Portfolio analysis essay

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With a risk-free asset, the straight line is the efficient frontier. This graph shows expected return (vertical) versus standard deviation. This is called the 'risk-expected return space.' every possible combination of risky assets, can be plotted in this risk-expected return space, and the collection of all such possible portfolios defines a region in this space. The left boundary of this region is a hyperbola, 3 and the upper edge of this region is the efficient frontier in the absence of a risk-free asset (sometimes called "the markowitz bullet. Combinations along this upper edge represent portfolios (including no holdings of the risk-free asset) for which there is lowest risk for a given level of expected return. Equivalently, a portfolio lying on the efficient frontier represents the combination offering the best possible expected return for given risk level. The tangent to the hyperbola at the tangency point indicates the best possible capital allocation line (CAL).

Portfolio return volatility (standard deviation σpσp2displaystyle sigma _psqrt sigma _p2 For a two asset portfolio: Portfolio return: operatorname e (R_p)w_Aoperatorname e (R_A)w_Boperatorname e (R_B)w_Aoperatorname e (R_A 1-w_A)operatorname e (R_B). Portfolio variance: sigma _p2w_A2sigma _A2w_B2sigma _B22w_Aw_Bsigma _Asigma _Brho _ab for a three asset portfolio: Portfolio return: operatorname e (R_p)w_Aoperatorname e (R_A)w_Boperatorname e (R_B)w_Coperatorname e (R_C) Portfolio variance: sigma _p2w_A2sigma _A2w_B2sigma _B2w_C2sigma _C22w_Aw_Bsigma _Asigma _Brho _AB2w_Aw_Csigma _Asigma _Crho _AC2w_Bw_Csigma _Bsigma _Crho _bc diversification edit An investor. In other words, investors can reduce their exposure to individual asset risk by holding a diversified portfolio of assets. Diversification may allow for the same portfolio expected return with reduced risk. These ideas have been started with Markowitz and then reinforced by other economists and mathematicians such as Andrew Brennan who have expressed ideas in the limitation of variance through portfolio theory. If all the asset pairs have correlations of 0—they are perfectly uncorrelated—the portfolio's return variance is lamb the sum over all assets of the square of the fraction held in the asset times the asset's return variance (and the portfolio standard deviation is the square root. If all the asset pairs have correlations of 1—they are perfectly positively correlated—then the portfolio returns standard deviation is the sum of the asset returns standard deviations weighted by the fractions held in the portfolio. For given portfolio weights and given standard deviations of asset returns, the case of all correlations being 1 gives the highest possible standard deviation of portfolio return. Efficient frontier with no risk-free asset edit main article: Efficient frontier see also: Portfolio optimization Efficient Frontier. The hyperbola is sometimes referred to as the 'markowitz bullet and is the efficient frontier if no risk-free asset is available.

portfolio analysis essay

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The exact trade-off will be the same for all investors, but different investors will evaluate the trade-off differently based on individual risk aversion characteristics. The implication is that a rational investor will not invest in a portfolio if a second portfolio exists with a more favorable risk-expected return profile. E., if for that level of risk an alternative portfolio exists that has better expected returns. Under the model: Portfolio return is the proportion-weighted thank combination of the constituent assets' returns. Portfolio volatility is a function of the correlations ρ ij of the component assets, for all asset pairs ( i, j ). In general: Expected return: E(Rp)iwiE(Ri)displaystyle operatorname e (R_p)sum _iw_ioperatorname e (R_i)quad where Rpdisplaystyle R_p is the return on the portfolio, ridisplaystyle R_i is the return on asset i and widisplaystyle w_i is the weighting of component asset idisplaystyle i (that is, the proportion of asset. Portfolio return variance: sigma _p2sum _iw_i2sigma _i2sum _isum _jneq iw_iw_jsigma _isigma _jrho _ij, where σdisplaystyle sigma is the (sample) standard deviation of the periodic returns on an asset, and ρijdisplaystyle rho _ij is the correlation coefficient between the returns on assets i and. Alternatively the expression can be written sigma _p2sum _isum _jw_iw_jsigma _isigma _jrho _ij, where ρij1displaystyle rho _ij1 for ijdisplaystyle ij, orσp2ijwiwjσijdisplaystyle sigma _p2sum _isum _jw_iw_jsigma _ij, where σijσiσjρijdisplaystyle sigma _ijsigma _isigma _jrho _ij is the (sample) covariance of the periodic returns on the two assets.

portfolio analysis essay

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It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets report is less risky than owning only one type. Its key insight is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return. It uses the variance of asset prices as a proxy for risk. Economist, harry markowitz introduced mpt in a 1952 essay, 2 for which he was later awarded. Nobel Prize in economics. Contents, mathematical model edit, risk and expected return edit, mpt assumes that investors are risk averse, meaning that given two portfolios that offer the same expected return, investors will prefer the less risky one. Thus, an investor will take on increased risk only if compensated by higher expected returns. Conversely, an investor who wants higher expected returns must accept more risk.

This makes soy milk an important factor in heart health, so people should consider switching to soy milk. "Portfolio analysis" redirects here. For the text book, see. For theorems about the mean-variance efficient frontier, see. Mutual fund separation theorem. For non-mean-variance portfolio analysis, see. Marginal conditional stochastic dominance. Modern portfolio theory mpt or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk.

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portfolio analysis essay

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After six months, her ldl dropped to 198 and her hdl rose to 45, which was a dramatic improvement. Our family all lost quite a bit of weight, as well: my mother lost fifteen pounds and my father lost more than twenty. Her doctor tells her that if she continues this lifestyle change, she will significantly reduce her chance of heart problems in the future. The second example not only contains more information, but it presents it in a believable and interesting way. By including specific details, the author appears to be an "expert so the evidence is more persuasive. Analysis, your day analysis or concluding observation is your way of "wrapping up" the information presented in your paragraph. It should explain why the evidence supports your claim and why this supports the main thesis in your paper.

