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Mathematics · Studypool

Mathematics Question

Overview

Part 1 complete discussion

  • Describe as comprehensively as possible, the definitions,
    and where appropriate, use equations to illustrate, 1)
    expected rate of return, 2) continuous probability
    distribution, and, 3) standard deviation and variance.

Part 2 reply to discussion

  1. Define the terms shown below using graphs or equations to illustrate your answers where feasible, 1) Capital Asset Pricing Model (CAPM), 2) Expected return on a portfolio, and 3) Beta coefficient

Hello Class

Here is a copy of the response for the three items noted.

CAPM is a model based upon the proposition that any stock’s required rate of return is equal to the risk-free rate of return plus a risk premium reflecting only the risk remaining after diversification.

The expected return on a portfolio. p, is simply the weighted-average expected return of the individual stocks in the portfolio, with the weights being the fraction of total portfolio value invested in each stock.

The market portfolio is a portfolio consisting of all stocks.

The beta coefficient is a measure of a stock’s market risk. A stock with a beta greater than 1 has stock returns that tend to be higher than the market when the market is up but tend to be below the market when the market is down. The opposite is true for a stock with a beta less than 1.

Again, thank you for your tremendous contribution.

Part 3 reply to discussion

Hello class,

pose a company estimates its overall cost of capital for the coming year to be 10%. What might be reasonable costs of capital for average-risk, high-risk, and low-risk projects?

adjustment for different risk levels would be: Average-risk projects: 10% (equal to the companies overall cost of capital). High-risk projects: 12-15% (higher to account for increased risk) Low-risk projects: 7-8% (lower due to reduced risk exposure).

Explanation:

Firms typically adjust their required return based on project risk using a risk-adjusted discount rate (Brigham & Ehrhardt, 2022). Higher-risk projects demands a higher return to compensate for uncertainty, while lower-risk projects can be financed at a lower rate (Ross, Westerfield, & Jaffe, 2021).