They only require a return for systematic risk. In this article, you will discover how risky investing is. 2. We shall see that it is possible to maintain returns (the good) while reducing risk (the bad). As N becomes very large the first term tends towards zero, while the second term will approach the average covariance. There’s also what are called guaranteed investments. EXPECTED RETURN Perfect negative correlation does not occur between the returns on two investments in the real world, ie risk cannot be eliminated, although it is useful to know the theoretical extremes. return of A plc                return                         premium The greater the amount of risk an investor is willing to take, the greater the potential return. A fundamental idea in finance is the relationship between risk and return. The third factor is return. THE STUDY OF RISK Risk and return: the record. Individuals and firms in the financial sector, Fintech, Exams, probationary period, right to practise, trainers, Transparency Measures - Mining, oil and gas, Share the page by e-mail, This link will open in a new window, Share the page on Facebook, This link will open in a new window, Share the page on Twitter, This link will open in a new window, Share the page on LinkedIn, This link will open in a new window. Introduction to Risk and Return. We can see that the standard deviation of all the individual investments is 4.47%. Measuring covariability One of our agents will be pleased to return your call. A positive covariance indicates that the returns move in the same directions as in A and B. 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). Ƀ Describe different types of financial risk. Chances are that you will end up with an asset giving very low returns. This approach has been taken as the risk-return story is included in two separate but interconnected parts of the syllabus. The logic is that an investor who puts all of their funds into one investment risks everything on the performance of that individual investment. Joe currently has his savings safely deposited in his local bank. 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. If we assume that investors are rational and risk averse, their portfolios should be well-diversified, ie only suffer the type of risk that they cannot diversify away (systematic risk). When investing, people usually look for the greatest risk adjusted return. This is not surprising and it is what we would expect from risk- averse investors. REQUIRED RETURN 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). There is a risky asset i on which limited information is available. The relationship between risk and return is a fundamental concept in finance theory, and is one of the most important concepts for investors to understand. Portfolio A+B – perfect positive correlation Jayson just had his first child and wants to begin setting aside money for his child’s college tuition. The missing factor is how the returns of the two investments co-relate or co-vary, ie move up or down together. THE PROOF THAT LARGE PORTFOLIOS INCREASE THE RISK REDUCTION EFFECT 0.1                               5 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. Risk refers to the possibility of the actual return varying from the expected return, ie the actual return may be 30% or 10% as opposed to the expected return of 20%. 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. The value of investments can fall as well as rise and you could get back less than you invest. They should hold the ‘Market portfolio’ in order to gain the maximum risk reduction effect. However, calculating the future expected return is a lot more difficult because we will need to estimate both next year ’s dividend and the share price in one year ’s time. 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 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%). 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. However, this approach is not required in the exam, as the exam questions will generally contain the covariances when required. 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. The idea is that some investments will do well at times when others are not. Section 7 presents a review of empirical tests of the model. The risk contributed by the covariance is often called the ‘market or systematic risk’. The following table gives information about four investments: A plc, B plc, C plc, and D plc. You could also define risk as the amount of volatility involved in a given investment. 7    A portfolio’s total risk consists of unsystematic and systematic risk. An NPV calculation compares the expected and required returns in absolute terms. The Barclay Capital Equity Gilt Study 2003 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. Covariability can be measured in absolute terms by the covariance or in relative terms by the correlation coefficient. This in turn makes the NPV calculation possible. The reason for squaring the deviations is to ensure that both positive and negative deviations contribute equally to the measure of variability.                                                 return (%)                        deviation (%) The expected return of a portfolio (Rport) is simply a weighted average of the expected returns of the individual investments. Therefore, we can say that the forecast actual and expected returns are almost the same in two out of the three conditions. He is currently trying to decide which one of the other three investments into which he will invest the remaining 50% of his funds. The risk-return relationship will now be measured in terms of the portfolio’s expected return and the portfolio’s standard deviation. Thus the variance represents ‘rates of return squared’. Think of lottery tickets, for example. 4. The risk-free return is the return required by investors to compensate them for investing in a risk-free investment. Should he save, invest, or speculate? 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. 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. Calculating the risk premium is the essential component of the discount rate. He is trying to determine if the shares are going to be a viable investment. The risk of receiving a lower than expected income return – for example, if you purchased shares and expected a dividend payout of 50 cents per share and you only received 10 cents per share. Savings, Investing, and Speculating 1. In reality, the correlation coefficient between returns on investments tend to lie between 0 and +1. 