Types of Return: Effective Annualized Return (EAR)

The Effective Annualized Return (EAR) is designed to provide a comparable annual rate of return when investments have different compounding frequencies.

• Definition:

  • Effective Annualized Return (EAR) is the actual annual rate of return taking into account the effect of compounding interest or returns more frequently than once a year. It standardizes returns to a common annual basis, allowing for meaningful comparisons. It can be used to show different risk structures.

• Formula (as provided):

  EAR = (1 + (Nominal Rate / n))^n - 1
  

• Components Explained:

  • EAR: Effective Annualized Return
  • Nominal Rate: The stated annual interest rate or return (also known as the APR: Annual Percentage Rate).
  • n: The number of compounding periods per year (e.g., annually = 1, semi-annually = 2, quarterly = 4, monthly = 12, daily = 365)

• Utility (as provided):

  • Useful for comparing investments with different compounding frequencies. This is its primary purpose.

• Further Elaboration on Utility:

  • Standardized Comparison: The most important strength is to let the user see a fair comparison for performance.

  • Accurate Representation: Accurately reflects the return earned in reality.

  • Accounts for "interest on interest":

    • If interest is paid out on regular intervals, the interest that was just paid is likely reinvested. EAR accounts for this factor.

• Limitations:

  • Assumes Constant Reinvestment: Assumes that all income is reinvested at the same rate throughout the year.

  • Does not address Risk: EAR is solely a measurement of returns. It does not address volatility.

• Example: * A bond pays out 10% annual interest in three scenarios: a) Annually, b) Semiannually, and c) Monthly. * Note that “nominal rate” is synonymous with annual percentage rate (APR). * a) With yearly compounding, the EAR is (1+ (0.10/1))^1-1 = 10% *b) With semiannual compounding, the EAR is (1 + (0.10 /2))^2 -1 = 10.25% *c) With monthly compounding, the EAR is (1 + (0.10 / 12))^12 -1 = 10.47%

Key Points:

• The EAR is a very important value to calculate when comparing debt instruments (such as bonds) where the compounding rate is not annual.
• EAR does not account for risks, which is a problem.

In conclusion, Effective Annualized Return (EAR) is a valuable metric for comparing investment returns, especially when compounding frequencies differ. However, it's crucial to remember its limitations and to consider it alongside other measures, particularly those that account for risk.