Its important to end with your own analysis of the information rather than with evidence. This keeps you "in control" of the paper; if you end with evidence, youre emphasizing ideas from your sources rather than your own. The reader relies on you to analyze the evidence in the paragraph and explain why it matters to the claim and to the rest of the paper. Here are some examples of weak and strong analysis/concluding observation sections: Analysis that is really evidence (weak experts at duke universitys School of Medicine agree that soy milk is a healthy choice. Analysis that doesnt relate evidence to claim and thesis statement (weak soy milk therefore prevents disease. Analysis that explains why evidence supports the claim and why this is important to the papers thesis (strong The disease-fighting and health-promoting components of soy milk have the potential to change peoples health and to improve their lives by affecting both cholesterol and weight.

The benefits of soy arent just limited to the heart, however. Soy milk and cheese made from soy milk may help with weight loss since they contain less saturated fat than regular dairy products, although they contain about the same amounts of fat as reduced-fat milk and cheese (Collins 1). Some researchers even believe that soy may help to stimulate the metabolism (duke 4). Note that the second example seems more "balanced because the author demonstrates knowledge of the subject and incorporates several expert opinions to back up the claim. Sometimes your assignment will not require you to conduct research into secondary sources, and you may need to use your own ideas or experiences as evidence to back up your claims. Try to be very specific.

If you include detailed examples and explanations, your evidence will be more interesting and more persuasive to the reader, and you will seem like more of an authority on your topic: evidence that isnt specific (weak evidence my mothers cholesterol was bad, and the doctor. Our family started eating more soy and soy milk, and her levels eventually got much better. During this time, all of us also lost quite a bit of weight. Evidence that is specific (stronger evidence two years ago, my mothers ldl bad cholesterol level was 242, and her hdl good cholesterol was 37, so she was considered "high risk." Since she was hesitant to take cholesterol-lowering medications, her internist suggested that she try. He believed that it was worthwhile to try this before placing her on medications. In order to support her, our entire family started drinking soy milk and walking in the evenings.

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Here are some examples of weak and strong evidence sections: evidence that includes information from one source (weak evidence according to collins, soy milk has more protein than cows evernote milk, and doesnt contain the saturated fat or cholesterol (1). Soybeans are "complete protein" because they contain all eight amino acids (Collins 1). Collins points out that "as little as 25 mg of soy protein a day may decrease levels of ldl cholesterol and Triglycerides" (1) and this may reduce the chance of heart disease. Since soy is a "low-glycemic index" food, it may help people trying to lose weight "feel more satisfied and less hungry until your next meal, which is beneficial for weight management and control" (1). Evidence that includes information from a variety of sources (stronger evidence scientists believe that soy milk has the potential to balance cholesterol levels in humans: "A diet with significant soy protein reduces Total Cholesterol, ldl cholesterol (the "bad" cholesterol) and triglycerides" (Tsang 1). Since soy milk is one of the easiest ways to incorporate soy into the diet, this is a good choice for people seeking to lower their ldl and triglycerides. Soy milk also may reduce the potential for heart disease. Asian countries, which traditionally consume more soy protein, have a much lower incidence of heart disease and many types of cancer (Berkeley 4).

portfolio analysis essay

The evidence will help to "prove" each claim to the reader. In a paper that incorporates research from secondary sources, your evidence may include information from articles, books, electronic sources, or any of the research you gathered. The evidence may take the form of a direct"tion, paraphrased material, statistical data, or any other information from one of your sources that helps to support your claim. Try to incorporate information from several sources into each paragraph. Avoid just "retelling" the information from a single author or article. Aim to represent a variety of opinions and views. This way, youre emerson not just telling the reader what one expert says, but youre explaining how your claim is supported by research from several experts in your field.

milk help to protect the body from disease and promote good health, so soy is a better choice. The first example is weak because it presents facts that cannot be disputed; the second example is stronger because it uses those facts to make an argument. As you can see, the second example not only tells the reader that soy contains healthy isoflavones and nutrients, but it also argues that these facts make soy milk a better choice. To evaluate whether your paper contains effective claims in each paragraph, read only the first sentence of each paragraph. You should be able to follow the development of the papers thesis by reading only the claim sentences. These should tell you the main points that you are making throughout the paper. Your claims will also prepare the reader for the second section of your paragraph. Evidence, this is how you support, or back up, your claims.

Just as in the thesis statement, your topic sentences should be debatable. In other words, they should be arguable claims that you will try to "prove" with your evidence. If you get stuck developing these claims, try to think of reasons why your thesis is true. Each claim should be a tree reason why the reader should believe your papers main idea. For example, perhaps youre writing an essay about whether people should drink soy milk instead of cows milk. Your "reasons" for this might include health benefits, environmental benefits, cost-effectiveness, and safety, so you would focus one paragraph on each of these topics. One of the most common mistakes is to present a topic sentence that is actually an observation of facts or a description of events rather than an active argument. When you make a claim based on a fact or event in your topic sentence, you arent presenting an arguable claim that you can back up with your evidence in that paragraph.

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Effective paragraphs are important in all types of writing. Your paragraphs guide your reader through the paper by helping to explain, substantiate, and support your thesis statement or argument. Each paragraph should pdf discuss one major point or idea. An effective paragraph has three parts: claim, evidence, and analysis. Claim, this is also sometimes called a topic sentence. This will be your way of announcing the main focus of your paragraph; it should tell the reader what your paragraph will be about. It may be helpful to think of your claims as mini arguments that support the papers main argument or thesis.

portfolio analysis essay
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