% | Stock B = 5%

To calculate the average return for each stock, the formula is:

Average Return = (Sum of Returns) / (Number of Years)

For Stock A:

Average Return A = (30% + 10% - 5% + 25% + 20%) / 5 = 18%

For Stock B:

Average Return B = (-14.60% + 20% + 15% + 10% + 5%) / 5 = 7.68%

Portfolio Rate of Return

Next, we will calculate the realized rate of return on the portfolio each year, which consists of 50% of Stock A and 50% of Stock B. The portfolio return can be calculated as follows:

Portfolio Return = (0.5 Return A) + (0.5 Return B)

During each of the 5 years, the portfolio returns would be calculated as:

• Year 1: Portfolio Return = (0.5 30%) + (0.5 -14.60%) = 7.20%
• Year 2: Portfolio Return = (0.5 10%) + (0.5 20%) = 15%
• Year 3: Portfolio Return = (0.5 -5%) + (0.5 15%) = 5%
• Year 4: Portfolio Return = (0.5 25%) + (0.5 10%) = 17.50%
• Year 5: Portfolio Return = (0.5 20%) + (0.5 5%) = 12.50%

The average return on the portfolio can be calculated similarly:

Average Portfolio Return = (7.20% + 15% + 5% + 17.50% + 12.50%) / 5 = 11.84%

Standard Deviation of Returns

Next, we will calculate the standard deviation of the returns for Stock A and Stock B as well as for the portfolio. The standard deviation provides a measure of the dispersion of returns and risk associated with an investment.

The formula for standard deviation is:

Standard Deviation = √(Σ(Return - Average Return)² / (N-1))

Calculating for Stock A:

• Standard Deviation A = √((30%-18%)² + (10%-18%)² + (-5%-18%)² + (25%-18%)² + (20%-18%)²)/4
• = √((144) + (64) + (529) + (49) + (4))/4 = 16.76%

Calculating for Stock B:

• Standard Deviation B = √((-14.60%-7.68%)² + (20%-7.68%)² + (15%-7.68%)² + (10%-7.68%)² + (5%-7.68%)²)/4
• = √((529.14) + (148.51) + (53.78) + (5.56) + (6.15))/4 = 16.16%

Calculating for the Portfolio:

• Standard Deviation Portfolio = √((7.20%-11.84%)² + (15%-11.84%)² + (5%-11.84%)² + (17.50%-11.84%)² + (12.50%-11.84%)²)/4
• = √((20.48) + (9.93) + (45.18) + (31.67) + (0.44))/4 = 9.95%

Risk-averse Investor's Preference

As a risk-averse investor considering holding Stock A, Stock B, or the portfolio, the decision will depend on comparing the risks (standard deviations) and returns (average returns) of each option.

Stock A offers better average returns than Stock B, but with a higher standard deviation, making it riskier. Stock B has lower averages but also less volatility. The portfolio provides a balance between the two. Therefore, the most suitable choice for a risk-averse investor may be to hold the portfolio, as it combines elements of both stocks while mitigating risk.

Conclusion

In conclusion, understanding returns and their standard deviations is crucial for making informed investment decisions. Stock A has the highest average return, while Stock B has the lowest standard deviation. However, the mixed portfolio can potentially provide a suitable middle-ground for investors focused on minimizing risks while also achieving a reasonable rate of return.

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