💰Intro to Finance Unit 4 – Risk and Return

Key Concepts and Definitions

• Risk involves uncertainty and potential for loss or negative outcomes in financial investments
• Return represents the gain or profit earned on an investment over a specific period
• Systematic risk affects the entire market and cannot be diversified away (economic downturns, interest rate changes)
• Unsystematic risk is specific to individual securities and can be reduced through diversification (company-specific events, management decisions)
• Standard deviation measures the dispersion of returns around the average return, indicating the level of risk
  • Higher standard deviation suggests greater variability and risk
• Beta coefficient compares the volatility of an individual security to the overall market
  • Beta > 1 indicates higher risk than the market, while Beta < 1 suggests lower risk

Types of Risk

• Market risk arises from fluctuations in the overall stock market (recessions, political events)
• Interest rate risk occurs when changes in interest rates affect the value of investments (bonds, fixed-income securities)
• Inflation risk erodes the purchasing power of money over time, reducing the real value of returns
• Liquidity risk involves the difficulty of selling an investment quickly without a significant price discount
• Credit risk relates to the possibility of a borrower defaulting on their obligations (bonds, loans)
• Currency risk arises from fluctuations in exchange rates when investing in foreign markets
• Political risk involves changes in government policies or instability that can impact investments (regulations, nationalization)

Measuring Risk

• Variance calculates the average squared deviation of returns from the mean, indicating the spread of returns
  • Formula: $Variance = \frac{\sum_{i=1}^{n} (x_i - \mu)^2}{n}$, where $x_i$ is each return, $\mu$ is the mean return, and $n$ is the number of returns
• Standard deviation is the square root of variance, providing a measure of risk in the same units as returns
  • Formula: $Standard Deviation = \sqrt{Variance}$
• Coefficient of variation compares the standard deviation to the mean, allowing for risk comparison across investments with different means
  • Formula: $Coefficient of Variation = \frac{Standard Deviation}{Mean}$
• Sharpe ratio measures the risk-adjusted return by comparing the excess return to the standard deviation
  • Formula: $Sharpe Ratio = \frac{R_p - R_f}{\sigma_p}$, where $R_p$ is the portfolio return, $R_f$ is the risk-free rate, and $\sigma_p$ is the portfolio standard deviation
• Value at Risk (VaR) estimates the maximum potential loss over a specific time horizon at a given confidence level
  • Helps assess the downside risk of an investment or portfolio

Understanding Return

• Holding period return (HPR) measures the total return earned over the entire investment period
  • Formula: $HPR = \frac{Ending Value - Beginning Value + Income}{Beginning Value}$
• Annualized return converts the holding period return into an annual rate for comparison across different time periods
  • Formula: $Annualized Return = (1 + HPR)^{\frac{1}{n}} - 1$, where $n$ is the number of years
• Nominal return represents the return without adjusting for inflation
• Real return accounts for the impact of inflation on the purchasing power of the return
  • Formula: $Real Return = \frac{1 + Nominal Return}{1 + Inflation Rate} - 1$
• Expected return is the weighted average of possible returns, considering their probabilities
  • Formula: $Expected Return = \sum_{i=1}^{n} p_i r_i$, where $p_i$ is the probability of each return $r_i$

Risk-Return Relationship

• Higher risk investments generally offer the potential for higher returns to compensate investors
• Risk-free rate represents the return on a theoretically risk-free investment (short-term government securities)
• Risk premium is the additional return required by investors to accept higher levels of risk
  • Calculated as the difference between the expected return and the risk-free rate
• Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return
  • Formula: $E(R_i) = R_f + \beta_i (E(R_m) - R_f)$, where $E(R_i)$ is the expected return of security $i$, $R_f$ is the risk-free rate, $\beta_i$ is the beta of security $i$, and $E(R_m)$ is the expected market return
• Security Market Line (SML) graphically represents the CAPM, showing the linear relationship between beta and expected return

Diversification and Portfolio Theory

• Diversification involves spreading investments across different assets, sectors, and markets to reduce risk
• Modern Portfolio Theory (MPT) emphasizes the importance of constructing efficient portfolios that maximize return for a given level of risk
• Efficient frontier represents the set of optimal portfolios that offer the highest expected return for a given level of risk
• Correlation measures the relationship between the returns of different assets
  • Ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation)
• Diversification works best when assets have low or negative correlations, as they tend to move independently
• Systematic risk cannot be diversified away, as it affects the entire market
• Unsystematic risk can be reduced through proper diversification, as it is specific to individual securities

Practical Applications

• Asset allocation involves dividing an investment portfolio among different asset classes (stocks, bonds, cash) based on risk tolerance and goals
• Rebalancing periodically adjusts the portfolio to maintain the desired asset allocation
  • Helps manage risk and maintain diversification over time
• Dollar-cost averaging invests a fixed amount at regular intervals, regardless of market conditions
  • Reduces the impact of market timing and can lower the average cost per share
• Risk management strategies include hedging (using derivatives to offset potential losses) and stop-loss orders (automatically selling when a certain price level is reached)
• Portfolio performance evaluation compares the returns and risk of a portfolio to benchmarks and peer groups
  • Considers risk-adjusted measures like Sharpe ratio and Treynor ratio

Advanced Topics and Current Trends

• Behavioral finance studies the psychological factors influencing investor decisions and market anomalies
  • Concepts include loss aversion, overconfidence, and herd mentality
• Factor investing focuses on specific factors (value, size, momentum) that have historically generated higher returns
• Environmental, Social, and Governance (ESG) investing considers non-financial factors in investment decisions
  • Aims to align investments with personal values and promote sustainable practices
• Robo-advisors use algorithms and technology to provide automated investment management services
  • Often offer low-cost, diversified portfolios based on risk tolerance and goals
• Alternative investments include assets beyond traditional stocks and bonds (real estate, private equity, hedge funds)
  • Can provide diversification benefits but may have higher fees and less liquidity
• Cryptocurrencies and blockchain technology have emerged as new investment opportunities, but with high volatility and regulatory uncertainty