Question

Your group manages an investment fund. Your job is to advise clients on what portfolio best suits their needs, given their characteristics. You have three different customer types: I. A young Deakin Commerce graduate (Stephanie) with a long and successful career ahead of her. II. A middle-aged couple (Harold and Meredith) who are high income earners. They plan to retire in 10 years’ time. III. An older member of the work force (Akhter) who is hoping to retire in the next 18 months. There are 3 different portfolio packages that you offer your clients: PORTFOLIO ALPHA: 70% shares; 20% property; 10% cash. PORTFOLIO BETA: 50% bonds; 30% shares; 20% property. PORTFOLIO GAMMA: 50% cash; 30% bonds; 20% property. Your task is to answer the following questions by referring to your textbook, other finance books, the media, the internet etc.: 1. By using the information in TABLE 1: (a) Calculate the historical returns for each of the above portfolios for the years between 2003 and 2017. Present the answers/numbers in the table. (b) Calculate the expected (average) return, denoted by E(R), and risk (standard deviation), denoted by σ, for each of the four asset classes as well as those three portfolios. Present your answers in Table 1. The completed table SHOULD be submitted with your assignment. Students are encouraged to employ Microsoft Excel for these workings. (5 marks) 2. Explain what is meant by expected return and risk in finance. You need to address the relationship between these two concepts in your explanation. Use your answers from Question 1 (for both assets and portfolios) above to illustrate this relationship. (5 marks) 3. Discuss the meaning of diversification in finance and how it impacts the risk and the return. You need to address the concept of correlation and how the correlation coefficient impacts on the risk of a portfolio in your discussion. Refer to your answers from Question 1 to illustrate diversification. (5 marks)4. How do we measure the systematic risk component of an asset? Assets A and B have betas of 0.5 and 2 respectively. Which asset is riskier? If the market return decreases/increases by 10%, how would such movement impact Assets A and B? (5 marks) 5. It is assumed that your investors are risk averse. Explain what is meant by ‘risk aversion’ as it relates to finance. Is risk aversion related to different stages of ‘investing life cycle’? (5 marks) 6. For each of the three customer types that you have, recommend the most suitable portfolio option and justify your choice. Use language here that the customers wilunderstand. You should use a graph here to show the historical return performance of each of your portfolios to assist with your recommendation. (5 marks)

TABLE1 Shares Property Bonds Cash 4.90% 5.60% Year Alpha Beta Gamma 8.80% | 2003 | 15.90%| 2004 | 27.60%| 32.00% 2005| 21.10%| 12.50% 2006 | 25.00% | 34.00% 2007 | 18.00% 2008| 2009| 39.60%| 2010 2011 | 2012 | 18.80%| 33.00% 2013 | 19.70% 2014 2015 2016 | 11.60% 13.20% 20171 12.50% 3.00% 7.00% 5.80% 3.10% 3.50% 14.90% 170% 6.00% 11.40% 1.10% 2.00% 9.80% 2.60% 2.90% 3.70% | | 5.70% 6.00% 6.70% 7.60% 3.50% 4.70% 5.00% 4.00% 2.90% 270% 2.30% 2.10% 1.70% -8.40% | -54.00% | %| -40.40%| 7.90 -0.40% 3.30% -11.40% | -1.50% | 7.10% 27.00% 14.30% | 5.00%| 3.80%| 5.70% E (R) Risk

Answer 1

Answer:

Part 1

Portfolio Return in a particular year= weightage of Shares* Return for shares+weightage of Property* Return for Property+weightage of Bonds* Return for Bonds+weightage of cash* Return for Cash

Sample Calculation for ALPH for year 2003

Portfolio return= 70%*15.90% +20%*8.80% +0%* 3.00% +10%* 4.90% =13.38%

E(r)= Sum of all returns from 2003 to 2017/15

Risk=Standard Deviation=$\sqrt{\sum ((r-E(r))^2)/15}$

Where r is the rate of return in a particular year.

