Question

Problem 6 In this problem, we will use the Independence Axiom to help Jack make investment decisions. A fair coin will be flipped twice. There are two companies Jack can invest in. A share in the first company pays $100 if the first toss comes up heads and $0 if it comes up tails. A share in the second company pays $100 if the second toss comes up heads and $0 otherwise Jack has to choose between two portfolios. The first portfolio consists of two shares of the first company. The second portfolio consists of one share of each company. (i Represent each portfolio as a lottery. (ii) Jack likes the Independence Axiom and wants his portfolio choices to be consistent with the axiom. In addition, he tells you that he is risk-averse, that is, for any given lottery, he prefers receiving the expected value of the lottery to the lottery itself. Note that the expected value of a lottery (pi, xi; ...; pn, Xn) is p1x1P2X2 + prefer the diversified portfolio, in which he holds one share of each company, to the 'all-eggs-in-one-basket' portfolio, in which he holds two shares of the first company pnn Given this information, show that Jack should

Answer 1

1st portfolio, E(RI) = 1x100 + / Xo = so lottery :- (-, 100; 12,0) in 2nd portfolio: E(hy) x the ist 1stross gets head) - WORD= 4x100 + xo {HH, HT, TH,TT} four cases can occuni- if 6 each have 1 probabilities as the fosses are independent trials.

EUR:) = x200 +(4x100)+(x100) + 12 - 50 + 25+25 ton = 100. he prefer lo teny: (+2, 2003 1,100; 1,100; 40) E (R2) > E(RI) and jack is Risk-avense So he prolfens the and cases i.e. Pulting Shares in two stocks..