Advanced Corporate Finance: Theoretical Financial Concepts

Advanced Corporate Financebook To Be Used Is Financial Theory And Corp

Advanced Corporate Financebook To Be Used Is Financial Theory And Corporate Policy, FOURTH EDITION, Copeland Weston Shastri Chapter . Let us assume a normal distribution of returns and risk averse utility functions. Under what conditions will all investors demand the same portfolio of risky assets?

The following data have been developed for the Donovan Company, the manufacturer of an advanced line of adhesives: Sate Probability Market Return Return for the firm 1 .1 -.15 -.30 2 .3 .05 .4 .15 .20 4 .2 .20 .50 The risk free rate I 6%. Calculate the following: a) The expected market return. b) The variance of the market return. c) The expected return for the Donovan Company. d) The covariance of the return for the Donovan Company with the market return. e) Write the equation of the security market line. f) What is the required return for the Donovan Company? How does this compare with its expected return? 3. What are the assumptions sufficient to guarantee that the market portfolio is an efficient portfolio? 4. In the CAPM is there any way to identify the investors who are more risk averse? Explain. How would your answer change if there were not a riskless asset? 5. Given risk free borrowing and lending, efficient portfolios have no unsystematic risk. True or False? Explain.

Paper For Above instruction

The principles of modern portfolio theory and the Capital Asset Pricing Model (CAPM) elucidate the conditions under which all investors demand the same portfolio of risky assets. Central to this understanding are the assumptions of normally distributed returns and investors possessing risk-averse utility functions. When investors evaluate portfolios under these assumptions, the concept of a single, market-dominant portfolio—commonly referred to as the market portfolio—emerges. This portfolio contains all assets weighted by their market values, and under the CAPM, it is efficient, meaning that it offers the highest expected return per unit of systematic risk. When investors are rational and seek to maximize utility, given their risk preferences, they will all choose to hold this market portfolio in combination with risk-free assets, resulting in identical demand for the same risky asset portfolio. This convergence occurs because the risk-return trade-offs are identical across rational investors, and their utility functions are aligned with mean-variance preferences, allowing diversification to eliminate unsystematic risk, eliminating any differences in individual asset demand beyond the market portfolio allocation.

Applying this understanding to specific asset data involves calculating expected returns, variances, covariances, and determining the security market line (SML). For the Donovan Company, based on the given probability-weighted returns, the expected market return is computed as the sum of the products of each outcome's probability and its market return. The variance of the market return measures the dispersion of possible outcomes around the expected return, crucial for assessing total risk. The company's expected return is similarly calculated, considering the individual probability-weighted firm returns. The covariance between Donovan’s returns and the market portfolio is indicative of how the company's stock moves relative to the overall market, vital for calculating beta and the required risk premium.

The security market line, derived from the CAPM, plots the expected return of a security against its beta, reflecting systematic risk. It is expressed as:

\( \text{Expected Return} = R_f + \beta ( R_m - R_f ) \)

where \( R_f \) is the risk-free rate, \( R_m \) is the expected market return, and \( \beta \) is the measure of systematic risk. The required return for Donovan is then determined by plugging in its beta into this equation, which should be compared with its expected return to evaluate whether the stock is fairly priced.

The assumptions guaranteeing the efficiency of the market portfolio include access to perfect information, no taxes or transaction costs, investors being rational and risk-averse, and markets being frictionless. Under these idealized conditions, the market portfolio is mean-variance efficient, lying on the efficient frontier, meaning it offers the best possible return for a given level of risk.

In the CAPM framework, identifying the most risk-averse investors involves examining their investment behaviors and asset allocations. More risk-averse investors prefer portfolios with lower systematic risk, often holding a larger proportion of risk-free assets relative to risky ones. In the absence of a riskless asset, the landscape changes—investors can only diversify among risky assets, and the original tangent portfolio concept still applies, but the composition and risk preferences become more complex to delineate directly.

Regarding the statement that, with risk-free borrowing and lending, efficient portfolios have no unsystematic risk, it is true. This outcome stems from the ability to diversify idiosyncratic risk across large portfolios effectively. When investors borrow and lend at the risk-free rate, they can combine these portfolios to eliminate unsystematic risk entirely, aligning their investment choices with the market portfolio’s systematic risk exposure. The result is that all unsystematic components are diversified away, leaving only systematic risk, which cannot be diversified through portfolio optimization.

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