Always remember: the greater the potential return, the greater the risk. Suppose that Joe is considering investing £100 in A plc with the intention of selling the shares at the end of the first year. Assume that our investor, Joe has decided to construct a two-asset portfolio and that he has already decided to invest 50% of the funds in A plc. 10    The preparation of a summary table and the identification of the most efficient portfolio (if possible) is an essential exam skill. What is the return? We are about to review the mathematical proof of this statement. The answer to this question will be given in the following article on the Capital Asset Pricing Model (CAPM). After reading this article, you will have a good understanding of the risk-return relationship. We just need to understand the conclusion of the analysis. The return on an investment is the result that you achieve in proportion to its value. While the traditional rule of thumb is “the higher the risk, the higher the potential return,” a more accurate statement is, “the higher the risk, the higher the potential return, and the less likely it will achieve the higher return.” To understand this relationship completely, you must know what your risk tolerance is and be able to gauge the relative risk of a particular investment correctly. The following table gives information about four investments: A plc, B plc, C plc, and D plc. Measuring covariability The expected return on a share consists of a dividend yield and a capital gain/loss in percentage terms. After investing money in a project a firm wants to get some outcomes from the project. There are two ways to measure covariability. As N becomes very large the first term tends towards zero, while the second term will approach the average covariance. Since these factors cause returns to move in the same direction they cannot cancel out. Risk refers to the variability of possible returns associated with a given investment. THE PROOF THAT LARGE PORTFOLIOS INCREASE THE RISK REDUCTION EFFECT Returning to the example of A plc, we will now calculate the variance and standard deviation of the returns. The required return consists of two elements, which are: In general, the more risk you take on, the greater your possible return. There is generally a close relationship between the level of investment risk and the potential level of growth, or investment returns, over the long term. However, the risk contributed by the covariance will remain. Risk and return: the record. Probability                 Return % 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). Higher risk means higher the returns can be. The expected return of a two-asset portfolio But most of all, you need to figure out what type of investor you are! Suppose that we invest equal amounts in a very large portfolio. The risk-return relationship is explained in two separate back-to-back articles in this month’s issue. 4. He is considering buying some shares in A plc. Section 7 presents a review of empirical tests of the model. We can see that the standard deviation of all the individual investments is 4.47%. There’s also what are called guaranteed investments. Based on the first version of the formula: The second version of the formula is the one that is nearly always used in exams and it is the one that is given on the formula sheet. Instructional Objectives Students will: Ƀ Explain the relationship between risk and reward. The chart below shows that the higher the potential return, the higher the risk! 16%                    =         6%                  +         (5% × 2) In this article we discuss the concepts of risk and returns as well as the relationship between them. It is known that the expected return of the asset is 9%, the volatility is bounded between 18% and 32%, and the covariance between the asset and the market is bounded between 0.014 and 0.026. The risk return relationship is a business concept referring to the risk involved in exchange for the amount of return gained on an investment. The forecast actual return is the same as the expected return under normal market conditions and almost the same under boom market conditions (20 v 21.25). The third term is the most interesting one as it considers the way in which the returns on each pair of investments co-vary. Risk is the chance that your actual return will differ from your expected return, and by how much. If an investor undertakes a risky investment he needs to receive a return greater than the risk-free rate in order to compensate him. Typically, it comes down to two big factors that you’ve probably heard of: Risk and return. 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. Sometimes they move together, sometimes they move in opposite directions (when the return on A goes up to 30%, the return on D goes down to 10%, when the return on A goes down to 10%, the return on D also goes down to 10%). Where investments have increasing levels of return accompanied by increasing levels of standard deviation, then the choice between investments will be a subjective decision based on the investor’s attitude to risk. Investors receive their returns from shares in the form of dividends and capital gains/ losses. REQUIRED RETURN 1. You also need to know the description of the investment, its potential return and its liquidity (possibility of withdrawing the investment quickly without a penalty). Saving and Investing Standard 3: Evaluate investment alternatives. Given that the expected return is the same for all the portfolios, Joe will opt for the portfolio that has the lowest risk as measured by the portfolio’s standard deviation. The risk-return relationship will now be measured in terms of the portfolio’s expected return and the portfolio’s standard deviation. Figure 6: relationship between risk & return. Different types of risks include project-specific risk, industry-specific risk, competitive risk, international risk, and market risk. He is currently trying to decide which one of the other three investments into which he will invest the remaining 50% of his funds. Some investments carry a low risk but also