The question for investors and their advisors is: How can you get higher returns with less risk? See Example 2. So what causes this reduction of risk? Charts of returns can show the amount of volatility in the short term and over the longer term. Company risk refers to the characteristics of specific businesses or firms that affect their performance, making them more or less vulnerable to economic and industry risks. Economic cycles fluctuate, and industry and firm conditions vary, but over the long run, an investment that has survived has weathered all those storms. The Barclay Capital Study calculated the average return on treasury bills in the UK from 1900 to 2002 as approximately 6%. If the information you have shows more than one year’s results, you can calculate the annual return using what you learned in Chapter 4 "Evaluating Choices: Time, Risk, and Value" about the relationships of time and value. Returns are always calculated as annual rates of return, or the percentage of return created for each unit (dollar) of original value. Finding out the standard deviation as a measure of risk can show investors the historical volatility of investments. In this article on portfolio theory we will review the reason why investors should establish portfolios. Based on data from Standard & Poor’s, Inc.. Please visit our global website instead, Relevant to ACCA Qualification Papers F9 and P4. As you can see, the link between risk and return is reciprocal. While it is common to speak of measuring things, we actually measure attributes of things. Risk and Return Considerations Risk refers to the variability of possible returns associated with a given investment. Thus, standard deviation can be used to define the expected range of investment returns. The total risk of a portfolio (as measured by the standard deviation of returns) consists of two types of risk: unsystematic risk and systematic risk. See Example 6. These characteristics include how much debt financing the company uses, how well it creates economies of scale, how efficient its inventory management is, how flexible its labor relationships are, and so on. Since these factors cause returns to move in the same direction they cannot cancel out. Starting from the top (the big picture) and working down, there are. Indeed, the returns on investments in the same industry tend to have a high positive correlation of approximately 0.9, while the returns on investments in different industries tend to have a low positive correlation of approximately 0.2. The return expected for an investment based on its average historical performance. So you could look at the average of the returns for each year. The risk-free return is the return required by investors to compensate them for investing in a risk-free investment. To calculate the risk premium, we need to be able to define and measure risk. to get investors to take on more risks, there must be greater expected returns What do the slopes of the risk-return … While information about current and past returns is useful, investment professionals are more concerned with the expected returnThe return expected for an investment based on its average historical performance. The economic cycle may swing from expansion to recession, for example; inflation or deflation may increase, unemployment may increase, or interest rates may fluctuate. What is the missing factor? Port A + B                               20                                     4.47 And then the portfolio risk needs to be calculated to … The expected return of a portfolio (Rport) is simply a weighted average of the expected returns of the individual investments. Changes in the inflation rate can make corporate bonds more or less valuable, for example, or more or less able to create valuable returns. An NPV calculation compares the expected and required returns in absolute terms. Investors are rewarded with returns for taking on risk – but that risk must be managed. Thus 5% is the historical average risk premium in the UK. The answer to this question will be given in the following article on the Capital Asset Pricing Model (CAPM). Assume that the expected return will be 20% at the end of the first year. The first method is called the covariance and the second method is called the correlation coefficient. Systematic/Market risk: general economic factors are those macro -economic factors that affect the cash flows of all companies in the stock market in a consistent manner, eg a country’s rate of economic growth, corporate tax rates, unemployment levels, and interest rates. Decision criteria: accept if the NPV is zero or positive. The covariance. We have just calculated a historical return, on the basis that the dividend income and the price at the end of year one is known. A wiser policy would be to spread the funds over several investments (establish a portfolio) so that the unexpected losses from one investment may be offset to some extent by the unexpected gains from another. It should clearly delineate what types of risk are rewarded and what are not, and provide a rationale for the delineation. Given that Joe requires a return of 16% should he invest? The theory defines investment risk in a way that can be measured, and then relates the measurable risk in any investment to the level of return that can be expected from that investment in a predictable way. What would be the market risk and the required return of a 50-50 portfolio of Alta Inds and Repo Men? For example, corporate stock is classified as large cap, mid cap, or small cap, depending on the size of the corporation as measured by its market capitalization (the