Math Finance / Combinatorics Problem

Prove that if a random variable y is measurable on fx, then there exists a function h : R  R such that for all ω ε Ω : Y (ω) = h [x(ω)] • For a random variable x, the coarsest partition on which k x is measurable is called the partition generated by x and is denoted fx. • Sample space: Ω = {ω1,…, ωK} See attached file for full problem description.

Math Finance /Combinatorics problem

The meet of the partitions f1,…,fI is the finest partition that is coarser then each fi. The join of the partitions f1,…,fI is the coarsest partition that is finer than each fi. The meet of partitions is denoted and the join of partitions is denoted I I Λ fi (meet) V fi (join) i = 1 i = 1 (a) If f1,…,fI represent the information of the different traders, what do the meet and join represent? (b) For: f1 = { {ω1},{ ω2, ω3, ω4},{ ω5, ω6, ω7} } f2 = { {ω1, ω2, ω3},{ω4},{ ω5, ω6,},{ω7} } ... click for more

CAPM and Valuation.

CAPM and Valuation. You are considering acquiring a firm that you believe can generate expected cash flows of $10,000 a year forever. However, you recognize that those cash flows are uncertain. a. Suppose you believe that the beta of the firm is .4. How much is the firm worth if the risk free rate is 4 percent and the expected rate of return on the market portfolio is 12 percent? b. By how much will you overvalue the firm if its beta is actually .6?

CAPM and Expected return.

CAPM and Expected return. If the risk-free rate is 6 percent and the expected rate of return on the market portfolio is 14 percent, is a security with a beta of 1.25 and an expected rate of return of 16 percent overpriced or under priced?

CAPM and Cost of Capital.

CAPM and Valuation. You are a consultant to a firm evaluating an expansion business. The cash-flow forecasts (in millions of dollars) for the project are: Years Cash Flow 0 -100 1–10 + 15 Based on the behavior of the firm's stock, you believe that the beta of the firm is 1.4. Assuming that the rate of return available on risk-free investments is 4 percent and that the expected rate of return on the market portfolio is 12 percent, what is the net present value of the project? What is the project IRR? What is the cost of capital for the project? Does the accept–reject decision using IRR agree with the decision using NPV?