The Standard Deviation Of Stock Returns For Stock A Is 42

the Standard Deviation Of Stock Returns For Stock A Is 42

Assess the calculation of Stock A's beta based on its standard deviation, market standard deviation, and correlation with the market. Additionally, compute the expected return and standard deviation of a two-asset portfolio, analyze the characteristics of Stock X and the NYSE in terms of average returns, standard deviations, beta coefficient, risk-free rate, and security market line positioning. Finally, evaluate the additional risk premium required by shareholders for Ethier Enterprise's financial leverage and interpret cash flow statements for Sunn Inc.

Sample Paper For Above instruction

The assessment of stock risk and return involves multiple financial metrics and models that investors use to make informed decisions. Understanding the relationships between a stock's volatility, market movements, and its expected performance is essential. This paper explores key concepts including beta calculation, portfolio diversification, characteristic line analysis, security market line (SML), and the impact of leverage on required risk premiums. Additionally, it discusses the interpretation of cash flows derived from financial statement analysis, providing comprehensive insights into investment risk management.

Calculating Stock A's Beta

The beta coefficient measures a stock's sensitivity to market movements, indicating its systematic risk. It can be derived from the relationship between the stock's standard deviation, the market's standard deviation, and their correlation. Given that Stock A's standard deviation is 42%, the market's standard deviation is 21%, and the correlation coefficient is 0.60, the beta (β) is calculated as:

β = (Correlation × Standard Deviation of Stock A) / Standard Deviation of Market

Substituting the values:

β = (0.60 × 42%) / 21% = (0.60 × 0.42) / 0.21 = 0.252 / 0.21 ≈ 1.20

Therefore, Stock A's beta is approximately 1.20, indicating it is somewhat more volatile than the market.

Portfolio Expected Return and Variance

A portfolio comprising 30% in Stock A and 70% in Stock B combines their individual expected returns and risks. Stock A's expected return is 12% with a standard deviation of 45%, while Stock B's expected return is 16% with a standard deviation of 55%. The correlation coefficient between the stocks is 0.2.

The expected return of the portfolio (E_P) is calculated as:

E_P = 0.30 × 12% + 0.70 × 16% = 0.30 × 0.12 + 0.70 × 0.16 = 0.036 + 0.112 = 0.148 or 14.80%

The portfolio's variance (σ_P²) considers the individual variances and their covariance:

σ_P² = (w_A)²×σ_A² + (w_B)²×σ_B² + 2×w_A×w_B×σ_A×σ_B×Correlation

Calculating each component:

• (0.30)² × (45%)² = 0.09 × 0.2025= 0.018225
• (0.70)² × (55%)² = 0.49 × 0.3025= 0.148225
• 2 × 0.30 × 0.70 × 45% × 55% × 0.2 = 2 × 0.21 × 0.2025 × 0.2 ≈ 0.01713

Adding these gives:

σ_P² ≈ 0.018225 + 0.148225 + 0.01713 = 0.18358

Standard deviation of the portfolio (σ_P) is:

σ_P ≈ √0.18358 ≈ 0.429 or 42.90%

Analysis of Stock X and the NYSE

Using historical data, the beta coefficient of Stock X is computed via linear regression against the NYSE index returns. Suppose the regression indicates a beta of 1.15; this suggests Stock X is slightly more volatile than the market. The average return and the standard deviation for both Stock X and the NYSE help assess their performance and risk profile.

Assuming the calculated average returns are 4% for Stock X and 5% for NYSE, with standard deviations of 12% and 10%, respectively, their positions on the Security Market Line (SML) indicate whether they are fairly valued. If Stock X's actual expected return exceeds the return predicted by its beta and the market risk premium, it suggests undervaluation; if less, overvaluation.

The risk-free rate (Rf) can be derived from the SML equation:

Expected Return of Stock X = Rf + β×(Market Risk Premium)

Given the data, if the expected return is 4%, β is 1.15, and Market Risk Premium is 4%, then:

4% = Rf + 1.15 × 4% → Rf = 4% - (1.15 × 4%) = 4% - 4.6% = -0.6%

This negative value implies adjustments in assumptions; generally, the risk-free rate is close to the yield on long-term government bonds, around 2-3%. In a realistic scenario, the positive values of Rf align with market conditions.

Additional Premium for Financial Risk

Ethier Enterprise's unlevered beta of 1.3 and levered beta of 1.6 indicate increased risk due to financial leverage. Using the Modigliani-Miller framework with corporate taxes ignored, the additional premium shareholders require for financial risk can be calculated by the difference in the cost of equity:

Additional Premium = (Levered Beta - Unlevered Beta) × Market Risk Premium = (1.6 - 1.3) × 4% = 0.3 × 4% = 1.20%

Thus, shareholders require an additional 1.20% to compensate for the financial risk associated with leverage.

Cash Flows and Financial Statement Analysis

To determine the net cash provided by operating activities for Sunn Inc. for 2017, adjustments are made starting from net income by adding back depreciation and accounting for changes in working capital. Using the indirect method:

• Net income = $153,000
• Add: Depreciation expense = $27,000
• Changes in current assets and liabilities: (Current assets increased by $2,000; current liabilities decreased by $3,000)

The calculation:

Net Cash Provided by Operating Activities = Net Income + Depreciation + Changes in Working Capital

= $153,000 + $27,000 + [Decrease in current liabilities ($3,000) - Increase in current assets ($2,000)] = $153,000 + $27,000 + (-$3,000) - $2,000 = $175,000

This figure indicates the cash generated from core operations, which is crucial for assessing liquidity and operational efficiency. It reflects Sunn Inc.'s ability to generate cash to fund expansion, pay debts, or return value to shareholders.

Conclusion

Understanding the interplay of risk and return measures like beta, standard deviation, and expected return enables investors to construct portfolios aligned with their risk appetite. The analysis of financial leverage emphasizes the importance of corporate structure in risk assessment, while cash flow analysis underpins liquidity evaluation. Informed application of these financial principles facilitates sound investment and management decisions, contributing to overall financial health and strategic growth.

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