aggregate value of its stock). The standard deviation is as a measure of risk; the higher the deviation, the higher the risk and hence, the lower the Sharpe Ratio. In each case, how did the type of risk affect investment performance. The returns of A and D are independent from each other. Measure and analyze risk and return of portfolios. Risk Adjusted Returns – Sharpe Ratio vs Treynor Ratio vs Jensen’s Alpha A positive NPV opportunity is where the expected return more than compensates the investor for the perceived level of risk, ie the expected return of 20% is greater than the required return of 16%. Most businesses are cyclical, growing when the economy grows and contracting when the economy contracts. Suppose that Joe is considering investing £100 in A plc with the intention of selling the shares at the end of the first year. If we have a large enough portfolio it is possible to eliminate the unsystematic risk. They tend to be more willing and able to finance purchases with debt or with credit, expanding their ability to purchase durable goods. For completeness, the calculations of the covariances from raw data are included. The rule set down in this connection is “the higher the probability distribution of expected future return, the smaller the risk of a given project and the vice versa.” Return on investment ratio. Thus the market only gives a return for systematic risk. Investors all face a trade-off between risk and return. Measures are widely used in science and in every-day activities. This can be proved quite easily, as a portfolio’s expected return is equal to the weighted average of the expected returns on the individual investments, whereas a portfolio’s risk is less than the weighted average of the risk of the individual investments due to the risk reduction effect of diversification caused by the correlation coefficient being less than +1. The variance of return is the weighted sum of squared deviations from the expected return. Figure 12.9 S&P 500 Average Annual ReturnBased on data from Standard & Poor’s, Inc., http://www2.standardandpoors.com/spf/xls/index/MONTHLY.xls (accessed November 24, 2009). We shall see that it is possible to maintain returns (the good) while reducing risk (the bad). The expected return is simply the weighted average of possible outcomes, where the weights are the relative chances of occurrence. The risk-return relationship is explained in two separate back-to-back articles in this month’s issue. What is ‘Risk and Return’? Investment risk is the possibility that an investment’s actual return will not be its expected return. The formula will obviously take into account the risk (standard deviation of returns) of both investments but will also need to incorporate a measure of covariability as this influences the level of risk reduction. return of A plc                return                         premium There are at least two costs to investing: the opportunity cost of giving up cash and giving up all your other uses of that cash until you get it back in the future and the cost of the risk you take—the risk that you won’t get it all back. Every airline is affected by such an event, as an increase in the price of airplane fuel increases airline costs and reduces profits. However, as already stated, in reality the correlation coefficients between returns on investments tend to lie between 0 and +1. Therefore, we can say that the forecast actual and expected returns are almost the same in two out of the three conditions. What do you need to know to estimate the expected return of an investment in the future? Returns are the benefits from investing, but they must be larger than its costs. Solving for r—the annual rate of return, assuming you have not taken the returns out in the meantime—and using a calculator, a computer application, or doing the math, you get 7 percent. Selecting a security to invest in, such as a stock or fund, requires analyzing its returns. 9    Investors who have well-diversified portfolios dominate the market. He asks the following questions: ‘What is the future expected return from the shares? He is currently trying to decide which one of the other three investments into which he will invest the remaining 50% of his funds. However, this approach is not required in the exam, as the exam questions will generally contain the covariances when required. Risk is composed of … Portfolio Return. We can see that the standard deviation of all the individual investments is 4.47%. The returns of A and C move in equal but opposite ways (when the return on A goes up to 30%, the return on C goes down to 10%, when the return on A goes down to 10%, the return on C goes up to 30%). The required return may be calculated as follows: A well-diversified portfolio is very easy to obtain, all we have to do is buy a portion of a larger fund that is already well-diversified, like buying into a unit trust or a tracker fund. However, the above analysis is flawed, as the standard deviation of a portfolio is not simply the weighted average of the standard deviation of returns of the individual investments but is generally less than the weighted average. Industry risks usually involve economic factors that affect an entire industry or developments in technology that affect an industry’s markets. See Example 4. So, demand for most goods and services increases as an economy expands, and businesses expand too. Therefore, when there is no correlation between the returns on investments this results in the partial reduction of risk. Statistical measures of variability are the variance and the standard deviation (the square root of the variance). Risk