Fin 534 Homework Set 3 2014 Strayer University All Ri 950457

Fin 534 Homework Set 3 2014 Strayer University All Rights Reserve

Answer the following questions based on provided financial data and statistical concepts. Explain your calculations or reasoning where applicable. Submit your completed work through the course submission link.

Paper For Above instruction

The assignment focuses on analyzing stock returns, calculating statistical measures, estimating beta coefficients, applying the Security Market Line (SML) model, forecasting dividends, valuing stocks, and evaluating options. It also covers fundamental statistical probability, hypothesis testing, sampling techniques, and decision analysis. To comprehensively address these elements, I will systematically perform calculations, interpret results, and align findings with theoretical models.

Analysis of Stock Returns and Statistical Measures

Initially, using the stock prices and dividends of Goodman Industries and Landry Incorporated, along with the market index from 2013 to 2014, I calculated annual returns. The return formula incorporates both capital gains (ending price minus beginning price) and dividends, divided by the beginning price, consistent with the provided instructions. For Goodman Industries in 2014, the return is:

Return = [(Price in 2014 - Price in 2013) + Dividend in 2014] / Price in 2013

Plugging in the data: [(73.13 - 25.88) + 1.43] / 25.88 ≈ (47.25 + 1.43) / 25.88 ≈ 48.68 / 25.88 ≈ 1.88, or 188%. Such high return suggests a possible misinterpretation; however, according to the data, the stock's return reflects the increase from 2013 to 2014. Repeating for Landry and the Market Index yields comparable annual return figures. Next, I computed the average annual returns over the period, obtaining mean returns for each stock and the index, which provide insights into expected performance.

Subsequently, I calculated the standard deviations of returns using the sample standard deviation formula, measuring the volatility of each asset's returns. The results highlight that Goodman and Landry have different risk profiles, supporting their investment characteristics.

Estimating Betas and the Capital Asset Pricing Model (CAPM)

To estimate beta coefficients for Goodman and Landry, I performed regression analyses with stock returns as the dependent variable and market returns as the independent variable, utilizing the Excel SLOPE function. The beta coefficients measure the stocks' sensitivity to market movements. The calculated betas, when plotted against the actual data, align with the regression lines, confirming their estimated risk profiles. Goodman, with a higher beta, signals more systemic risk, whereas Landry's beta indicates lower sensitivity.

Market Risk Premium and Required Returns

The risk-free rate is 6.04%, and the market risk premium is 5%. Applying the CAPM formula: Required Return = Risk-Free Rate + Beta × Market Premium, I derived the expected return on the market: 6.04% + 5% = 11.04%. For individual stocks, their required returns were then computed using their betas, illustrating the relationship between systematic risk and return.

Portfolio Beta and Return Calculation

Constructing a 50/50 portfolio of Goodman and Landry stocks, the portfolio beta is the weighted sum of individual betas: 0.5 × Beta_Goodman + 0.5 × Beta_Landry. Due to the linearity of beta, this calculation yields a composite beta that reflects the combined risk. The portfolio's required return is calculated using the same weighted CAPM formula, emphasizing the importance of diversification and risk assessment in portfolio management.

Dividend Forecasting

Using the dividend growth model, I projected dividends for the next three years: D₁, D₂, and D₃, based on D₀ = $1.50 and a growth rate of 5%. The formulas are D₁ = D₀ × (1 + g), D₂ = D₁ × (1 + g), and D₃ = D₂ × (1 + g). The results forecast steady dividend increases, illustrating valuation approaches under growth assumptions.

Stock Valuation and Price Limits

Given the current stock price of $27.05, a required return of 13%, and dividend projections, I calculated the present value of dividends D₁, D₂, D₃, and the anticipated selling price. Discounting each cash flow using the required return, I determined the maximum price an investor should pay today, ensuring rational investment decisions based on future cash flows and valuation models.

Option Pricing with Black-Scholes Model

For the call option on Goodman Industries stock with a current price of $30, strike price of $35, 4 months to expiration, risk-free rate of 5%, and variance of 0.25 (implying volatility σ = 0.5), I used the Black-Scholes formula. Calculating d₁ and d₂, considering compounding and volatility, I derived the option's fair value, illustrating the application of advanced option pricing techniques in risk management.

Statistical Concepts and Probability Rules

The empirical rule indicates that approximately 99.7% of observations fall within three standard deviations of the mean. Numerical data, such as measurements or survey data, are classified as statistics, which are essential for decision-making. Excel functions like MIN() help identify minimum values in datasets. Metrics derived from counts are called nominal or discrete metrics.

The core principles in statistical thinking concern understanding process variability and systemic causes of variation. Customer outcomes like satisfaction and complaints are considered customer-focused outcomes, important for service quality assessments. Distribution features such as kurtosis describe data behavior; a flat distribution with wide dispersion has kurtosis less than 3.

The correlation coefficient measures the strength and direction of linear relationships, ranging between -1 and +1. For the sum of calls modeled as a uniform distribution over six outcomes, the mean is calculated by summing the outcomes weighted by their probabilities. Mutual exclusivity entails that probabilities of events can be added if they cannot occur simultaneously.

Standard deviation and variance relate through their mathematical definitions; the standard deviation is the square root of the variance, describing data dispersion. In probability, the complement of a favorable event's probability is used to assess risks, such as the likelihood of rainy weather or project delays, modeled via normal distribution parameters. Confidence intervals estimate the range within which the true parameter lies with a specified probability, calculated considering sample size, standard deviation, and confidence level.

Sample and population concepts, such as finite population correction factors, improve estimator accuracy. Hypotheses tests involve null and alternative hypotheses, with rejection criteria based on significance levels (alpha). Critical values derive from probability distributions; the power of a test indicates its ability to detect true effects. Decision trees depict options and outcomes to aid complex decision-making processes.

Market research and probability calculations, including binomial models, evaluate customer responses and behaviors. The number of combinations for lock codes with repeated digits can be computed owing to factorial and permutation principles. Understanding probabilities of tracking behaviors or market participation assists in strategic planning.

In hypothesis testing, rejecting the null hypothesis when p-value

References

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