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Lecture_7-_Diversification_-_Portfolio_Theory - 1 Lecture...

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Money Markets and Finance Lecture 7 Diversification: Portfolio Theory 1. Lecture Overview During this lecture, we will discuss the concepts of portfolio theory and diversification . Diversification allows an individual to reduce the risk of their investment without sacrificing any expected return simply by spreading their wealth over a portfolio comprising a number of assets in an appropriate way. During the course of the lecture we will discuss: What diversification is; How including multiple assets in a portfolio can achieve diversification; Which assets to include in order to achieve the greatest level of diversification; and, How to construct a diversified portfolio in practice. 2. Review of Statistics Before we start discussing portfolio theory and the concept of diversification, we will briefly review the statistical terms discussed last lecture. These terms are important to understand as they are central to portfolio theory. More specifically, we will revisit the definitions of: Random variables; Expected values; and, Standard deviation and variance. 2. Review of Statistics Random Variables: A random variable is one that can take on any number of different values. Each value has an associated probability of occurring. The uncertainty associated with the outcome of a random variable is described by a probability distribution, with the most commonly used distribution being the normal distribution , see below: -75 -65 -55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75 0.020 0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 Probability density Stock market return 2. Review of Statistics Expected Values: The value we expect a random variable ( X ) to take is known as its expected value or mean. Standard Deviation: Standard deviation, σ , is a measure of spread. It is based on how far each value of X varies from the mean. A small standard deviation means that the data doesn’t vary a lot from the mean. A large standard deviation means that the data is more spread out. Variance: The variance, σ 2 , is simply the standard deviation squared. 3. Diversification Recall from last week the assumption that investors are risk averse and therefore prefer less risk to more. Diversification provides a means of reducing risk faced by investors without sacrificing expected return by combining assets that don’t move perfectly together in a portfolio. Note that the ideas we are about to discuss can be extended to consider more than 2 assets. You will consider these extensions in FINM3001 Investments.
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3.1 Measuring How Assets Move Together Correlation and Covariance: The covariance between variables X and Y , σ XY , is a measure of association between the two variables. For example, we may be interested in whether there is an association between the return on a company’s stock and the return on the stock market in general: If the market always went up at the same time company’s stock went up, the covariance would be positive; If the return on the stock and the return on the market were
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Lecture_7-_Diversification_-_Portfolio_Theory - 1 Lecture...

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