Utility Theory in Investment

Introduction

• Subject: CM 2nd Year
• Chapter: Utility Theory
• Focus on economic systems, personal preferences, investment decisions

Key Concepts of Utility Theory

1. Utility & Consumer Preferences:
   • Definition and significance
   • Association with consumer goods
   • Different units of measurement
2. Investment Decisions:
   • Evaluating total wealth
   • Investment as a lottery
   • Profit expectations

Expected Outcomes of Investments

1. Probabilities in Investments:
   • Probability of profit vs. loss
   • Example: Investment with 15% loss probability
2. **Associated Utilities: **
   • These probabilities affect expected utilities
   • Calculation of expected utilities
3. Investors' Risk Appetite:
   • Influence on utility function
   • Different risk appetites yield different utility outcomes

Theoretical Framework

1. **Maximizing Expected Utility: **
   • Objective to maximize expected utility rather than wealth
   • Example of investment decisions and expected utility calculation
2. Investment Replication Issues:
   • It’s challenging to replicate all variables exactly
   • Investors’ varied utility functions

Practical Calculation of Utilities

1. Logarithmic Utility Functions:
   • Simplified for calculation under risk
2. Utility Calculation Example:
   • Case study involving expected returns and utility functions

Decision Making Under Uncertainty

1. Expected Wealth & Utility Calculations:
   • Investment distribution among different assets
   • Expected return calculations considering multiple scenarios
2. **Account Investments: **
   • Breakdown of wealth in various accounts (interest-bearing & non-interest-bearing)

Analysis and Conclusion

1. **Optimal Investment Strategy: **
   • Using utility functions to determine optimal investment amounts
2. **Consumer and Investor Behavior: **
   • Defining and comparing behavior under different conditions
   • Application of utility theory to real-world investment decisions

Investment Lotteries

1. Concept of Investment Lottery:
   • Combining outcomes with different probabilities
2. Analyzing Lotteries:
   • Examining separate outcomes for utility comparison
3. Practical Example:
   • Comparison between investments' utility using hypothetical lotteries

Summary & Key Takeaways

1. Importance of Utility Theory:
   • Guiding investment decisions
2. Different Risk Preferences:
   • Impact on investment choices and outcomes
3. **Utility Maximization as an Objective: **
   • Practical steps to maximize utility in finance

Conclusion

• Understanding utility theory is crucial in making informed investment decisions. Investors should focus on maximizing their expected utility rather than just wealth to align with personal preferences and risk appetite.
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