generate a lower return. This is the only situation where the portfolio’s standard deviation can be calculated as follows: σ port (A,C) = 4.47 × 0.5 - 4.47 × 0.5 = 0 Please visit our global website instead, Can't find your location listed? However, as already stated, in reality the correlation coefficients between returns on investments tend to lie between 0 and +1. RISK AND RETURN This chapter explores the relationship between risk and return inherent in investing in securities, especially stocks. This is the utopian position, ie where the unexpected returns cancel out against each other resulting in the expected return. The firm must compare the expected return from a given investment with the risk associated with it. Let us then assume that there is a choice of investing in either A plc or Z plc, which one should we choose? Before we perform these calculations let us review the basic logic behind the idea that risk may be reduced depending on how the returns on two investments co -vary. Covariability can be measured in absolute terms by the covariance or in relative terms by the correlation coefficient. Increased potential returns on investment usually go hand-in-hand with increased risk. First we turn our attention to the concept of 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. You could also define risk as the amount of volatility involved in a given investment. Thus their required return consists of the risk-free rate plus a systematic risk premium. A characteristic line is a regression line thatshows the relationship between an … understand and be able to explain why the market only gives a return for systematic risk. Why? This risk cannot be diversified away. Therefore, we can say that the forecast actual and expected returns are almost the same in two out of the three conditions. Remember that the SFM paper is not a mathematics paper, so we do not have to work through the derivation of any formulae from first principles. An NPV calculation compares the expected and required returns in absolute terms. Analysts normally consider the different possible returns in alternate market conditions and try and assign a probability to each. The idea is that some investments will do well at times when others are not. Hence there is no reduction of risk. In reality, the correlation coefficient between returns on investments tend to lie between 0 and +1. The return on treasury bills is often used as a surrogate for the risk-free rate. + read full definition and the risk-return relationship. Portfolio A+C – perfect negative correlation The risk-free return compensates investors for inflation and consumption preference, ie the fact that they are deprived from using their funds while tied up in the investment. The variance of return is the weighted sum of squared deviations from the expected return. Understanding the relationship between risk and return is a crucial aspect of investing. 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. EXPECTED RETURN The correlation coefficient as a relative measure of covariability expresses the strength of the relationship between the returns on two investments. The expected return of a portfolio (Rport) is simply a weighted average of the expected returns of the individual investments. 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. Risk, along with the return, is a major consideration in capital budgeting decisions. 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). Risk and Return Considerations. Risk-free return + Risk premium Return are the money you expect to earn on your investment. False, if a … This in turn makes the NPV calculation possible. We already know that the covariance term reflects the way in which returns on investments move together. 6. as well as within each asset class (by investing in multiple types of … In other words, it is the degree of deviation from expected return. Written by Clayton Reeves for Gaebler Ventures. Thus the variance represents ‘rates of return squared’. Summary table Risk – Return Relationship. While investors would love to have an investment that is both low risk and high return, the general rule is that there is a more or less direct trade-off between financial risk and financial return. Source: Fidelity: One of the core concepts in finance is the relationship between risk and return. Thus the market only gives a return for systematic risk. The individual risk of investments can also be called the specific risk but is normally called the unsystematic risk. For completeness, the calculations of the covariances from raw data are included. EXPECTED is an important term here because there are no guarantees. There’s a wide range of financial products to choose from. See Example 2. 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. But how quickly does the risk increase and to what level do you dare to go? The portfolio’s standard deviation under this theoretical extreme of perfect positive correlation is a simple weighted average of the standard deviations of the individual investments: σport (A,B) = 4.47 × 0.5 + 4.47 × 0.5 = 4.47 Thus 16% is the return that Joe requires to compensate for the perceived level of risk in A plc, ie it is the discount rate that he will use to appraise an investment in A plc. Investment                             Expected                         Standard This approach has been taken as the risk-return story is included in two separate but interconnected parts of the syllabus. Fortunately, data is available on the risk and return relationship of the three main asset classes: • Equities • Bonds • Cash (i.e. 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. Introduction to Risk and Return. A + C is the most efficient portfolio as it has the lowest level of risk for a given level of return. By the end of this article you should be able to: UNDERSTANDING AN NPV CALCULATION FROM AN INVESTOR’S PERSPECTIVE Try finding an asset, where there is no risk. 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. 