The Heart of Mathematics: An Invitation to Effective Thinking, WileyPLUS NextGen Card with Loose-leaf Set Single Semester: An Invitation to Effective Thinking (Key Curriculum Press)

4th Edition

ISBN: 9781119760054

Author: Burger, Edward B. , Starbird, Michael

Publisher: Wiley (WileyPLUS Products)

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Textbook Question

Chapter 8.1, Problem 20MS

Pennies from heaven (H). Residents of your dormitory decide to collect pennies as a fund-raiser for a charity. The donations are kept in a large container in the RA’s room. One Saturday night, after an intense study session in the library, the RA decides to stand at the top of the stairs above the dorm comm on room and empty the pennies out so they rain down on the floor below. If 62% of the pennies land heads up, and 1900 pennies land tails up, how much money was collected for charity?

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Chapter 8.1, Problem 19MS

Chapter 8.1, Problem 21MS

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1 (Expected Shortfall) Suppose the price of an asset Pt follows a normal random walk, i.e., Pt = Po+r₁ + ... + rt with r₁, r2,... being IID N(μ, o²). Po+r1+. ⚫ Suppose the VaR of rt is VaRq(rt) at level q, find the VaR of the price in T days, i.e., VaRq(Pt – Pt–T). - • If ESq(rt) = A, find ES₁(Pt – Pt–T).

2 (Normal Distribution) Let rt be a log return. Suppose that r₁, 2, ... are IID N(0.06, 0.47). What is the distribution of rt (4) = rt + rt-1 + rt-2 + rt-3? What is P(rt (4) < 2)? What is the covariance between r2(2) = 1 + 12 and 13(2) = r² + 13? • What is the conditional distribution of r₁(3) = rt + rt-1 + rt-2 given rt-2 = 0.6?

3 (Sharpe-ratio) Suppose that X1, X2,..., is a lognormal geometric random walk with parameters (μ, o²). Specifically, suppose that X = Xo exp(rı + ...Tk), where Xo is a fixed constant and r1, T2, ... are IID N(μ, o²). Find the Sharpe-ratios of rk and log(Xk) — log(Xo) respectively, assuming the risk free return is 0.

Chapter 8 Solutions

The Heart of Mathematics: An Invitation to Effective Thinking, WileyPLUS NextGen Card with Loose-leaf Set Single Semester: An Invitation to Effective Thinking (Key Curriculum Press)

Ch. 8.1 - Doors galore. The 21st-century version of Lets...Ch. 8.1 - Birthday surprise. How many people would you need...Ch. 8.1 - Opposite of heads. Suppose you flip a coin 100...Ch. 8.1 - Penny percent. Suppose you flip a penny 50 times,...Ch. 8.1 - Party time. At a nephews party, you decide to...Ch. 8.1 - Flipping Lincoln. Flip a penny 100 times and...Ch. 8.1 - Flashing cards. Shuffle a standard deck of 52...Ch. 8.1 - King for a day. Remove three cards from a deck of...Ch. 8.1 - A card deal stick. Remove three cards from a deck...Ch. 8.1 - A card deal switch. Remove three cards from a deck...

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