Markowitz Portfolio Optimization Essay

Introduction Markowitz (1952, 1956) pioneered the development of a quantitative method that takes the diversification benefits of portfolio allocation into account. Modern portfolio theory is the result of his work on portfolio optimization. Ideally, in a mean-variance optimization model, the complete investment opportunity set, i.e. all assets, should be considered simultaneously. However, in practice, most investors distinguish between different asset classes within their portfolio-allocation frameworks. In our analysis, we view the process of asset allocation as a four-step exercise like Bodie, Kane and Marcus (2005). It consists of choosing the asset classes under consideration, moving forward to establishing capital market expectations, followed by deriving the efficient frontier until finding the optimal asset mix. We take the perspective of an asset-only investor in search of the optimal portfolio. An asset-only investor does not take liabilities into account. The investment horizon is 5 – 10 years and the opportunity set consists of twelve asset classes. The investor pursues wealth maximization and no other particular investment goals are considered. We solve the asset-allocation problem using a mean-variance optimization based on excess returns. The goal is to maximize the Sharpe ratio (risk-adjusted return) of the portfolio, bounded by the restriction that the exposure to any risky asset class is greater than or equal to zero and that the sum of the weights adds up to one. The focus is on the relative allocation to risky assets in the optimal portfolio. In the mean-variance analysis, we use arithmetic excess returns. Geometric returns are not suitable in a mean-variance framework. The weighted average of geometric returns does not equal the geometric return of a simulated portfolio with the same composition. The observed difference can be explained by the diversification benefits of the portfolio allocation. We derive the arithmetic returns from the geometric returns and the volatility. a) The CIO has sent some of the results you have done above to the IPC. After the members of the IPC perused the results, some of them asked the CIO to explain why the equal-weighted portfolio underperformed the mean-variance optimal portfolio for the periods studied. Explain to the CIO using only the whole period results. First, let’s quickly look at some of the values of the fields that are used to draw the capital allocation line. As an example to my explanation let’s go through 2 possible capital allocation lines from the risk-free rate (rf = 3.5%). The first possible CAL is drawn for naively diversified portfolio for the whole period with rf = 3.5%. The expected return for this portfolio is 0.006224053, and its standard deviation is 0.025002148, the reward-to-volatility ratio, which is the slope of the CAL is 0.132284095. The second CAL is drawn for the Optimal portfolio for the whole period with rf = 3.5%. The expected return for this portfolio is 0.009508282, and its standard deviation is 0.00734826, the re- reward-to-volatility ratio is 0.897030832. We can see from the numbers that the optimal portfolio does better than the naively diversified portfolio because the RTV is higher for the optimal portfolio. The reason for that is that we’ve identified the optimal portfolio of risky assets by finding the portfolio weights that result in steepest CAL. The CAL that is supported by the optimal portfolio is tangent to the efficient frontier. The bottom line is that we have chosen the optimal portfolio that has the portfolio weights that lie on the capital allocation line that is tangent to the efficient frontier. Which means a portfolio of risky assets that provides the lowest risk for the expected return and thus this selected portfolio is bound to outperform the naively diversified. b) The IPC has noticed that the optimal allocations of sub-period 1 and sub-period 2 are very different (based on different scenarios of target returns and investment limits). They asked why. Would you please explain (using the set of results for 3.5% risk free rate)? This entails an analysis of the economic conditions for different periods. The most important insight we get is that in a diversified portfolio, the contribution to portfolio risk of a particular security will depend on the covariance of that security’s return with those of other securities. If you see the correlation matrix for the 2 sub periods, we can see that the economic-wide risk factors have imparted positive correlations among the stock returns for Sub Period 2 (03 – 10). This was the time of economic crisis (08-10) and since most of the risk was economic, the optimal portfolio incorporates less risky assets. While the sub period 1 (95 – 03) went through a healthy growth period, had mostly firm specific risk and lesser economic risk. c) The CIO wants to propose investment limits on certain asset classes to the IPC for consideration, but the CIO may not be aware of the likely impact on the performance of the Fund. Since you have run some analysis above based on the proposed limits, present your analysis and make a recommendation regarding investment limits for the historical arithmetic average (target) return and the 6% p.a. target return. The fundamental concept behind MPT is that the assets in an investment portfolio should not be selected individually, each on their own merits. Rather, it