Assignment0_solution - Page 1 of 5 The Johnson School at...

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Unformatted text preview: Page 1 of 5 The Johnson School at Cornell University Professor George Gao NBA 6730 Fall 2010 Answers to Assignment 0 (Pre-Week 1) Note: Do not hand in this assignment. This assignment is a self-test so that you can decide on your own whether you have the necessary technical background for this course. These questions help you review some basics from investment, probability, statistics, and calculus that will be used in this course. TA will discuss this assignment at the review session scheduled during the first week of class. Conventions : Here are some conventions that we will adopt throughout the course. These conventions are also common in finance. (1) Interest rate is annualized. This is true, even when we are using semi-annual or quarterly compounding. The frequency of compounding has nothing to do with whether an interest rate is annualized or not. Thus, we always assume it is annualized. (2) The word “logarithm” refers to natural logarithm (both symbols “log” and “ln” mean the same thing). (3) Time is measured in years. For example, if t is today and T is the time at which a bond matures, then ܶ െ ݐ ൌ 2 means the bond matures 2 years from now; ܶ െ ݐ ൌ 0.5 means the bond matures 6 months from now. Questions related to interest rate 1. A bank quotes you a rate of interest of 10% per annum with quarterly compounding. What is the equivalent rate with (a) continuous compounding, and (b) annual compounding? (Read Hull’s Chapter 4.2 if you need to review continuous compounding.) Note that if we invest $1 for a year, the different rate quotes on this same investment should give us the same amount of interest plus principle in the end. (a) ሺ1 ൅ ଴.ଵ ସ ሻ ସ ൌ ݁ ௥ൈଵ , and we get ݎ ൌ 9.877% (b) ሺ1 ൅ ଴.ଵ ସ ሻ ସ ൌ 1 ൅ ݎ , and we get ݎ ൌ 10.3813% Page 2 of 5 2. Let ݐ denote the present, ܶ ൐ ݐ denote sometime in the future, and ܤሺݐ, ܶሻ denote the current price of a zero-coupon bond maturing at ܶ with a face value of $1. (Note: we will often think of ܤሺݐ, ܶሻ as the present (discounted) value of $1 that is paid at...
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This note was uploaded on 10/19/2010 for the course JOHNSON 6730 taught by Professor Georgegao during the Fall '10 term at Cornell.

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Assignment0_solution - Page 1 of 5 The Johnson School at...

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