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 chart below shows that the higher the potential return, the higher the risk! (article continues below) There is a risky asset i on which limited information is available. The risk contributed by the covariance is often called the ‘market or systematic risk’. Calculation of the risk premium Required return = See Example 6. Thus 5% is the historical average risk premium in the UK. In a portfolio, such random factors tend to cancel as the number of investments in the portfolio increase. We shall see that it is possible to maintain returns (the good) while reducing risk (the bad). In this article on portfolio theory we will review the reason why investors should establish portfolios. money market). The logic is that an investor who puts all of their funds into one investment risks everything on the performance of that individual investment. See Example 5. Investors who have well-diversified portfolios dominate the market. Ideally, the investor should be fully diversified, ie invest in every company quoted in the stock market. What extra return would I require to compensate for undertaking a risky investment?’ Let us try and find the answers to Joe’s questions. Risk-free return Required             =         Risk free         +         Risk There are two primary concerns for all investors: the rate of return they can expect on their investments and the risk involved with that investment. Thus the key motivation in establishing a portfolio is the reduction of risk. As it is easier to discuss risk as a percentage rate of return, the standard deviation is more commonly used to measure risk. Shares in Z plc have the following returns and associated probabilities: The greater the amount of risk an investor is willing to take, the greater the potential return. 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). Others provide higher potential returns but are riskier. Intuitively, we probably feel that it does not matter which portfolio Joe chooses, as the standard deviation of the portfolios should be the same (because the standard deviations of the individual investments are all the same). Given that Joe requires a return of 16% should he invest? There’s also what are called guaranteed investments. Risk Fallacy Number 1: Taking more risk will lead to a higher return. Suppose that Joe believes that the shares in A plc are twice as risky as the market and that the use of long-term averages are valid. 0.1                               35 The best way to manage your risk and protect yourself is to practice proper diversification. The missing factor is how the returns of the two investments co-relate or co-vary, ie move up or down together. RISK AND RETURN ON TWO-ASSET PORTFOLIOS Below are some popular types of financial products and an indication of the level of risk associated with each type: Guaranteed investment certificate with a fixed rate of interest at maturity. Let us now assume investments can be combined into a two-asset portfolio. Note the only difference between the two versions is that the covariance in the second version is broken down into its constituent parts, ie. We provide a brief introduction to the concept of risk and return. A balance between risk and return in investing: Whether you are a conservative, moderate or aggressive investor you will have to manage risk and try to achieve as high returns as possible without compromising your risk management principles. You can do this by splitting your money between different asset classes (by investing in stocks, bonds, etc.) Port A + D                               20                                     3.16 Given that the expected return is the same for both companies, investors will opt for the one that has the lowest risk, ie A plc. In a large portfolio, the individual risk of investments can be diversified away. The returns of A and D are independent from each other. Others provide higher potential returns but are riskier. We need to understand the principles that underpin portfolio theory, before we can appreciate the creation of the Capital Asset Pricing Model (CAPM). Risk and return are always linked when investing: the higher the risk, the greater the (potential) return. If the forecast actual return is the same as the expected return under all market conditions, then the risk of the portfolio has been reduced to zero. Generally, higher returns are better. As discussed previously, the type of risks you are exposed to will be determined by the type of assets in which you choose to invest. Joe currently has his savings safely deposited in his local bank. The value of investments can fall as well as rise and you could get back less than you invest. The standard deviation of a two-asset portfolio The next question will be how do we measure an investment’s systematic risk? Port A + B                               20                                     4.47 the systematic risk or "beta" factors for securities and portfolios. Savings, Investing, and Speculating 1. There is a clear (if not linear) relationship between risk and returns. Each product has its own special features. The decision is equally clear where an investment gives the highest expected return for a given level of risk. Chances are that you will end up with an asset giving very low returns. So far we have confined our choice to a single investment. WHAT IS THE IDEAL NUMBER OF INVESTMENTS IN A PORTFOLIO? An investor who has a well-diversified portfolio only requires compensation for the risk suffered by their portfolio (systematic risk). 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%. The third factor is return. Virtual classroom support for learning partners, Support for students in Australia and New Zealand, The risk and return relationship – part 1, How to approach Advanced Financial Management, understand an NPV calculation from an investor’s perspective, calculate the expected return and standard deviation of an individual investment and for two asset portfolios, understand the significance of correlation in risk reduction, understand and explain the nature of risk as portfolios become larger. The extent of the risk reduction is influenced by the way the returns on the investments co-vary. 7    A portfolio’s total risk consists of unsystematic and systematic risk. Some investments carry a low risk but also generate a lower return. They should hold the ‘Market portfolio’ in order to gain the maximum risk reduction effect. 