is important to consider how each asset changes in price relative to how every other asset in the portfolio changes in price. The optimal portfolios derived from the analysis are tangency portfolios and represents the combination offering the best possible expected return for given risk level. If we change the investment limits it could result in sub-optimal portfolios. This can be easily from the tables from (comparing naà ¯ve allocation to optimal allocation): Optimal Portfolio: When we draw the CAL and the efficient frontier using the above values, we see that the weights in the optimal portfolio result in the highest slope of the CAL. We can see this with the improved reward-to-volatility ratio of the portfolios. We also saw from the analysis where we constrained the portfolio return to 6% pa, the weights of the optimal portfolio changed and the RTV was lower than the un constrained optimal portfolio. Constrained:Unconstrained: d) The CIO would like to test the sensitivity of the mean-variance optimization to a change in the portfolio target return. Since you have done some runs using the historical arithmetic average return and 6% p.a. target return, present what you’ve learned from your analysis to the CIO using your results. We have tested the sensitivity of the mean-variance analysis to the input parameters. Table below shows the impact on the optimal portfolio of an increase and a decrease in the expected volatility of an asset, all other things being equal. Note that a change in volatility affects both the arithmetic return and the covariance matrix. Again, this table demonstrates the sensitivity of a mean-variance analysis to the input parameters. An increase in expected volatility leads to a lower allocation to that asset class. High yield even vanishes completely from the optimal portfolio. It is noteworthy that commodities are hardly affected by a higher standard deviation. A decrease in volatility mostly leads to a higher allocation. Government bonds, despite their expected zero risk premium, add value due to the strong diversification benefit. In this analysis, they appear to be insensitive to a change in their expected volatility. Credits and bonds are quite similar asset classes and, in a mean-variance context, the optimal portfolio tends to incline towards one or the other. In short, the mean-variance analysis suggests that adding real estate, stocks and high yield to the traditional asset mix of stocks and bonds creates most value for investors. Assets| Optimal Portfolio| Optimal Portfolio (6%)| SPTR Index| 0| 0| RTY Index| 0| 0| MXEA Index| 0| 0.747626014| MXEU Index| 0| 0| MXEF Index| 0| 0| SPGSCITR Index| 0| 0| FNCOTR Index| 0.862665445| 0.179140105| H15T3M Index| 0| 0.05| WOG1| 0| 0| C0A0| 0| 0| H0A0| 0| 0| G0Q0| 0.137334555| 0.023233881| e) Could we use the optimal weights from a previous period, say sub-period 1 or sub-period 2 or the whole period, as the recommended asset allocation for the next 5 or 10 years? Explain your answer with the out-of-sample test results you have done. No, we cannot recommend asset allocation based on the out-of-sample test results. The in-sample MV efficient frontiers overestimate the return associated with portfolio optimization not only with respect to resampled efficiency but importantly with respect to out-of-sample investment performance. Even with good inputs, MV efficiency error maximizes the risk and returns inputs, creates upward biased estimates of future performance, and substantially underperforms resampled efficiency. f) Based on the above analyses, what lessons and implications can be learned from your analysis on the mean-variance portfolio optimization? Key lessons: The fundamental goal of portfolio theory is to optimally allocate your investments between different assets. Mean variance optimization (MVO) is a quantitative tool which allows you to make this allocation by considering the trade-off between risk and return. Markowitz Portfolio Optimization The single period Markowitz algorithm solves the following problem: Single Period Problem * Inputs: * The expected return for each asset * The standard deviation of each asset (a measure of risk) * The correlation matrix between these assets * Output: * The efficient frontier, i.e. the set of portfolios with expected return greater than any other with the same or lesser risk, and lesser risk than any other with the same or greater return. The Markowitz algorithm is intended as a single period analysis tool in which the inputs provided by the user represent his/her probability beliefs about the upcoming period. The expected return, standard deviation, and correlation matrix are computed using standard statistical formulae. The expected return represents the simple (probability weighted) average of the possible returns for each asset, and the standard deviation represents the uncertainty about the outcome. The correlation matrix is a symmetric matrix, with unity on the diagonal, and all other elements between -1 and +1. A positive correlation between two assets A and B indicates that when the return of asset A turns out to be above (below) its expected value, then the return of asset B is likely also to be above (below) its expected value. A negative correlation suggests that when A’s return is above its expected value, and then B’s will be below its expected value, and vice versa. Input Data Issues A major issue for the methodology is the