	Weightage
Portfolio	Shares	Property	Bonds	Cash
Alpha	70%	20%	0%	10%
Beta	30%	20%	50%	0%
Gamma	0%	20%	30%	50%
Year	Shares	Property	Bonds	Cash	Alph	Beta	Gamma
2003	15.90%	8.80%	3.00%	4.90%	13.38%	8.03%	5.11%
2004	27.60%	32.00%	7.00%	5.60%	26.28%	18.18%	11.30%
2005	21.10%	12.50%	5.80%	5.70%	17.84%	11.73%	7.09%
2006	25.00%	34.00%	3.10%	6.00%	24.90%	15.85%	10.73%
2007	18.00%	-8.40%	3.50%	6.70%	11.59%	5.47%	2.72%
2008	-40.40%	-54.00%	14.90%	7.60%	-38.32%	-15.47%	-2.53%
2009	39.60%	7.90%	1.70%	3.50%	29.65%	14.31%	3.84%
2010	3.30%	-0.40%	6.00%	4.70%	2.70%	3.91%	4.07%
2011	-11.40%	-1.50%	11.40%	5.00%	-7.78%	1.98%	5.62%
2012	18.80%	33.00%	7.70%	4.00%	20.16%	16.09%	10.91%
2013	19.70%	7.10%	2.00%	2.90%	15.50%	8.33%	3.47%
2014	5.00%	27.00%	9.80%	2.70%	9.17%	11.80%	9.69%
2015	3.80%	14.30%	2.60%	2.30%	5.75%	5.30%	4.79%
2016	11.60%	13.20%	2.90%	2.10%	10.97%	7.57%	4.56%
2017	12.50%	5.70%	3.70%	1.70%	10.06%	6.74%	3.10%
E(R)	11.34%	8.75%	5.67%	4.36%	10.12%	7.99%	5.63%
Risk	18.69%	21.71%	3.87%	1.79%	16.49%	8.10%	3.77%

Part 2) Expected return is average of all return for given time period for a particular asset. It tell us how much return we can expect from an asset looking at its past performance.

E(r)= Sum of all returns from 2003 to 2017/15

Standard Deviation is used to quantify the amount of variation or dispersion of a set of rate of return.A low standard deviation indicates that the returns tend to be close to the mean (also called the expected rate of return) of the set, while a high standard deviation indicates that the returns are spread out over a wider range of values. Since standard deviation is measured around expected rate of return so if standard deviation is low then there asset is low risky and there is high chances of getting expected return and if standard deviation is high then there asset is high risky and there is less chances of getting expected return.

standard deviation is calculating from below formula

Risk=Standard Deviation=$\sqrt{\sum ((r-E(r))^2)/15}$

From above table we can find that property is more risky than other assets.

Part 3)

Diversification is a means of managing risk, and it is accomplished by mixing a variety of assets within a single portfolio. The goal of diversification is to minimize the impact that the performance of any one security will have on the overall performance of the whole portfolio. As such, diversification lowers the risk associated with the portfolio.
Correlation measure the relationship between the changes of two or more financial variables over time. if the two assets are positively correlated than increase or decrease in one asset will also increase or decrease in another asset. It means the portfolio is not well diversified and it is more risky.

if the two assets are negatively correlated than increase or decrease in one asset will also decrease or increase in another asset. It means the portfolio is well diversified and it is less risky. Examples are Shares and Bonds are negatively correlated.

From above table we found that portfolio Alpha is not diversified because it has higher standard deviation where as portfolio gamma is well diversified because it has lower standard deviation.

Part 4)

Systematic Risk: Systematic risk is the risk inherent to the entire market. Systematic risk, also known as “undiversifiable risk,” “volatility” or “market risk,” affects the overall market, not just a particular stock or industry. This type of risk is both unpredictable and impossible to completely avoid.

For systematic risk we measure Beta, which measures how volatile that investment is compared to the overall market. A beta of greater than 1 means the investment has more systematic risk than the market, while less than 1 means less systematic risk than the market. A beta equal to one means the investment carries the same systematic risk as the market.

For Asset B ( Beta =2) is more riskier than asset A(beta=0.5) because asset B has beta value greater than 1 where as asset A has beta value less than 1.

if market return increase or decrease by 10% then asset A will increase / decrease by beta*10%=0.5*10%=5% .whereas

asset B will increase/decrease by 2*10%=20%.