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Equivalent Annual Return (EAR) 🗓️

In the previous chapter, we learned how to calculate the total return over a holding period. However, how do you compare a 5% return earned in 3 months with a 10% return earned in 2 years? To make a fair comparison, we need to bring all returns to a common timeframe—usually one year. This is where Equivalent Annual Return (EAR) comes into play.

1. Concept of Annualizing Returns

Annualizing is the process of converting a return earned over a different period (either shorter or longer than a year) into an annual (12-month) rate. It allows investors to see the "efficiency" of their capital over time.

Important

EAR tells you what your return would be if you held the investment for exactly one year, assuming the performance continues at the same rate.

time might be better than a high total return that took a decade to achieve.

2. Difference between HPR and EAR

While both measure return, they serve different purposes.

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3. Formulas for Annualizing Returns

There are two ways to annualize: Simple (APR) and Compounded (EAR). In Portfolio Management, the compounded version is more common.

Compounded EAR Formula:

EAR = [(1 + HPR_decimal) ^ (1/n)] - 1

Where:

  • HPR (decimal): Total return in decimal format (e.g., 10% = 0.10).
  • n: Number of years the investment was held.
    • If held for 3 months, n = 0.25 (or 3/12).
    • If held for 2 years, n = 2.

4. Problems on Equivalent Annual Return

Problem 1: Return for a Period Less than a Year

An investor earned a 4% return on a stock in just 3 months. What is the Equivalent Annual Return?

Solution:

  • HPR = 4% = 0.04
  • Number of months = 3
  • Holding period in years (n) = 3/12 = 0.25
EAR = [(1 + 0.04) ^ (1/0.25)] - 1
EAR = (1.04 ^ 4) - 1
EAR = 1.1698 - 1 = 16.98%

The EAR is 16.98%. This shows that earning 4% in 3 months is highly productive.

Problem 2: Return for a Period More than a Year

A mutual fund gave a total return of 45% over a period of 3 years. Calculate the Equivalent Annual Return.

Solution:

  • HPR = 45% = 0.45
  • n = 3 years
EAR = [(1 + 0.45) ^ (1/3)] - 1
EAR = (1.45 ^ 0.333) - 1
EAR = 1.1318 - 1 = 13.18%

The mutual fund grew at an annualized rate of 13.18%.

Summary

  • EAR standardizes returns to a 12-month period.
  • It is essential for comparing investments with different time horizons.
  • It uses compounding, which is mathematically more accurate than simple division.
  • Formula: (1 + HPR)^(1/n) - 1.

Quiz Time! 🎯

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