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

2). Construct an efficient portfolio. Assume the risk free rate over the period is 4.45%. Calculate the Efficient Frontier and Capital Allocation Line (CAL) for the five asset classes using the Excel Solver Tool (see prescribed Textbook Chapter 7, Appendix A for guidance). You will also need to calculate and provide the ‘Bordered Covariance’ and ‘Correlation Matrices’. Discuss the implications of these five assets on efficient frontier and CAL.

3). Economic indicators are often used to predict the business cycle. Provide an outlook for the economy based on data showing that the index of consumer expectations has risen and the initial claims for unemployment insurance has fallen. Discuss the consequences of that from a portfolio management perspective, elaborating on the choice of assets from cyclical and defensive industries.

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

5). Assume the current futures price for platinum for delivery 10 days from 23 March is AUD\$1,260.49 per ounce. Suppose that from 24 March 2017 to 6 April 2017 the platinum prices were as in Table 3. Assume one futures contract consists of 100 ounces of platinum. 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 short 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].

6). Evaluate a fund’s portfolio performance in terms of the market (e.g. outperformance or underperformance) using the Sharpe ratio, Treynor measure, Jensen’s alpha and the Information ratio using data from Table 4. Assume the risk-free rate is 4.45%. Briefly discuss each of the four measures plus the Morningstar risk-adjusted return model.

## Efficient Portfolio and Capital Allocation Line

1.Mentioning about five asset classes and depicting about its nature based on Arithmetic Mean (AM), Geometric Mean (GM) and Standard Deviation of each:

 Year Australian Shares Australian Bonds (RBA cash rate) S&P500 (USD) US Fed Funds Rate (USD) Brent Oil (USD) 1996 9.90% 6.00% 22.96% 5.30% 31.80% 1997 8.40% 5.00% 33.36% 5.50% -28.20% 1998 5.90% 4.80% 28.58% 4.80% -44.10% 1999 14.70% 5.00% 21.04% 5.50% 172.60% 2000 2.80% 6.30% -9.10% 6.50% -15.20% 2001 6.60% 4.30% -11.89% 1.80% -15.70% 2002 -12.40% 4.80% -22.10% 1.30% 58.00% 2003 10.10% 5.30% 28.68% 1.00% 4.90% 2004 22.80% 5.30% 10.88% 2.30% 30.10% 2005 17.40% 5.50% 4.91% 4.30% 39.40% 2006 19.10% 6.30% 15.79% 5.30% 10.00% 2007 11.70% 6.80% 5.49% 4.30% 47.00% 2008 -42.00% 4.30% -37.00% 0.10% -56.60% 2009 32.00% 3.80% 26.46% 0.10% 81.90% 2010 -2.00% 4.80% 15.06% 0.10% 29.70% 2011 -14.50% 4.30% 2.11% 0.10% 17.20% 2012 14.60% 3.00% 16.00% 0.10% -0.10% 2013 14.90% 2.50% 32.39% 0.10% 2.80% 2014 1.10% 2.50% 13.69% 0.10% -47.50% 2015 -1.90% 2.00% 1.38% 0.40% -37.60% 2016 7.00% 1.50% 11.96% 0.60% 46.70%
 Particulars Australian Shares (ASX 200; with dividends and splits) Australian Bonds (RBA cash rate) S&P500 (USD) US Fed Funds Rate (USD) Brent Oil (USD) Geometric Mean 4.71% 4.47% 8.36% 2.34% 5.32% Arithmetic Mean 6.01% 4.48% 10.03% 2.36% 15.58% Standard Deviation 0.1547 0.0147 0.1828 0.0238 0.5197

Take 1: Portraying the AM, GM and SD of each stock

(Source: As created by the author)

The above table mainly helps in identifying the overall Arithmetic Mean, Geometric Mean, and Standard Deviation of the five-asset class. This derivation of the risk and return capacity could help in identifying the investment scope, which might improve return of investors. In this context, Denny (2017) stated that with the help of relevant risk and return attributes investors can draft adequate portfolio, which could generate higher returns from investment. The classification of all the five stocks are depicted as follows.

