9.1 Risk and Return Fundamentals

Risk and return are crucial concepts in finance. They help investors understand potential gains and losses from investments. Expected returns, standard deviation, and variance are key metrics used to quantify these factors.

Investor attitudes toward risk shape investment decisions. Risk-averse individuals prefer safer options, while risk-seekers chase higher returns. The risk-return tradeoff and risk premium explain why riskier investments often offer higher potential rewards.

Risk and Return Metrics

Calculating Expected Returns and Risk

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• Expected return represents the average return an investor anticipates earning from an investment over time
  • Calculated as the probability-weighted average of all possible returns
  • Formula: $[Expected Return](https://www.fiveableKeyTerm:Expected_Return) = \sum_{i=1}^{n} p_i * r_i$, where $p_i$ is the probability of each return and $r_i$ is each possible return
• Standard deviation measures the dispersion of returns around the expected return
  • Indicates the level of risk or volatility associated with an investment
  • Higher standard deviation implies greater risk and potential for returns to deviate from the expected return
  • Formula: $Standard Deviation = \sqrt{\sum_{i=1}^{n} p_i * (r_i - Expected Return)^2}$
• Variance is another measure of risk that quantifies the average squared deviation of returns from the expected return
  • Variance is the square of the standard deviation
  • Formula: $Variance = \sum_{i=1}^{n} p_i * (r_i - Expected Return)^2$

Probability Distributions in Risk Assessment

• Probability distribution depicts the likelihood of different outcomes occurring
• In the context of investments, probability distributions show the range of possible returns and their associated probabilities
• Normal distribution (bell curve) is commonly used to model returns
  • Assumes returns are symmetrically distributed around the mean
  • Majority of returns fall within one standard deviation of the mean
• Other probability distributions (lognormal, binomial) may be used depending on the nature of the investment and its return characteristics

Risk Attitudes

Investor Risk Preferences

• Risk aversion refers to an investor's preference for lower risk investments, even if they offer lower expected returns
  • Risk-averse investors prioritize the preservation of capital over potential higher returns
  • They are willing to accept lower returns in exchange for lower risk exposure
• Risk-seeking investors, on the other hand, are willing to take on higher levels of risk in pursuit of higher potential returns
  • They have a higher tolerance for volatility and potential losses
• Risk-neutral investors are indifferent between investments with the same expected return, regardless of their risk levels

Risk-Return Tradeoff and Risk Premium

• The risk-return tradeoff is the principle that higher expected returns are associated with higher levels of risk
  • Investors must be compensated with higher potential returns to accept greater risk
• The risk premium is the additional return an investor requires to compensate for the higher risk of an investment compared to a risk-free alternative
  • It represents the premium above the risk-free rate (U.S. Treasury bills) that investors demand for bearing risk
  • Formula: $Risk Premium = Expected Return - Risk-Free Rate$
• Investors' risk attitudes determine the level of risk premium they require
  • Risk-averse investors demand a higher risk premium to hold riskier assets
  • Risk-seeking investors may accept a lower risk premium for the chance of higher returns