Finance: Risk and Return Fundamentals

Risk and Return Fundamentals

• Key financial decisions involve evaluating risk and return.
• Risk: Measure of uncertainty in investment returns; variability in returns associated with an asset.
• Return: Total gain or loss from an investment over a specific period.
• Rate of return formula: ( r_t = \frac{C_t + (P_t - P_{t-1})}{P_{t-1}} ).

Understanding Risk

• Risk preferences categorize investors as:
  • Risk Averse: Require higher returns for increased risk.
  • Risk-Neutral: Prefer higher returns regardless of associated risks.
  • Risk-Seeking: Favor riskier investments even with lower expected returns.

Single Asset Risk Assessment

• Scenario analysis evaluates risk using various possible outcomes: pessimistic, most likely, and optimistic.
• Range: Calculated as the difference between optimistic and pessimistic returns.
• Probability distributions associate probabilities with potential outcomes, helping assess risk.

Risk Measurement

• Standard deviation (( \sigma_r )): Indicates dispersion around the expected return; higher standard deviation signifies greater risk.
• Coefficient of Variation (CV): Measures the relative dispersion relative to expected return; useful for comparing different assets.

Portfolio Risk

• Portfolio risk assessment considers existing assets when evaluating new investments.
• Efficient Portfolio: Aims for maximum returns with a given level of risk.
• Portfolio return: Weighted average of individual asset returns, accounting for each asset's percentage in the portfolio.

Correlation and Diversification

• Correlation: Indicates the relationship between two assets; can be positive, negative, or uncorrelated.
• Diversification reduces overall portfolio risk by combining assets with low correlations.

International Diversification

• Adding international assets tends to improve portfolio performance by reducing correlation with domestic market movements.
• Unique risks in international investing include currency and political risks.

Capital Asset Pricing Model (CAPM)

• CAPM: Links risk (beta) and return, quantifying expected additional return per unit of risk.
• Total risk consists of diversifiable (firm-specific) and non-diversifiable (market) risk.
• Beta coefficient measures an asset's non-diversifiable risk in relation to market movements.

CAPM Formula

• ( r_j = R_F + [b_j \times (r_m - R_F)] )
• Historical returns and market performance guide the estimation of required returns.

Security Market Line (SML)

• Visual representation of CAPM showing the required return across various levels of non-diversifiable risk (beta).
• Shifts in SML can occur due to changes in inflation or shifts in risk aversion among investors.

Important Considerations

• CAPM relies on historical data, which may not accurately predict future variability.
• Assumes market efficiency, which while idealistic, is supported by observations in active markets like the NYSE.