Australian Shares (ASX 200; with dividends and splits):

Australian shares are mainly related to stocks that have both risk and return attributes, which could eventually help investors to form adequate portfolio that would provide higher returns. Australian shares are enlisted in a ASX market, which could be traded freely with the help of SX exchange and broker. The Asset class mainly has high arithmetic mean of 6.01%, while the geometric mean is at the levels of 4.71%. This indicates that the compounded income of the company is relatively lower than the normal return. On the other hand, the SD is at the levels of 0.1547, which is relatively higher and might hamper its profits. Therefore, among all the five asset classes Australian shares have third highest standard deviation, Arithmetic, and geometric mean, which indicates that with the help of adequate diversification optimal portfolio can be created from the asset class (Filbeck, Preece, and Zhao 2016).

Australian Bonds (RBA cash rate):

Australian bonds fall under risk free asset, which provides riskless return to the investors. The state for investment is mainly conducted by conservative investors who are not willing to increase their risk.  investment provides a constant return to the investor news is relatively not hai agitators provider from other investment classes. From the calculation of Geometric and Arithmetic mean the investment has the least risk involved, as it might help investors in reducing the overall portfolio risk.  however, Australian Bond asset class mainly has the fourth highest return from Geometric mean and Arithmetic mean (Gasser, Rammerstorfer and Weinmayer 2017). This indicates that the investment score could eventually allow the investor to generate constant returns. The arithmetic mean is at the levels of 4.48% and geometric mean value is 4.47% with a SD of 0.0147.

## Economic Indicators and Portfolio Management

S&P500 (USD):

The asset class mainly holds investment scope for international investors, as S&P 500 (USD) is mainly considered an international investment. both risk and return category of the international investment is relatively high, which would allow investors to draft its portfolio. investment in share market, whereas S&P 500 is an index comprising of shares in US market. This could eventually allow the investors in identifying different levels of risk return attributes that can be generated from their portfolio. The arithmetic mean is at the levels of 10.03% and geometric mean value is 8.36% with a SD of 0.1828. This indicates that the with adequate risk the Asset class could provide higher returns from investment. The Arithmetic of the asset class is in second position, while Geometric mean is at first position. This directly indicates high quality of the investment to generate returns for investors. Therefore, using the investment scope could eventually allow the investor in drafting adequate portfolio providing higher returns (Kaplanski and Levy 2015).

US Fed Funds Rate (USD):

US Fed Funds is one of the risk free international investments that allows investors to draft portfolios that could provide higher returns with less risk. This investment scope could allow the investors to reduce the actual risk involved in the portfolio and improve its return capability.  desert class mainly comprises of fixed interest rates that is provided to the investors for the investment. This would eventually help the investors to accommodate high risk in stocks in the portfolio and draft the optimal portfolio. The arithmetic mean is at the levels of 2.36% and geometric mean value is 2.34% with a SD of 0.0238. The actual use of the asset is relatively close to bond and risk-free assets, as there is no difference between geometric and Arithmetic mean, why the standard deviation is relatively lower and close to Australian bonds. Hence, using asset in the portfolio could be useful to the investors for generating higher Returns and reducing risk involved in investment (Mizgier and Pasia 2016).

Brent Oil (USD):

Brent oil is mainly an investment scope in oil sector, where its return and risk is relatively higher than all the five assets. This investment scope is mainly for active investors who are willing to accumulate risk for generating higher returns from their investment. The risk attributes of the investment are relatively higher in comparison with any other asset listed in the five-asset class. However, inclusion of the Asset in the portfolio would eventually increase risk and return attributes. The arithmetic mean is at the levels of 15.58% and geometric mean value is 5.32% with a SD of 0.5197. The overall Arithmetic mean in relatively higher than the geometric mean, which indicates that returns provided from Brent oil is not constant. This is the main reason geometric mean of the returns is relatively lower than the actual Arithmetic mean. Moreover, the standard deviation of the asset is relatively higher from the all five-asset class, which indicates the high risk involved in investment (Nakata 2016).

## Option Pricing using Black-Scholes

Figure 1: Depicting the CAL and efficient frontier of the portfolio

(Source: as created by the author)

The above figure mainly portrays me CL line and efficient Frontier of the five-asset class, which relatively forms the optimal portfolio. Efficient portfolio is mainly calculated by identifying the actual position and weight of the front assets, which could help in improving profitability and return from Investments. Currently, the portfolio return is calculated to be at the levels of 5%, while the risk is close to 1.36%. This could eventually help in generating higher returns from investment while reducing the overall risk (Yang 2013).

