# Calculating Real Returns

### Abdulla Javeri

Chances are when someone quotes a figure for investment returns it’s likely to be on a nominal or gross basis, without taking into account the effects of inflation. Purchasing power only increases if returns outstrip inflation over a given period. Abdulla addresses this fact and explains how to measure real returns for a single period, and over time, to help us understand inflation-adjusted returns.

Chances are when someone quotes a figure for investment returns it’s likely to be on a nominal or gross basis, without taking into account the effects of inflation. Purchasing power only increases if returns outstrip inflation over a given period. Abdulla addresses this fact and explains how to measure real returns for a single period, and over time, to help us understand inflation-adjusted returns.

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### Calculating Real Returns

4 mins 42 secs

Overview

Real returns are in other words, inflation adjusted returns. Over the long-term, it’s important to consider the impact of inflation on returns to determine if we are wealthier. We increase our purchasing power or wealth, if our returns outstrip inflation over a given period.

Key learning objectives:

• Identify the two methods in calculating real returns

• Use the calculation to determine if wealth has increased or decreased

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Summary

#### What are the two methods of calculating real returns?

1. Fisher Effect Equation: Nominal rate - Inflation Rate. However, this disregards the effect of time
2. Real Rate = (1+ Nominal rate) / (1+ Inflation rate) - 1

#### Real returns impact which parties?

Real returns are good for savers and investors. However, if you’re a borrower, you would prefer negative real rates, because it means you’re paying back devalued money.

#### Using the information in the table, how do we calculate the inflation index, inflation rate, fisher, real rates and investment?

 Years Inflation Index Nominal Rates/Returns Inflation Rate Fisher Real Rates Investment 0 100.00 100.00 1 102.00 5.00% 2.00% 3.00% 2.94% 105.00 2 104.50 3.00% 2.45% 0.55% 0.54% 108.15 3 107.00 6.00% 2.39% 3.61% 3.52% 114.64 4 109.20 2.00% 2.06% -0.06% -0.05% 116.93 5 113.00 7.00% 3.48% 3.52% 3.40% 125.12
1. Inflation Rate
• Year 1: (102/100) -1 = 2%
• Year 2: (104.5/102) -1 = 2.45%
2. Fisher: (Nominal rate - Inflation rate)
• Year 1: (5% - 3%) = 2%
• Year 2: (3%-2.45%) = 0.55%
3. Real Rate
• Year 1: (1+ 0.05) / (1 + 0.02) - 1 = 2.94%
• Year 2: (1+0.03) / (1+ 0.0245) - 1 = 0.54%
4. Investment
• Year 1: 100 x (1+0.05) = 105
• Year 2: 105 x (1+ 0.03) = 108.15

#### Have we increased our wealth over this 5-year period?

• Nominal Return (5Yrs): (125.12/100) - 1 = 25.12%
• Inflation (5Yrs): (113.00/100.00) - 1 = 13%
• Annualised 5-Year Real Return: (1+0.2512) / (1+ 0.13) -1 = 2.0581%

Given those returns and those inflation rates, we have increased our wealth, on average, by 2.0581% above inflation.