Questions

**What is the Expected Rate of Return on an investment and what does it tell us about the probability of the risk involved with a particular investment?****In terms of risk, what are the advantages (and/or disadvantages) of a well-diversified portfolio?**

**Investments are based on the belief that the rate of return justifies or compensates the investor for the risk associated with that particular investment. The risk associated with this investment is associated with the chance that a loss will be incurred. Or, to put it another way, the greater the chance of a loss the riskier the investment. Therefore, some statistical measures of the risk involved with an investment are necessary before the investment is made.**

Answers

**Introduction**

The risk and return analysis is a part of the standard investment decision-making process. It is a process in which we compare the expected returns of an investment with the risk associated with it. The general rule for any investor is that the higher the risk of an investment, the higher the expected return. This rule is critical to the decision-making process as the main objective for any investor is to maximize the return on their investment and minimize potential losses. Risk is a measurable possibility of losing or not gaining value. Whereas, return is the reward for taking the risk. Both of them have the same connotation throughout this chapter as in the higher risk or low-risk investment and its effect on the investment’s potential return. Often investors are not concerned with the risk of an investment in its entirety but more the risk of a poor outcome. In this case, the poor outcome would occur when the actual return on an investment is less than what was expected. A poor outcome may have various implications, for example, an individual expecting to finance his retirement with an investment in stocks might consider a poor outcome to be an investment value less than the financing of a comfortable retirement. A main element in the process of risk and return analysis is determining which investment decisions affect the certainty of expected future cash flows. This is because the analysis aims to compare the expected returns with the risk and if there are no changes to the expected returns of an investment then the risk has no impact. This is unlikely to be the case, for example, currency fluctuations and changes in economic conditions can all affect the expected return on an investment. Therefore a decision by the investor to hold onto the investment, invest in it more or take money out of it should be considered as an investment decision that affects the future cash flows and should be included in the analysis. A decision to include it in the analysis may result in the investment in question showing various rates of return and have a different risk. This decision is known as a marginal decision and the analysis of it using the marginal expected return and the marginal rate of time preference is an important aspect of the general risk and return analysis.

**1.1 What is the Expected Rate of Return?**

The expected rate of return often represents the mean of a distribution of all possible results and is often a probability-weighted calculation influencing the probability that a certain rate of return will happen. This does not have to represent an actual return at all and could be a guess. For example, an investment in the shares of a relatively new and small company with a chance to take a stake in the market of a big industry leader by a takeover of a likely inflated share price could have an expected return, considering the probability of this happening, of say 20% higher than the market, despite only being issued a dividend rate based on the shares.

The expected rate of return is a crucial concept in investment due to the fact that it measures the profitability of an investment or a business. By totaling up the expected earnings from a provided investment over its whole life, then reducing that figure by the original investment, we get the net profit. But in order to determine the profit and the risk of the investment, we need a way of comparing it with other investments of similar magnitude. This is where the expected rate of return is beneficial. By determining the rate of return, we can compare an investment to others to see if it is more or less profitable. And by using the return and risk as a single measure, we can compare to see which is more or less preferable. This is valuable to individuals and businesses, and certainly to financial and investment groups, such as corporate investors and pension funds.

**1.2 Understanding the Risk-Return Tradeoff**

The concept of risk is intuitively understood. An investor would prefer to receive a higher future payment with certainty than a lower one or one that may or may not eventuate. Probability of distribution of possible future returns is a determinant of the risk involved. Every investment has a possible range of future outcomes to the investor, some more certain than others. A US Treasury bill is regarded as a nearly risk-free investment because the borrowing of current funds by the government issued any no direct value to the bill holder so the bill can be repaid by any future revenue. However, bonds on the other hand are not as certain in terms of a return as stock it is also an uncertain investment. An example would be General Motors buying back many of its bonds prior to maturity and thus avoiding the interest and the principal repayment because of their uncertain financial position in relation to the bond issue. GM may be willing to buy the bond back at a higher price than it issued it for in which case there would be capital gains to the bond holder. So the bond has still uncertain future outcome for GM and the bond holder.

Investment can be broken down into financial and real investment. Using the tuition fee example, it is a real investment as it is an outlay that is expected to produce future benefits (a higher paying job). Financial investment on the other hand is the purchase of a financial asset e.g. a stock or share with the expectations of future income which will be spent on consumption. Whether you are buying stocks or paying tuition fees both can be considered taking a risk as there is always the chance of receiving all or some of the money paid back in the future. Foregone earnings on an investment have the same value as the income that could have been obtained from the job or unemployment requires no spending of the earnings so it is effectively saving the amount of the job and not earning any more than that amount.

An investment is the current commitment of dollars for a period of time in order to derive future payments that will compensate the investor for: (1) the time the funds are committed to the investment and (2) bearing uncertainty about the future size of those payments. There are two types of investment. You are considered to be an investor if you put aside £20 of your weekly income. Your £20 can be looked upon as capital to be invested in a financial or a real asset. However, not all capital expenditure will be considered an investment from an economic perspective. An economics student paying tuition fees can be effectively thought of as investing in themselves but the payment is not included in investment.

**Risk Measures in Investment Analysis**

**2.1 Standard Deviation as a Risk Indicator**

**2.2 Beta Coefficient and Systematic Risk**

**2.3 Sharpe Ratio and Risk-Adjusted Return**

**Evaluating Investment Risk**

**3.1 Advantages of a Well-Diversified Portfolio**

**3.1.1 Spreading Risk Across Different Assets**

**3.1.2 Reducing Unsystematic Risk**

**3.1.3 Potential for Stable Returns**

**3.2 Disadvantages of a Well-Diversified Portfolio**

**3.2.1 Lower Potential for High Returns**

**3.2.2 Limited Exposure to Individual Asset Performance**

**3.2.3 Potential for Lower Market Timing Opportunities**

**Quantifying Risk in Investments**

**4.1 Risk-Adjusted Return Measures**

**4.1.1 Treynor Ratio and Portfolio Performance**

**4.1.2 Jensen’s Alpha and Manager’s Skill**

**4.1.3 Information Ratio and Active Management**

**4.2 Value at Risk (VaR) and Downside Risk Analysis**

**4.2.1 Estimating Potential Losses**

**4.2.2 Assessing Tail Risk**

**4.2.3 Portfolio Optimization and Risk Control**

**Conclusion**

**Investment Risk and Return Analysis**

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