 Bordered Covariance Australian Shares Australian Bonds S&P500 (USD) US Fed Funds Rate (USD) Brent Oil (USD) Australian Shares 0.022779896 0.000255875 0.019195137 0.001030846 0.032198356 Australian Bonds (RBA cash rate) 0.000255875 0.000205583 -0.000149117 0.000240499 0.001440431 S&P500 (USD) 0.019195137 -0.000149117 0.031816532 0.000704594 0.017572778 US Fed Funds Rate (USD) 0.001030846 0.000240499 0.000704594 0.000540998 0.002100909 Brent Oil (USD) 0.032198356 0.001440431 0.017572778 0.002100909 0.25727542

Take 2: Portraying the Bordered Covariance of the five assets

(Source: As created by the author)

 Bordered Correlation Australian Shares (ASX 200; with dividends and splits) Australian Bonds (RBA cash rate) S&P500 (USD) US Fed Funds Rate (USD) Brent Oil (USD) Australian Shares (ASX 200; with dividends and splits) 1 0.118238556 0.71299902 0.293643316 0.42058975 Australian Bonds (RBA cash rate) 0.118238556 1 -0.058305304 0.721143939 0.19806143 S&P500 (USD) 0.71299902 -0.058305304 1 0.169830176 0.194229353 US Fed Funds Rate (USD) 0.293643316 0.721143939 0.169830176 1 0.178078067 Brent Oil (USD) 0.42058975 0.19806143 0.194229353 0.178078067 1

Take 3: Portraying the Correlation Matrices of the five assets

(Source: As created by the author)

## Futures Contract - Mark-to-Market Settlements and Basis Risk

The above tables any comprise of bordered covariance and bordered correlation which is calculated from the returns of the fives assets. Both the calculations are mainly conducted to identify the optimal portfolio, which is calculated based on derived results. Hence, the derivation of the calculation could eventually allow investors in identifying the portfolio that has least risk with highest returns (Lee and Su 2014).

c. Discussing about the economic indicator on the perspective of portfolio stating assets from cyclical and defensive industries:

The evaluation economic indicators such as employment rate, GDP and consumer index could be identified as one of the relevant measures which allow investors to formulate their investment. The detection of employment rate could eventually allow the investor in identifying the minimum unemployed persons with in the economy. This would eventually mean that business is being conducted smoothly, which allows your organization to increase the level of profit from operations. The cyclical stocks mainly do good business during economic boom, as consumers have adequate spending power where they can spend on luxury items to fulfill the needs. On the other hand, defensive stocks are progressive during economic downturn, as consumers need to fulfill their basic needs such as electricity water and gas. moreover, defensive stocks comprise of companies providing utilities to consumers, which cannot be stopped during economic crisis (Guérin et al. 2015).

d. Depciting the call and put prices with Black-Scholes formula:

 Particulars Value Stock price, S0 48 Exercise price, X 42 Standard deviation, σ 18% Interest rate, r 3.5% Time to expiration, T 0.5 d1 1.25 d2 1.12 Call \$   7.05 Put \$   0.33

Take 4: Portraying Call and Put value

(Source: As created by the author)

e. Depicting about the basic risk associated with the investment and the daily mark-to-market settlements:

 Day Futures Price CV Initial Margin Maintenance Margin Total Margin M2M Cash balance 23-Mar-17 1,260.49 126,049 12,605 6,302.45 18,907 18,907 24-Mar-17 1,264.04 126,404 12,640 6,320.20 18,961 355.00 19,262 27-Mar-17 1,270.76 127,076 12,708 6,353.80 19,061 672.00 19,934 28-Mar-17 1,246.93 124,693 12,469 6,234.65 18,704 -2,383.00 17,551 29-Mar-17 1,242.71 124,271 12,427 6,213.55 18,641 -422.00 17,129 30-Mar-17 1,240.24 124,024 12,402 6,201.20 18,604 -247.00 16,882 31-Mar-17 1,245.34 124,534 12,453 6,226.70 18,680 510.00 17,392 3-Apr-17 1,257.61 125,761 12,576 6,288.05 18,864 1,227.00 18,619 4-Apr-17 1,269.01 126,901 12,690 6,345.05 19,035 1,140.00 19,759 5-Apr-17 1,268.83 126,883 12,688 6,344.15 19,032 -18.00 19,741 6-Apr-17 1,270.20 127,020 12,702 6,351.00 19,053 137.00 19,878 Total income 971

