Expected Return and Investment Decision Making

Expected return is determined by taking each possible outcome and multiplying it by the probability of that outcome occurring. Summing these products gives a weighted average, reflecting the likelihood and impact of each outcome, which provides a comprehensive measure of the expected return on an investment.

To find the expected return, multiply each outcome by its probability: (0.6 * 0.10) + (0.4 * -0.05) = 0.06 - 0.02 = 0.04, or 4%. This calculation reflects the weighted average of the potential returns based on their likelihoods.

Investors often face a trade-off between risk and return. Generally, higher expected returns are associated with higher levels of risk, as riskier investments have the potential for greater rewards. Conversely, lower-risk investments tend to offer more modest returns, reflecting the principle that increased risk can lead to increased potential returns.

Standard deviation quantifies the amount of variation or dispersion in a set of investment returns. A higher standard deviation indicates greater volatility, meaning the returns can fluctuate significantly from the average, while a lower standard deviation suggests more stable returns. Thus, it effectively measures the risk associated with an investment's performance.

To find the expected return, calculate the average of the three equally likely outcomes: (15% + 10% + 5%) / 3 = 10%. This reflects the average return an investor can anticipate, given the equal probability of each return scenario.

The expected return of a portfolio is calculated by taking the weighted average of the individual asset returns, where the weights reflect the proportion of each asset in the portfolio. This relationship holds true under the assumption that returns are linear and that the individual asset returns can be combined in this manner.

Expected return calculations focus on probabilities and potential outcomes rather than past performance. Historical stock prices reflect what has happened, not what is expected to occur in the future. Therefore, they are not typically included in the calculation of expected returns, which relies on probabilities and potential returns from various scenarios.

The "more is better" preference principle reflects the idea that, when faced with equal levels of risk, investors will always choose investment options that offer higher returns. This principle underscores the fundamental investor behavior of seeking maximum returns for the same level of risk, emphasizing a preference for greater financial rewards.

Investors aim to maximize returns while managing risk. When comparing two stocks, preferring the one with a higher expected return is rational only if both stocks have the same risk level. This ensures that the investor is not taking on additional risk for potentially higher returns, allowing for a more accurate assessment of value.

Diversification involves spreading investments across various assets to reduce exposure to any single asset's risk. While it lowers overall portfolio risk, it also typically leads to a decrease in expected returns, as higher-risk assets that could yield greater returns are balanced out by safer, lower-return investments. Thus, the statement is true.

To calculate the expected return, multiply each return by its probability and sum the results: (0.3 * 8%) + (0.7 * 4%) = 2.4% + 2.8% = 5.2%. This reflects the average return considering the likelihood of each outcome.

Required return is the lowest return an investor expects to earn from an investment, accounting for the risk involved. It serves as a benchmark for evaluating investment opportunities, ensuring that the potential rewards justify the risks taken. This concept helps investors make informed decisions by comparing actual returns against their required threshold.