Note3 - FI 478 Investment Strategies and Speculative...

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FI 478 Investment Strategies and Speculative Markets Professor Fan Yu Lecture 3 Pricing Forwards and Futures This Version: January 26, 2008 c 2008 Fan Yu. All Rights Reserved. 1

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Return Calculation Continuously compounded interest rates are used in this course because most of the derivatives pricing literature is based on the assumption of con- tinuous trading (including the Black-Scholes formula). To fully understand it, we have to start with simple interest and compound interest. Holding period return The most basic return is given by what you have at the end of your investment period divided by what you invested at the beginning, minus 1 . Since the length of this holding period does not enter the calculation, it is hard to compare returns for di/erent investment horizons. R HPR = ( V 1 + c ) =V 0 1 ; where V 0 = initial asset price, V 1 = price of asset at the end, c = end of period value of cash payment received (dividend, coupon interest, etc) Example 1 Buy one share of XYZ at 50, receive \$1 dividend and sell in 3 month at 52. R HPR = (52 + 1) = 50 1 = 1 : 06 1 = 6% : Annualizing returns To compare across several holding period returns, they are normally expressed on an annual basis. There are several ways to do this. ± Simple interest Assumes that you earn the same interest per hold period for a year, as if all were received at the end. ± Compounded interest Assumes that you receive the principal and interest at the end of the holding period, the reinvest at the same holding period return. This compounds as many times as there are holding periods in a year. ± Continuous compounding Similar to compounded interest, except that the length of the holding period is essentially zero. If r is the annualized continuously compounded interest rate, an investment of \$1 will grow to \$1 ² e r at the end of one year. 2
Simple interest R SIMPLE = N R HPR ; where N = number of holding periods per year. ± If the holding period is n calendar days, then N = 365 =n . ± If the holding period is n trading days, then N = ( about ) 255 =n . ± If the holding period is n months, N = 12 =n . Example 2 Buy one share of XYZ at 50, receive \$1 dividend and sell in 3 months at 52. Holding period return is 6%. Annualizing at simple interest gives R SIMPLE = 12 = 3 6 = 24% : Compound interest R COMPOUND = (1 + R HPR ) N ² 1 where N = number of holding periods per year. Example 3 Buy one share of XYZ at 50, receive \$1 dividend and sell in 3 months at 52. Holding period return is 6%. Annualizing at compound interest gives R COMPOUND = 1 : 06 12 = 3 ² 1 = 26 : 25% : 3

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Annual Percentage Rate (APR) and E/ective Annual Rate (EAR) When you are quoted an APR and told that it is compounded periodically out the holding period return. The APR is actually a simple interest based on the holding period return. Therefore R HPR = n= 365 R APR : Invested at this rate with compounding, the total amount accumulated at
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This note was uploaded on 03/19/2008 for the course FI 478 taught by Professor Yu during the Spring '08 term at Michigan State University.

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Note3 - FI 478 Investment Strategies and Speculative...

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