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FMA 101 Topic 6 – Risk and Return Assignment Answers

 

 

FMA 101 Topic 6 : LEARNING OUTCOMES

After completing this topic, you should be able to:

• Define risk and return and explain the role and functions of risk analysis and the rate of return in a business entity.
• Identify, list and explain different sources of risk affecting business organisations and shareholders.
• Discuss the elements included in the calculation of a rate of return and calculate the expected return of an asset.
• Discuss the different risk preferences found in organisations and the use of scenario analysis and probability distributions to assess the risk of an asset.
• Explain the purposes and functions of different risk measurements as quantitative measures of the risk of a single asset and calculate the values of these risk measurements, and analyse and interpret the outcomes of such calculations.
• Calculate the expected return, standard deviation and coefficient of variation of an investment portfolio, and analyse and interpret the outcomes of such calculations.
• Explain the role of correlation and diversification in the assessment of the risk and return of an investment portfolio.

 

READING FMA 101 Topic 6 :

Before continuing with this topic, please read the following:

• Gitman et al. (2015: Chapter 8)

Please make sure that you also read this study guide carefully as it contains additional information that is not in the prescribed textbook.

 

FMA 101 RISK AND RETURN FUNDAMENTALS

The key concepts that you must focus on are:

• the meaning of a single asset and a portfolio
• the concept of risk relating to assets
• sources of risk
• the concept of return on an asset
• the formula to calculate the return on an asset
• different risk preferences

You must be able to define as well as discuss or explain the concepts of risk and return regarding how these concepts apply to a single asset and a portfolio of assets. You need to be able to present examples that demonstrate asset risk and return.

You must be able to identify the different components of an asset that are used to calculate its expected return and use the formula presented to calculate the rate of return on a single asset.

You must also pay attention to the different types of risks that organisations and shareholders have to deal with and must be able to discuss or explain these different types of risk and their impact on organisations.

Pay special attention to the different risk preferences found in organisations. You must be able to list and discuss these risk preferences and indicate how these different preferences can affect financial decisions.

Pay attention to Figure 8.1 – Risk preferences: Risk preference behaviours. You must be able to prepare a graphical comparison of the different risk preferences to demonstrate the risk and expected return to determine a particular risk preference.

 

THE RISK OF A SINGLE ASSET

The key concepts that you must focus on are:

• risk assessment using scenario analysis
• risk assessment using probability distributions
• the range of returns

You must be able to explain what scenario analysis and probability distributions are and their application to the risk assessment of an asset. You must also be able to use the given information to perform the necessary calculations to demonstrate the use of scenario analysis and probability distributions in risk assessment.

Table 6.1 below illustrates a scenario analysis for two assets. The “scenarios” are based on different expectations of business conditions and for each of the business scenarios a specific expected return is specified.

Table 6.1              Scenario analysis

Scenario	ASSET A Expected return	ASSET B Expected return
Pessimistic	6%	10%
Most likely	11%	13%
Optimistic	15%	15%

THE RISK RANGE BASED ON BUSINESS SCENARIOS

The scenario specified in Table 6.1 can be used to assess the general level of risk associated with a specific asset. This is done by calculating the risk range for the assets across the scenarios specified as follows:

Risk range Asset A = Highest return – Lowest return Risk range Asset A = 15% – 6%

Risk range Asset A = 9%

For Asset A, the risk range = 9% indicates that by investing in Asset A, the investor assumes the risk that the expected return can vary by as much as 9% from the expected return.

The higher the risk range, the higher the risk of the investment. The risk range for Asset B = 5%.

The risk range (and therefore the risk) for an investor is therefore much lower by investing in Asset B (5%) than by investing in Asset A (9%).

You must be able to explain, calculate, analyse and interpret the standard deviation and coefficient of variation of a single asset.

 

RISK BASED ON PROBABILITY DISTRIBUTIONS

Probability in general terms refers to the “chance of occurrence”. It is a quantitative way of expressing the chance (probability) of something occurring or not occurring.

Scenarios are expressed in terms of their probabilities of occurring. All scenarios are specified and the chance (probability) of each scenario occurring is then also specified. Table 6.2 below demonstrates how the business scenarios demonstrated in Table 6.1 for Asset A can be specified using probabilities.

Note that in Table 6.2 the probabilities are expressed both as percentages and as decimals. Either way of expressing probabilities is acceptable.

