Lecture 3: Return and Risk

1. Concept of Expected Return vs. Actual Return

• Expected Return :
  The expected return is the anticipated profit or loss an investor predicts on an investment, based on historical data, market analysis, and probability distributions. It represents the weighted average of possible returns, where weights are the probabilities of occurrence.
  Formula:

  E(R)=∑[Pi​×Ri​]
   

  Where:

  • $E(R)$: Expected Return
  • Pi​: Probability of scenario $i$
  • Ri​: Return in scenario $i$
   

• Actual Return :
  The actual return is the real profit or loss achieved on an investment over a specific period. It reflects the realized performance of the investment, which may differ from the expected return due to unforeseen market conditions or events.

2. Measuring Return

• Absolute Return :
  Absolute return measures the total gain or loss on an investment over a specific period, expressed in monetary terms or as a percentage.
  Formula:

  Absolute Return=Initial ValueFinal Value−Initial Value​×100

• Relative Return :
  Relative return compares the performance of an investment to a benchmark or another investment. It is often used to evaluate the effectiveness of portfolio management.
  Formula:

  $$\text{Relative Return}=\text{Investment Return}-\text{Benchmark Return}$$

3. Concept of Risk and Types of Risks

Risk refers to the uncertainty or variability in investment returns. It is an inherent part of investing, and understanding its types is crucial for effective risk management.

• Market Risk :
  Also known as systematic risk, it arises from factors that affect the overall market, such as economic downturns, political instability, or changes in interest rates.

• Credit Risk :
  The risk of default by a borrower or counterparty. It is particularly relevant in bonds and loans.

• Liquidity Risk :
  The risk that an asset cannot be sold quickly enough to prevent a loss or meet financial obligations.

• Operational Risk :
  The risk of losses caused by inadequate internal processes, people, systems, or external events (e.g., fraud, cyberattacks).

• Inflation Risk :
  The risk that inflation will erode the purchasing power of returns over time.

• Currency Risk :
  The risk of losses due to fluctuations in exchange rates, especially in international investments.

4. Measuring Risk

To quantify risk, several statistical tools are used:

• Standard Deviation :
  A measure of the dispersion of returns around the mean. A higher standard deviation indicates greater volatility and risk.
  Formula:

  σ=N∑(Ri​−Rˉ)2​​
   

  Where:

  • $\sigma$: Standard Deviation
  • Ri​: Individual return
  • Rˉ: Average return
  • $N$: Number of observations
   

• Variance :
  Variance measures the average squared deviation of returns from the mean. It is the square of the standard deviation.
  Formula:

  Variance=σ2

• Beta Coefficient ($\beta$) :
  Beta measures the sensitivity of an investment's returns to market movements. A beta greater than 1 indicates higher volatility than the market, while a beta less than 1 indicates lower volatility.
  Formula:

  β=Var(Rm​)Cov(Ri​,Rm​)​
   

  Where:

  • Cov(Ri​,Rm​): Covariance between the investment's returns and market returns
  • Var(Rm​): Variance of market returns

Key Takeaways

1. Return can be measured in absolute or relative terms, and understanding expected vs. actual return is crucial for evaluating investment performance.
2. Risk encompasses various types, including market risk, credit risk, liquidity risk, and operational risk, each requiring specific management strategies.
3. Risk Measurement tools like standard deviation, variance, and beta help investors quantify and manage uncertainty in their portfolios.

By balancing return expectations with risk tolerance, investors can make informed decisions to achieve their financial goals.