is associated with the possibility that realized returns will be less than the returns that were expected. The formulae for the standard deviation of returns of a two-asset portfolio, The first two terms deal with the risk of the individual investments. As it is easier to discuss risk as a percentage rate of return, the standard deviation is more commonly used to measure risk. Unsystematic/Specific risk: refers to the impact on a company’s cash flows of largely random events like industrial relations problems, equipment failure, R&D achievements, changes in the senior management team etc. The firm must compare the expected return from a given investment with the risk associated with it. The coefficient of variation shows the risk per unit of return, and it provides a more meaningful basis for comparison when the expected returns on two alternatives are not the same. Port A + C                               20                                     0.00 Calculation of the risk premium The reason for squaring the deviations is to ensure that both positive and negative deviations contribute equally to the measure of variability. A negative covariance indicates that the returns move in opposite directions as in A and C. A zero covariance indicates that the returns are independent of each other as in A and D. Investments (assets) are categorized in terms of the markets they trade in. The returns on most investments will tend to move in the same direction to a greater or lesser degree because of common macro- economic factors affecting all investments. To calculate the annual rate of return for an investment, you need to know the income created, the gain (loss) in value, and the original value at the beginning of the year. The extent of the risk reduction is influenced by the way the returns on the investments co-vary. Investment                             Expected                         Standard They should hold the ‘Market portfolio’ in order to gain the maximum risk reduction effect. Therefore, we will need a new formula to calculate the risk (standard deviation of returns) on a two -asset portfolio. The parameters of the risk and return of any stock explicitly belong to that particular stock, however, the investor can adjust the return to risk ratio of his/ her portfolio to the desired level using certain measures. We just need to understand the conclusion of the analysis. See Example 7. However, these only relate to specific instances where the investments being compared either have the same expected return or the same standard deviation. Let us then assume that there is a choice of investing in either A plc or Z plc, which one should we choose? The standard deviation of a two-asset portfolio We need to understand the principles that underpin portfolio theory, before we can appreciate the creation of the Capital Asset Pricing Model (CAPM). In addition, changes in a market can affect an investment’s value. The next question will be how do we measure an investment’s systematic risk? In reality, the correlation coefficient between returns on investments tends to lie between 0 and +1. See Example 5. This is the utopian position, ie where the unexpected returns cancel out against each other resulting in the expected return. He is trying to determine if the shares are going to be a viable investment. This is the most basic possible example of perfect positive correlation, where the forecast of the actual returns are the same in all market conditions for both investments and thus for the portfolio (as the portfolio return is simply a weighted average). Characterize the relationship between risk and return. If there is no gain or loss, if Ending value − Original value = 0 (is the same), then your return is simply the income that the investment created. Return refers to either gains and losses made from trading a security. The required return on a risky investment consists of the risk-free rate (which includes inflation) and a risk premium. The risk contributed by the covariance is often called the ‘market or systematic risk’. We can see from Portfolio A + D above where the correlation coefficient was zero, that by investing in just two investments we can reduce the risk from 4.47% to just 3.16% (a reduction of 1.31 percentage points). It is strictly limited to a range from -1 to +1. Investment risk is the idea that an investment will not perform as expected, that its actual return will deviate from the expected return. The market risk premium is part of the Capital Asset Pricing Model (CAPM) which analysts and investors use to calculate the acceptable rate interest rate risk, purchasing power risk, and exchange rate risk. Estimating the expected return is complicated because many factors (i.e., current economic conditions, industry conditions, and market conditions) may affect that estimate. A good risk and return model should… 1. Then the formula for the variance of the portfolio becomes: The first term is the average variance of the individual investments and the second term is the average covariance. Economic risks are risks that something will upset the economy as a whole. The risk-free return is the return required by investors to compensate them for investing in a risk-free investment. However, a well-diversified portfolio only suffers from systematic risk, as the unsystematic risk has been diversified away. In a portfolio, such random factors tend to cancel as the number of investments in the portfolio increase. Explain the following A) Measure of historical returns (Single Asset) B) Measure of historical returns (Portfolio) C) Measure of expected… Unless you have some reason to believe that next year will not be an average year, the average return can be your expected return. The definition of risk that is often used in finance literature is based on the variability of the actual return from the expected return. This approach has been taken as the risk-return story is included in two separate but interconnected parts of the syllabus. 