Table 6.2              Probability distribution

Scenario	ASSET A Expected return	ASSET A Probability	ASSET A Probability
Pessimistic	6%	20%	0.20
Most likely	11%	50%	0.50
Optimistic	15%	30%	0.30
		100%	1.00

It is very important to note that the sum of the probabilities of all the scenarios specified must always equal 100% (if percentages) or 1.00 (if decimals).

 

FMA 101 RISK MEASUREMENT

The key concepts that you must focus on are the:

• standard deviation
• coefficient of variation

You need to be able to discuss and explain the meaning of both the standard deviation and the coefficient of variation as measures of the risk of a single asset.

You have to be able to calculate both the standard deviation and the coefficient of variation for single assets using data and information provided and the relevant formulas.

Take note that the Greek letter sigma (σ) is generally used to present the standard deviation.

The squared value of the standard deviation is known as the variance (σ²).

The standard deviation is, therefore, the square root value of the variance, for example:

? = √?2

The variance of the risk of an asset is calculated as follows: σ² = [The expected return (R) – Average return (?̅)]²

The calculation of the standard deviation is very well demonstrated in Table 8.4 in the prescribed textbook, while Examples 8.6 and 8.7 demonstrate the calculation of the coefficient of variation. You need to study both these examples very well to gain a thorough understanding of how to calculate the two risk measurements.

Study Example 8.8 very well to gain an understanding of how the values of a standard deviation and coefficient of variation are interpreted for purposes of risk assessment.

 

THE RISK OF A PORTFOLIO

The key concepts that you must focus on are:

• an investment portfolio
• the weight of an asset in a portfolio
• correlation
• diversification

You must be able to explain what a portfolio of investment is as well as what an efficient portfolio is.

You need not be able to perform any calculations to determine the return on or standard deviation of an investment portfolio.

Students generally grapple with understanding how to calculate the weights (w) of the assets in an investment portfolio.

Table 6.3 below demonstrates how the weights of the individual assets of a three- asset portfolio are calculated.

Table 6.3              Weights of assets in a portfolio

	Value (Rand)	Weight (Decimals)	Weight (Percentages)
Asset A	R500	0.32	32%
Asset B	R450	0.29	29%
Asset C	R620	0.39	39%
	R1 570	1.00	100%

The weight of an asset is calculated as follows:

Weight Asset A = Value Asset A / Value of portfolio Weight Asset A = R500 / R1 570

Weight Asset A  = 0.32 (Decimal)

Weight Asset A = 32% (0.32 × 100) (Percentage)

Note: The sum of the weights in a portfolio must always be 1.00 or 100%.

 

CORRELATION

You must be able to explain or discuss correlation in the context of an investment portfolio. You must further be able to distinguish between positive correlation (ρ

> 1), negative correlation (ρ < 1) and zero correlation (ρ = 0).

You must also be able to explain or discuss the relationship between correlation, risk and return.

 

DIVERSIFICATION

You must be able to explain or discuss the role and purposes of diversification in the context of an investment portfolio.

You must also be able to explain or discuss the relationship between correlation, diversification and the risk and return of an investment portfolio.

You need to study the contents of Table 8.8 in the prescribed textbook very well as this table demonstrates the relationship between diversification, correlation and portfolio risk and returns very well.

 

INTERNATIONAL DIVERSIFICATION

The section on international diversification is excluded for assignment and examination purposes. You need not study this section in the prescribed textbook.

 

RISK AND RETURN: THE CAPITAL ASSET PRICING MODEL (CAPM)

Section 8.4 in the prescribed textbook dealing with the capital asset pricing model (CAPM) is not required for assignment and examination purposes. You need not study this section in the prescribed textbook.

 

ADDITIONAL SOURCES TO ACCESS

Access the following websites to broaden your understanding of risk and return in the context of financial management:

• Financial concepts: The risk/return trade-off. Investopedia. http://www.investopedia.com/university/concepts/concepts1.asp, accessed 4 November
• Risk and return. Reference for Business: Encyclopaedia of Business, 2^nd http://www.referenceforbusiness.com/small/Qu-Sm/Risk-and-Return.html, accessed 4 November 2010.

 

FMA 101 Topic 6 SELF-ASSESSMENT EXERCISES

At the end of this chapter, there is a series of different self-test problems, warm- up exercises, problems and a more comprehensive case study. You should attempt to answer these questions, perform the calculations and use them to practise and re-enforce your learning and understanding. You may submit any of your answers to the lecturer for assessment and feedback.

SBS also shares copies of previous exam papers with you during the semester. The questions in these exam papers are very good examples of what you are expected to know and be able to do having studied and mastered the content of chapter 8 of the prescribed textbook and having followed the guidance provided in this topic.