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. Risk simply means that the future actual return may vary from the expected return. Total risk is normally measured by the standard deviation of returns ( σ ). In what follows we’ll define risk and return precisely, investi-gate the nature of their relationship, and find that there are ways to limit exposure to in-vestment risk. Therefore, systematic/market risk remains present in all portfolios. See Example 3. The covariance term is multiplied by twice the proportions invested in each investment, as it considers the covariance of A and B and of B and A, which are of course the same. Portfolio A+B – perfect positive correlation The risk-free return is the return required by investors to compensate them for investing in a risk-free investment. In this article, you will discover how risky investing is. As a general rule, investments with high risk tend to have high returns and vice versa. A widely used definition of investment risk, both in theory and practice, is the uncertainty that an investment will earn its expected rate of return. This is neatly captured in the old saying ‘don’t put all your eggs in one basket’. In the exam it is unlikely that you will be asked to undertake these basic calculations. In some cases, only the money initially invested by you, known as the principal, is guaranteed; in others, both the principal and the money you earn on the investment, known as the return, are guaranteed. Portfolio A+D – no correlation 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. One of the most difficult problems for an investor is to estimate the highest level of risk he is able to assume. However, a well-diversified portfolio only suffers from systematic risk, as the unsystematic risk has been diversified away. Another way to look at it is that for a given level of return, it is human nature to prefer less risk to more 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. 0.1                               5 No mutual fund can guarantee its returns, and no mutual fund is risk-free. It is strictly limited to a range from -1 to +1. The higher the risk of an asset, the higher the EXPECTED return. This is, of course, heavily tied into risk. The Relationship between Risk and Return. As portfolios increase in size, the opportunity for risk reduction also increases. Please visit our global website instead, Relevant to ACCA Qualification Papers F9 and P4. So what causes this reduction of risk? 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. Statistical measures of variability are the variance and the standard deviation (the square root of the variance). Therefore, when there is no correlation between the returns on investments this results in the partial reduction of risk. The reason for squaring the deviations is to ensure that both positive and negative deviations contribute equally to the measure of variability. Calculating the risk premium is the essential component of the discount rate. Imagine how much risk we could have diversified away, had we created a large portfolio of say 500 different investments or indeed 5,000 different investments. What is the missing factor? The risk-free return is the return required by investors to compensate them for investing in a risk-free investment. 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. Ƀ Analyze a saving or investing scenario to identify financial risk. Assume the market portfolio has an expected return of 12% and a volatility of 28%. In investing, risk and return are highly correlated. The good news is that we can construct a well-diversified portfolio, ie a portfolio that will benefit from most of the risk reduction effects of diversification by investing in just 15 different companies in different sectors of the market. Thus total risk can only be partially reduced, not eliminated. The risk of investing in mutual funds is determined by the underlying risks of the stocks, bonds, and other investments held by the fund. The risk reduction is quite dramatic. The NPV is positive, thus Joe should invest. When investing, people usually look for the greatest risk adjusted return. Thus investors have a preference to invest in different industries thus aiming to create a well- diversified portfolio, ensuring that the maximum risk reduction effect is obtained. However, this approach is not required in the exam, as the exam questions will generally contain the covariances when required. To calculate the risk premium, we need to be able to define and measure risk. 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. Investing: What’s the relationship between risk and return. They only require a return for systematic risk. The more risky the investment the greater the compensation required. Higher returns might sound appealing but you need to accept there may be a greater risk of losing your money. The meaning of return is simple. 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%). Portfolio theory demonstrates that it is possible to reduce risk without having a consequential reduction in return, ie the portfolio’s expected return is equal to the weighted average of the expected returns on the individual investments, while the portfolio risk is normally less than the weighted average of the risk of the individual investments. The formula for calculating the annual return on a share is: Suppose that a dividend of 5p per share was paid during the year on a share whose value was 100p at the start of the year and 117p at the end of the year: The total return is made up of a 5% dividend yield and a 17% capital gain. The fact that a relationship between risk and reward exists on average does not mean that the same relationship holds for individual stocks. The current share price of A plc is 100p and the estimated returns for next year are shown. 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