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. Calculation of the risk premium 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%. Portfolio A+C – perfect negative correlation This model provides a normative relationship between security risk and expected return. Different types of risks include project-specific risk, industry-specific risk, competitive risk, international risk, and market risk. It also calculated that the average return on the UK stock market over this period was 11%. The risk reduction is quite dramatic. LEARNING OBJECTIVES The Barclay Capital Study calculated the average return on treasury bills in the UK from 1900 to 2002 as approximately 6%. 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. Decision criteria: accept if the NPV is zero or positive. This is neatly captured in the old saying ‘don’t put all your eggs in one basket’. 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. The relationship between risk and return is often represented by a trade-off. Always remember: the greater the potential return, the greater the 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. Shares in Z plc have the following returns and associated probabilities: Why? He asks the following questions: ‘What is the future expected return from the shares? Try finding an asset, where there is no risk. Higher returns might sound appealing but you need to accept there may be a greater risk of losing your money. 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 answer to this question will be given in the following article on the Capital Asset Pricing Model (CAPM). As portfolios increase in size, the opportunity for risk reduction also increases. This Interactive investing chart shows that the average annual return on treasury bills since 1935 was 4.5%, compared to a 9.6% return on Canadian stocks. Thus if an investor had invested in shares that had the same level of risk as the market, he would have to receive an extra 5% of return to compensate for the mark et risk. 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. 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. Risk and Return Considerations. If we have a large enough portfolio it is possible to eliminate the unsystematic risk. Required return = Risk free return + Systematic risk premium The risk-return relationship is explained in two separate back-to-back articles in this month’s issue. + read full definition and the risk-return relationship. The meaning of return is simple. A + C is the most efficient portfolio as it has the lowest level of risk for a given level of return. 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 their required return consists of the risk-free rate plus a systematic risk premium. 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. 16%                    =         6%                  +         (5% × 2) 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. Suppose that Joe is considering investing £100 in A plc with the intention of selling the shares at the end of the first year. 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. But how quickly does the risk increase and to what level do you dare to go? 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 covariance. An investor who has a well-diversified portfolio only requires compensation for the risk suffered by their portfolio (systematic risk). The exam questions normally provide you with the expected returns and standard deviations of the returns. Statistical measures of variability are the variance and the standard deviation (the square root of the variance). Suppose that we invest equal amounts in a very large portfolio. Risk, along with the return, is a major consideration in capital budgeting decisions. Portfolio A+D – no correlation Thus the market only gives a return for systematic risk. After investing money in a project a firm wants to get some outcomes from the project. In this article on portfolio theory we will review the reason why investors should establish portfolios. money market). Thus total risk can only be partially reduced, not eliminated. The relationship between risk and return can be observed by examining the returns actually earned by investors in various types of securities over long periods of time. The expected return on a share consists of a dividend yield and a capital gain/loss in percentage terms. See Example 5. Thus the key motivation in establishing a portfolio is the reduction of risk. 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. 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 There’s a lot at stake to lose with high risk. One of the most widely accepted theories about risk and return holds that there is a linear relationship between risk and return But there are many fallacies and misconceptions about risk. as well as within each asset class (by investing in multiple types of … 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. WHAT IS THE IDEAL NUMBER OF INVESTMENTS IN A PORTFOLIO? 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. Investment                             Expected                         Standard understand and be able to explain why the market only gives a return for systematic 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. 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. The return on treasury bills is often used as a surrogate for the risk-free rate. Others provide higher potential returns but are riskier. See Example 7. The investment in A plc is risky. Increased potential returns on investment usually go hand-in-hand with increased risk. 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. This risk cannot be diversified away. 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 already know that the covariance term reflects the way in which returns on investments move together. The more risky the investment the greater the compensation required. In a portfolio, such random factors tend to cancel as the number of investments in the portfolio increase. Let us now assume investments can be combined into a two-asset portfolio. What extra return would I require to compensate for undertaking a risky investment?’ Let us try and find the answers to Joe’s questions. The Relationship between Risk and Return. 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. The extent of the risk reduction is influenced by the way the returns on the investments co-vary. (article continues below) So what causes this reduction of risk? Remember that the real joy of diversification is the reduction of risk without any consequential reduction in 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. You are a risky asset i on which limited information is available them for investing in stocks bonds... Investments is 4.47 % correlation between the returns on investments this results the. Basic calculations attention to the variability of possible returns associated with a level. 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