Portfolio Risk and Return: Part I
Refresher reading access
Introduction
Construction of an optimal portfolio is an important objective for an investor. In this reading, we will explore the process of examining the risk and return characteristics of individual assets, creating all possible portfolios, selecting the most efficient portfolios, and ultimately choosing the optimal portfolio tailored to the individual in question.
During the process of constructing the optimal portfolio, several factors and investment characteristics are considered. The most important of those factors are risk and return of the individual assets under consideration. Correlations among individual assets along with risk and return are important determinants of portfolio risk. Creating a portfolio for an investor requires an understanding of the risk profile of the investor. Although we will not discuss the process of determining risk aversion for individuals or institutional investors, it is necessary to obtain such information for making an informed decision. In this reading, we will explain the broad types of investors and how their risk–return preferences can be formalized to select the optimal portfolio from among the infinite portfolios contained in the investment opportunity set.
The reading is organized as follows: Section 2 discusses the investment characteristics of assets. In particular, we show the various types of returns and risks, their computation and their applicability to the selection of appropriate assets for inclusion in a portfolio. Section 3 discusses risk aversion and how indifference curves, which incorporate individual preferences, can be constructed. The indifference curves are then applied to the selection of an optimal portfolio using two risky assets. Section 4 provides an understanding and computation of portfolio risk. The role of correlation and diversification of portfolio risk are examined in detail. Section 5 begins with the risky assets available to investors and constructs a large number of risky portfolios. It illustrates the process of narrowing the choices to an efficient set of risky portfolios before identifying the optimal risky portfolio. The risky portfolio is combined with investor risk preferences to generate the investor’s optimal portfolio. A summary concludes this reading.
Learning Outcomes
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calculate and interpret major return measures and describe their appropriate uses;
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compare the money-weighted and time-weighted rates of return and evaluate the performance of portfolios based on these measures;
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describe characteristics of the major asset classes that investors consider in forming portfolios;
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calculate and interpret the mean, variance, and covariance (or correlation) of asset returns based on historical data;
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explain risk aversion and its implications for portfolio selection;
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calculate and interpret portfolio standard deviation;
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describe the effect on a portfolio’s risk of investing in assets that are less than perfectly correlated;
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describe and interpret the minimum-variance and efficient frontiers of risky assets and the global minimum-variance portfolio;
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explain the selection of an optimal portfolio, given an investor’s utility (or risk aversion) and the capital allocation line.
Summary
This reading provides a description and computation of investment characteristics, such as risk and return, that investors use in evaluating assets for investment. This was followed by sections about portfolio construction, selection of an optimal risky portfolio, and an understanding of risk aversion and indifference curves. Finally, the tangency point of the indifference curves with the capital allocation line allows identification of the optimal investor portfolio. Key concepts covered in the reading include the following:
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Holding period return is most appropriate for a single, predefined holding period.
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Multiperiod returns can be aggregated in many ways. Each return computation has special applications for evaluating investments.
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Risk-averse investors make investment decisions based on the risk–return trade-off, maximizing return for the same risk, and minimizing risk for the same return. They may be concerned, however, by deviations from a normal return distribution and from assumptions of financial markets’ operational efficiency.
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Investors are risk averse, and historical data confirm that financial markets price assets for risk-averse investors.
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The risk of a two-asset portfolio is dependent on the proportions of each asset, their standard deviations and the correlation (or covariance) between the assets’ returns. As the number of assets in a portfolio increases, the correlation among asset risks becomes a more important determinate of portfolio risk.
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Combining assets with low correlations reduces portfolio risk.
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The two-fund separation theorem allows us to separate decision making into two steps. In the first step, the optimal risky portfolio and the capital allocation line are identified, which are the same for all investors. In the second step, investor risk preferences enable us to find a unique optimal investor portfolio for each investor.
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The addition of a risk-free asset creates portfolios that are dominant to portfolios of risky assets in all cases except for the optimal risky portfolio.
2 PL Credit
If you are a CFA Institute member don’t forget to record Professional Learning (PL) credit from reading this article.