Take 5: Portraying mark-to-market settlements

## Fund Portfolio Performance Evaluation using Sharpe Ratio, Treynor Measure, Jensen's Alpha, and Information Ratio

(Source: As created by the author)

The above table mainly helps in depicting the overall profit that are generated from relevant investments. Investment conducted in the above table does not comply with the hedging process, which relatively increases the risk attributes of the investment. Moreover, the practice conducted in the above table is not feasible in real world practice, as relevant increment in risk can be seen from investment. Investors mainly need to hedge their overall financial investment conducted in future contracts to reduce the overall risk from investment (Denny 2017).

f. Using Sharpe ratio, Jensen’s alpha, Information, and Treynor ratio for assessing performance of the fund, while discussing about Morningstar risk-adjusted return model:

 Particulars Fund Portfolio Market Average return, x? 18% 11% Beta, β 1.18 1 Standard deviation, σ 26% 17% Tracking error (nonsystematic risk), σ(e) 11% 0 the risk-free rate 4.45% Formula Value Sharpe ratio 52.12% Treynor measure 11.48% Jensen’s alpha 5.82% Information ratio 52.92%

Take 6: Portraying performance of the portfolio by using different formulas

(Source: As created by the author)

Sharpe ratio of the portfolio is relatively at the levels of 52.12%, which indicates the risk adjusted returns that will be provided from the portfolio. this indicates that the portfolio has higher returns in comparison with risk free rate which would allow investors to raise the level of Returns. The Treynor ratio is at the levels of 11.48%, which indicates the excess return from investment that was not diversifiable by the portfolio. Moreover, the Jensen's Alpha was at the level of 5.82%, which indicates capability of the portfolio to acquire abnormal returns. Lastly, the information ratio is at the levels of 52.92%, which indicates the ability of the portfolio to generate access returns in comparison with the benchmark. This indicates that the portfolio can generate higher returns from investments.

The formula detected in the above figure is derived from Morningstar Risk adjusted return model, which allows the investor to identify the return that could be generated from its portfolio (Morningstar.com 2017). Moreover, the model uses risk-adjusted method for drafting adequate portfolio that could increase return from investment while acquiring the least risk. Different access return these are used in the model to identify the returns that could be generated from an investment.

Reference:

Denny, M., 2017. The fallacy of the average: on the ubiquity, utility and continuing novelty of Jensen's inequality. Journal of Experimental Biology, 220(2), pp.139-146.

Filbeck, G., Preece, D. and Zhao, X., 2016. The ABA Top Performing Banks in a Time of Financial Crisis: Can They Outperform the Worst?. Banking & Finance Review, 8(1).

Gasser, S.M., Rammerstorfer, M. and Weinmayer, K., 2017. Markowitz revisited: Social portfolio engineering. European Journal of Operational Research, 258(3), pp.1181-1190.

Guérin, G., Jain, M., Thomsen, K.J., Murray, A.S. and Mercier, N., 2015. Modelling dose rate to single grains of quartz in well-sorted sand samples: The dispersion arising from the presence of potassium feldspars and implications for single grain OSL dating. Quaternary Geochronology, 27, pp.52-65.

Kaplanski, G. and Levy, H., 2015. Value-at-risk capital requirement regulation, risk taking and asset allocation: a mean–variance analysis. The European Journal of Finance, 21(3), pp.215-241.

Lee, M.C. and Su, L.E., 2014. Capital Market Line Based on Efficient Frontier of Portfolio with Borrowing and Lending Rate. Universal Journal of Accounting and Finance, 2(4), pp.69-76.

Mizgier, K.J. and Pasia, J.M., 2016. Multiobjective optimization of credit capital allocation in financial institutions. Central European Journal of Operations Research, 24(4), pp.801-817.

Morningstar.com. (2017). Risk-Adjusted Return. [online] Available at: https://www.morningstar.com/InvGlossary/risk-adjusted-return.aspx [Accessed 4 Feb. 2018].

Nakata, T., 2016. Optimal fiscal and monetary policy with occasionally binding zero bound constraints. Journal of Economic Dynamics and Control, 73, pp.220-240.

Yang, F., 2013. Investment shocks and the commodity basis spread. Journal of Financial Economics, 110(1), pp.164-184.

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