Risk and Return in Financial Management

To calculate the total stock return, first determine the profit from selling the stock. The selling price is ₱48, and the purchase price is ₱40, resulting in a capital gain of ₱8 per share. Adding the dividend of ₱2 gives a total return of ₱10 per share. The total return percentage is calculated by dividing the total return (₱10) by the purchase price (₱40) and multiplying by 100, which results in a 25% return.

Dividend yield is a financial ratio that indicates how much a company pays out in dividends each year relative to its stock price. It is calculated by dividing the total annual dividends received by the initial stock price. This measure helps investors assess the income generated from their investment in relation to its cost, providing insight into the investment's profitability and attractiveness compared to other options. A higher dividend yield suggests a more favorable return on investment through dividends.

To calculate the capital gain return, subtract the purchase price from the selling price, which gives a gain of ₱8 (₱58 - ₱50). Then, divide the gain by the purchase price: ₱8 ÷ ₱50 = 0.16. To express this as a percentage, multiply by 100, resulting in a capital gain return of 16%. This percentage reflects the increase in the value of the investment relative to its original cost.

Standard deviation quantifies the degree of variation or dispersion in a set of data points, such as a stock's returns. A higher standard deviation indicates that the returns are spread out over a wider range, suggesting greater volatility. This volatility reflects the uncertainty and risk associated with the stock's performance; larger fluctuations in returns can lead to increased potential for both gains and losses. Therefore, investors use standard deviation as a key indicator of risk when evaluating investment options.

To calculate the average return, sum all the monthly returns: 5% + 8% - 3% + 4% + 6% = 20%. Then, divide the total by the number of months, which is 5. Therefore, 20% divided by 5 equals 4%. This average return reflects the overall performance of the investment over the specified period.

A higher standard deviation of stock returns signifies greater variability in the returns, indicating that the stock's performance is less predictable. This increased volatility implies that the investment could experience larger swings in value, both positive and negative, over time. Consequently, investors face a greater chance of experiencing significant losses, which is a key component of investment risk. Therefore, a stock with a higher standard deviation is considered riskier than one with a lower standard deviation.

To find the expected return, multiply each scenario's return by its probability and sum the results. For the recession, the contribution is 0.20 * (-10%) = -2%. For the normal scenario, it is 0.50 * 8% = 4%. For the boom, it is 0.30 * 20% = 6%. Adding these contributions gives: -2% + 4% + 6% = 8%. Thus, the expected return of the stock is 8%, reflecting a weighted average of the potential outcomes based on their probabilities.

To find the standard deviation, take the square root of the variance. Given a variance of 108, the standard deviation is calculated as √108, which is approximately 10.39%. This value represents the stock's volatility or risk, indicating how much the stock's returns are expected to deviate from the average return of 8%. A higher standard deviation signifies greater risk and uncertainty in the stock's returns.

Harry Markowitz introduced the Efficient Frontier as a key component of Modern Portfolio Theory, which he developed in the 1950s. This concept illustrates the optimal risk-return trade-off for a portfolio of assets, demonstrating how investors can maximize returns for a given level of risk. By analyzing the relationships between different assets, Markowitz's work laid the foundation for portfolio diversification and investment strategies, emphasizing the importance of balancing risk and return to achieve financial goals. His contributions revolutionized investment management and earned him the Nobel Prize in Economic Sciences in 1990.

The Minimum Variance Portfolio represents the combination of assets that minimizes risk for a given level of expected return. On the Efficient Frontier, it is located at the leftmost point, indicating the lowest possible risk among all portfolios. This portfolio is crucial for investors seeking to minimize volatility while still achieving returns, making it a foundational concept in modern portfolio theory.

The Capital Market Line (CML) represents the risk-return trade-off for efficient portfolios that combine risk-free assets and the market portfolio. The point where the CML is tangent to the Efficient Frontier indicates the optimal portfolio, known as the market portfolio, which offers the highest expected return for a given level of risk. This portfolio includes all risky assets weighted according to their market values, providing investors with a benchmark for achieving the best possible risk-adjusted returns.

To calculate the expected return of the stock using the Capital Asset Pricing Model (CAPM), the formula is: Expected Return = Risk-Free Rate + Beta × (Market Return - Risk-Free Rate). Substituting the given values: Expected Return = 4% + 1.5 × (10% - 4%) = 4% + 1.5 × 6% = 4% + 9% = 13%. This indicates that with a beta of 1.5, the stock is expected to yield a return of 13%, reflecting its risk relative to the market.

CAPM, or the Capital Asset Pricing Model, posits that investors are only compensated for systematic risk, which is the inherent risk associated with the market as a whole. Unsystematic risk, also known as diversifiable risk, can be mitigated through diversification and does not warrant additional returns. Therefore, investors are not rewarded for taking on unsystematic risk, as it can be eliminated through a well-diversified portfolio. This principle emphasizes that only the risk that cannot be diversified away is relevant for expected returns.

When the expected return of a stock exceeds its CAPM-required return, it indicates that the stock is likely undervalued or offers additional compensation for the risk taken. In this case, the expected return of 15% is 3.8% higher than the required return of 11.2%. This excess return suggests that investing in the stock could be favorable, as it provides a potential reward that exceeds the minimum required by investors for taking on systematic risk. Therefore, the stock may be considered an attractive investment opportunity.