7456 Words30 Pages

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 dened 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*…show more content…*

The e ective annual rate is greater than the simple annual rate due to the payment of interest on interest. The general relationship between the simple annual rate with payments time per year and the e ective annual rate, is (1 + Given the simple rate µ )= 1+ µ = 1+ Given the e ective annual rate = £ (1 + ¶ ¶ we can solve for the e ective annual rate using 1 (1.5) we can solve for the simple rate using )1 ¤ 1 The relationship between the e ective annual rate and the simple rate that is compounded continuously is (1 + Hence, = 1 = ln(1 + )= ) Example 4 Determine e ective annual rates. 6 CHAPTER 1 RETURN CALCULATIONS The e ective annual rates associated with the investments in Example 2 are given in the table below: Compounding Frequency Value of $1000 at end of 1 year ( Annually ( Quarterly ( Weekly ( Daily ( = 1) = 4) = 52) = 365) = ) 1100 1103.8 1105.1 1105.515 1105.517 = 10%) 10% 10 38% 10 51% 10 55% 10 55% Continuously ( ¥ Example 5 Determine continuously compounded rate from e ective annual rate Suppose an investment pays a periodic interest rate of 5% every six months ( =2 2 = 0

The e ective annual rate is greater than the simple annual rate due to the payment of interest on interest. The general relationship between the simple annual rate with payments time per year and the e ective annual rate, is (1 + Given the simple rate µ )= 1+ µ = 1+ Given the e ective annual rate = £ (1 + ¶ ¶ we can solve for the e ective annual rate using 1 (1.5) we can solve for the simple rate using )1 ¤ 1 The relationship between the e ective annual rate and the simple rate that is compounded continuously is (1 + Hence, = 1 = ln(1 + )= ) Example 4 Determine e ective annual rates. 6 CHAPTER 1 RETURN CALCULATIONS The e ective annual rates associated with the investments in Example 2 are given in the table below: Compounding Frequency Value of $1000 at end of 1 year ( Annually ( Quarterly ( Weekly ( Daily ( = 1) = 4) = 52) = 365) = ) 1100 1103.8 1105.1 1105.515 1105.517 = 10%) 10% 10 38% 10 51% 10 55% 10 55% Continuously ( ¥ Example 5 Determine continuously compounded rate from e ective annual rate Suppose an investment pays a periodic interest rate of 5% every six months ( =2 2 = 0

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