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Chapter 13 Answers
Chapter 13 Answers

... We can also answer this question using the reward-to-risk ratio. All assets must have the same reward-to-risk ratio. The reward-to-risk ratio is the risk premium of the asset divided by its . We are given the market risk premium, and we know the  of the market is one, so the reward-to-risk ratio f ...
FM11 Ch 04 Mini
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... The standard deviation gets smaller as more stocks are combined in the portfolio, while rp (the portfolio’s return) remains constant. Thus, by adding stocks to your portfolio, which initially started as a 1-stock portfolio, risk has been reduced. In the real world, stocks are positively correlated w ...
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... Have you read her blog?!? You should! Not only did she analyze her portfolio and the market on a daily basis, but she brilliantly ties it all back the farm with stories from her childhood. Amanda is the Queen of strategy! Who needs Bloomberg. Maybe she’ll offer subscriptions. ...
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... This presumption, that the law of large numbers applies to a portfolio of securities, cannot be accepted. The returns from securities are too intercorrelated. Diversification cannot eliminate all variance. The portfolio with maximum expected return is not necessarily the one with minimum variance. T ...
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... 24. Since the beta for Portfolio F is zero, the expected return for Portfolio F equals the risk-free rate. For Portfolio A, the ratio of risk premium to beta is: (10%  4%)/1 = 6% The ratio for Portfolio E is higher: (9% 4%)/(0.6) = 8.33% This implies that an arbitrage opportunity exists. For inst ...
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... Average Stock Returns and Risk-Free Returns • Risk Premium is the additional return (in excess of riskfree rate) resulting from bearing risk. • One of the most significant observations of stock market data is this long-run excess of stock return over the riskfree return. – The average excess return ...
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Inv Club 04_09_10 - Sites at Lafayette

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Modern portfolio theory

Modern portfolio theory (MPT) is a theory of finance that attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets. Although MPT is widely used in practice in the financial industry and several of its creators won a Nobel memorial prize for the theory, in recent years the basic assumptions of MPT have been widely challenged by fields such as behavioral economics.MPT is a mathematical formulation of the concept of diversification in investing, with the aim of selecting a collection of investment assets that has lower overall risk than any other combination of assets with the same expected return. This is possible, intuitively speaking, because different types of assets sometimes change in value in opposite directions. For example, to the extent prices in the stock market move differently from prices in the bond market, a combination of both types of assets can in theory generate lower overall risk than either individually. Diversification can lower risk even if assets' returns are positively correlated.More technically, MPT models an asset's return as a normally or elliptically distributed random variable, defines risk as the standard deviation of return, and models a portfolio as a weighted combination of assets, so that the return of a portfolio is the weighted combination of the assets' returns. By combining different assets whose returns are not perfectly positively correlated, MPT seeks to reduce the total variance of the portfolio return. MPT also assumes that investors are rational and markets are efficient.MPT was developed in the 1950s through the early 1970s and was considered an important advance in the mathematical modeling of finance. Since then, some theoretical and practical criticisms have been leveled against it. These include evidence that financial returns do not follow a normal distribution or indeed any symmetric distribution, and that correlations between asset classes are not fixed but can vary depending on external events (especially in crises). Further, there remains evidence that investors are not rational and markets may not be efficient. Finally, the low volatility anomaly conflicts with CAPM's trade-off assumption of higher risk for higher return. It states that a portfolio consisting of low volatility equities (like blue chip stocks) reaps higher risk-adjusted returns than a portfolio with high volatility equities (like illiquid penny stocks). A study conducted by Myron Scholes, Michael Jensen, and Fischer Black in 1972 suggests that the relationship between return and beta might be flat or even negatively correlated.
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