Construct an efficient portfolio assume the risk free rate

Question

Assignment

Read the brief and instructions thoroughly.

Write a report which addresses the questions (a to f) below. Where relevant, base your analysis on the data provided.

Table 1: Asset returns on different asset ¬classes over the period 1990 to 2010

Year­	Australian Shares % r­eturn (ex dividends)	Australian Bonds % re­turn	Cash Rate % average r­eturn	International Shares ­% return
1990­	-20.1­	12.1­	14.8­	-18.7­
1991­	22.2­	9.4­	10.3­	16­
1992­	-6.0­	8.9­	6.5­	-7.1­
1993­	39.1­	6.7­	5.1­	20.4­
1994­	-9.2­	10.0­	5.4­	3.4­
1995­	16.5­	8.2­	7.5­	18.7­
1996­	7.2­	7.4­	7.0­	11.7­
1997­	7.9­	6.1­	5.4­	14.2­
1998­	7.7­	5.0­	5.0­	22.8­
1999­	13.5­	7.0­	4.8­	23.6­
2000­	2.9­	5.5­	6.0­	-14.1­
2001­	2.6­	6.0­	4.9­	-17.8­
2002­	-9.6­	5.2­	4.6­	-21.1­
2003­	8.7­	5.6­	4.8­	30.8­
2004­	22.8­	5.3­	5.3­	12.8­
2005­	15.7­	5.2­	5.5­	7.6­
2006­	19.8­	5.9­	5.8­	18.0­
2007­	17.9­	6.3­	6.4­	7.1­
2008­	-45.8­	4.0­	6.6­	-42.1­
2009­	34.1­	5.7­	3.2­	27.0­
2010­	2.2­	5.5­	4.4­	9.6­

Source: Brailsford et¬ al. 2012, RBA 2016, viewed 24 March, 2016, https://www.rba.gov.au/statistics/cash-rate/, MSCI World index.

a. Briefly discuss the four asset classes in Table 1. Using the data from Table 1, calculate the Arithmetic Mean (AM), Geometric Mean (GM) and Standard Deviation (σ) of re-turns of each of the four asset classes. Briefly discuss the risk-return characteristics of each asset class with reference to these measures.

b. Construct an efficient portfolio. Assume the risk free rate over the period is 6.4%. Calculate the Efficient Frontier and Capital Allocation Line (CAL) for three asset classes: Australian Shares, Australian Bonds and the Australian Cash Rate using the Excel Solver Tool (see prescribed Textbook Chapter 7, Appendix A for guidance). You will also need to calculate and provide 'Bordered Covariance' and 'Correlation Matrices'. Repeat the above steps with all four asset classes i.e. include International Shares and add the new efficient frontier and CAL to the previous graph. Discuss the implications of the -addition of international shares on the efficient frontier and CAL compared with the first three assets efficient frontier and CAL.

c. Briefly explain how fiscal and monetary policy can influence an¬ economy. Discuss the three main factors that determine how sensitive a firm's earnings are to the business cycle.

d. Using the Black-Scholes formula and the cumulative normal distribution (i.e. see Table 21.2, p. 740 of the prescribed textbook), compute the call and put option prices ¬using the data from Table 2.

Table 2: Option information

Stock price, ­S­0­	39­
Exercise price,­ X­	35­
Interest rate, ­r­	0.053 (5.3% per year)
Time to expiration, ­T­	0.5 (6 months or half­ a year)
Standard deviation, σ	0.3 ( 30% per year)­

First compute d1 and d2, then using Table 21.2, find the N(d)'s and use interpolation if needed to find the exact call and put prices.

e. Assume the current futures price for gold ¬for delivery 10 days from 8 February is US-$1,197.90 per ounce. Suppose that from 9 February 2016 to 22 February 2016 the gold -prices were as in Table 3. Assume one futures contract consists¬ of 100 ounces of gold. Also, assume the maintenance margin is 5% and the initial margin is 10%. Calculate the daily mark-to-market settlements for each contract held by the long position. Briefly discuss basis risk (i.e. you can give an example if it makes it easier to discuss) [Hint: see Chapter 22 and examples 22.1 and 22.2 of the textbook].

Table 3: Gold prices in US Dollars per ounce

Day­	Futures Price (US Dol­lar per ounce)
8 Feb 2016­	1197.90­
9 Feb 2016­	1198.70­
10 Feb 2016­	1194.70­
11 Feb 2016­	1247.90­
12 Feb 2016­	1239.10­
15 Feb 2016­	1239.10­
16 Feb 2016­	1207.90­
17 Feb 2016­	1211.10­
18 Feb 2016­	1226.10­
19 Feb 2016­	1230.40­
22 Feb 2016 (delivery­)	1209.50­

Briefly discuss the main differences between options and futures.

f. 0Evaluate a fund's portfolio performance in terms of the market (e.g. outperformance -or underperformance) using the Sharpe ratio, Trey nor measure, Jensen's alpha, Information ratio and the M2 measure using data from Table 4. Assume -the risk-free rate is 5.5%. Briefly discuss each of the five methods.

Table 4: Portfolio performance data

	Fund Portfolio­	Market­
Average return, x¯­	12%­	8%­
Beta, β­	1.15­	1.0­
Standard deviation, σ	33%­	25%­
Tracking error (nonsy­stematic risk), σ(e)	14%­	0­

Note: This assessment is an individual assessment (i.e. this is not a group assessment). Please ensure you avoid collusion and¬ other practices which compromise individual assessment work.

This assessment is an individual assessment (ie this is not a group assessment).Please ensure you avoid collusion and other practices which compromise individual -assessment work. 

Words:- 2500

Reference:- Harvard 10