Chapter 1 Return Calculations
In this Chapter we cover asset return calculations with an emphasis on equity returns. Section 1.1 covers basic time value of money calculations. Section 1.2 covers asset return calculations, including both simple and continuously compounded returns. Section 1.3 illustrates asset return calculations using R. Updated: June 23, 2011

1.1

The Time Value of Money

This section reviews basic time value of money calculations. The concepts of future value, present value and the compounding of interest are dened and discussed.

1.1.1

Future value, present value and simple interest.

Consider an amount $ invested for years at a simple interest rate of per annum (where is expressed as a decimal). If compounding takes place only at the end of the year the future value after years is: = $ (1 + ) × · · · × (1 + ) = $ · (1 + ) (1.1)

Over the rst year, $ grows to $ (1+ ) = $ +$ × which represents the initial principle $ plus the payment of simple interest $ × for the year. Over the second year, the new principle $ (1+ ) grows to $ (1+ )(1+ ) = $ (1 + )2 and so on. 1

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CHAPTER 1 RETURN CALCULATIONS

Example 1 Future value with simple interest. Consider putting $1000 in an interest checking account that pays a simple annual percentage rate of 3% The future value after = 1 5 and 10 years is, respectively,
1 5 10

= $1000 · (1 03)1 = $1030 = $1000 · (1 03)5 = $1159 27 = $1000 · (1 03)10 = $1343 92

Over the rst year, $30 in interest is paid; over three years, $159 27 in interest is accrued; over ve years, $343 92 in interest is accrued ¥ The future value formula (1.1) denes a relationship between four variand Given three variables, the fourth variable can be ables: determined. Given and and solving for gives the present value formula: (1.2) = (1 + ) Given as: and the annual interest rate on the investment is dened =