0.1                               5 Value at Risk (VaR) is a statistical measure used to assess the level of risk associated with a portfolio or company. The standard deviation on the rate of return on an investment is a measure of its volatility, or risk. Chapter 5: Measuring Risk—Introduction page 3 LRT . Therefore, to measure the degree of risk we need to know the probability of each possible outcome of a decision. Compare traditional portfolio Principles of portfolio planning The Capital Asset Pricing Model (CAPM) If the same stock paid a dividend of $2, then your return = [2 + (105 − 100)] ÷ 100 = 7 ÷ 100 = 7%. Probability                 Return % Risk refers to variability. If the ending value is less, then Ending value − Original value < 0 (is less than zero), and you have a loss that detracts from your return. In this article, we will learn how to compute the risk and return of a portfolio of assets. Standard deviation is a measure of how much an investment's returns can vary from its average return. As Figure 12.9 "S&P 500 Average Annual Return" shows, an investment may do better or worse than its average. Define the different kinds of investment risk. He is considering buying some shares in A plc. For example, if you buy a share of stock for $100, and it pays no dividend, and a year later the market price is $105, then your return = [0 + (105 − 100)] ÷ 100 = 5 ÷ 100 = 5%. Returning to the example of A plc, we will now calculate the variance and standard deviation of the returns. So, in any given year, the S&P 500 is expected to return 9.16 percent but its return could be as high as 67.78 percent or as low as −49.46 percent, based on its performance during that specific period. Expected return is the average return the asset has generated based on historical data of actual returns. Standard Deviation as a Measure of Risk: Probability distribution provides the basis for measuring the risk of a project. RISK AND RETURN ON TWO-ASSET PORTFOLIOS The third term is the most interesting one as it considers the way in which the returns on each pair of investments co-vary. It should come up with a measure of risk that applies to all assets and not be asset-specific. As N becomes very large the first term tends towards zero, while the second term will approach the average covariance. What kinds of risk are included in investment risk? To compare A plc and Z plc, the expected return and the standard deviation of the returns for Z plc will have to be calculated. Measure and analyze risk and return of portfolios. If the time period you are looking at is long enough, you can reasonably assume that an investment’s average return over time is the return you can expect in the next year. Portfolio A+B – perfect positive correlation An investor who has a well-diversified portfolio only requires compensation for the risk suffered by their portfolio (systematic risk). For example, we don’t measure a meeting, but we may measure the duration of a meeting or the size of a meeting. Portfolio A+D – no correlation Risk is measured by the amount of volatility, that is, the difference between actual returns and average (expected) returns. Returns are also your compensation for investing, for taking on some or all of the risk of the investment, whether it is a corporation, government, parcel of real estate, or work of art. This compares with only one condition when there is perfect positive correlation (no reduction of risk) and all three conditions when there is perfect negative correlation (where risk may be eliminated). We find that two thirds of an investment’s total risk can be diversified away, while the remaining one third of risk cannot be diversified away. THE STUDY OF RISK LEARNING OBJECTIVES The loss in market efficiency further affects the value of assets traded. Actual return includes any gain or loss of asset value plus any income produced by the asset during a period. Port A + D                               20                                     3.16 It also calculated that the average return on the UK stock market over this period was 11%. 0.1                               35 Thus total risk can only be partially reduced, not eliminated. This is not surprising and it is what we would expect from risk- averse investors. The risk-free rate can be 91 or 364-day Treasury-Bill issued by the government. Systematic risk includes market risk,Market Risk PremiumThe market risk premium is the additional return an investor will receive (or expects to receive) from holding a risky market portfolio instead of risk-free assets. Once the systematic risk of an investment is calculated, it is then divided by the market risk, to calculate a relative measure of systematic risk. You can use risk and return ratios to judge how successful your business investments are and find out what effect further investment may have in specific areas of the business. Risk aversion explains the positive risk-return relationship. An industry such as real estate is vulnerable to changes in interest rates. This difference is referred to as the standard deviationIn finance, the statistical measure that calculates the frequency and amount by which actual returns differ from the average or expected returns.. 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