selection of input data. The use of historical data provides a very convenient means of providing the inputs to the MVO algorithm, but there are a number of reasons why this may not be the optimal way to proceed. All these reasons have to do with the question of whether this method really provides a valid statistical picture of the upcoming period. The most serious problem concerns the expected returns, because these control the actual return which is assigned to each portfolio. Failure of underlying hypothesis When you use historical data to provide the MVO inputs, you are implicitly assuming that * The returns in the different periods are independent. * The returns in the different periods are drawn from the same statistical distribution. * The N periods of available data provide a sample of this distribution. These hypotheses may simply not be true. The most serious inaccuracies arise from a phenomenon called mean reversion, in which a period, or periods, of superior (inferior) performance of a particular asset tend to be followed by a period, or periods, of inferior (superior) performance. Suppose, for example, you have used 5 years of historical data as MVO inputs for the upcoming year. The outputs of the algorithm will favor those assets with high expected return, which are those which have performed well over the past 5 years. Yet if mean reversion is in effect, these assets may well turn out to be those that perform most poorly in the upcoming year. Error in the estimated mean Even if you believe that the returns in the different periods are independent and identically distributed, you are of necessity using the available data to estimate the properties of this statistical distribution. In particular, you will take the expected return for a given asset to be the simple average R of the N historical values, and the standard deviation to be the root mean square deviation from this average value. Then elementary statistics tells us that the one standard deviation error in the value R as an estimate of the mean is the standard deviation divided by the square root of N. If N is not very large, then this error can distort the results of the MVO analysis considerably. Summary The above discussion does not mean to imply that the Markowitz algorithm is incorrect, but simply to point out the dangers of using historical data as inputs to a optimization strategy. If you make your own estimates of the MVO inputs, based on your own beliefs about the upcoming period, single period MVO can be an entirely appropriate means of balancing the risk and return in your portfolio.

Dream House Essay

Everyone has their own thoughts about their dream house.  These days homes are more affordable because of the economy and all the foreclosures makes it much easier to afford a really nice house. My dream house is not a fancy house that I could never afford; its a home I could see my wife and I having in the future. I have seen many homes that I thought to myself, this house would be perfect. A few characteristics I want to describe about my dream house are the appearance, location, and decor. I want my house to have a nice large home with coffee stained wood finish on the outside full of crystal clear windows of all different sizes. I imagine as you walk into my home there would be high ceilings and hanging over the entryway would be a big crystal chandelier. When entering the home, there would also be a place for you to hang your coat, rest, and take off your shoes from a long day’s work. I want a house that is not brand new but not too old either because I do not want to have fix the house constantly or hear the creaking floors while walking around. I always thought it would be nice to have solar panels, a windmill, and a garden so I can be self reliant. The grass would be a bright healthy green almost as if it was not real. Around the house would be a large fence to allow for our privacy and to keep the animals in. My dream house will be in a community, but I want it to be in an area that is not to busy for convenience and for the safety of our future children. I always thought it would be nice to have a couple of acres for my dogs to run about and a beautiful lake stocked with fish for the dogs to go into and cool off during the hot summers. Illinois is a beautiful state and would be a nice place to settle down and have this dream house. Another significant thing about the home would be the long cobblestone driveway you would have to travel up leading to our home and front porch. It would also be nice to have a day room attached to the house with windows that easily open and close so my wife could sit out there in the winter to smoke and not be so cold. I want the inside to be tasteful, like I imagine a doctor’s home looking. There would be two floors and a basement. When you first walk in, you see the family room which is very calm and relaxing. You continue to the kitchen and dining room with an open floor plan. The basement would be split in half for both my wife and I. My part of the basement would be man themed, full of energy and excitement. There would be a pool table, arcade style games, a shadow box full of military memorabilia, big televisions, and gaming systems. My wife and I would have the master suite upstairs with a California king Temporpedic bed sitting with a beautiful oak finished baseboard and headboards, an enormous television, big bay windows to allow the cool breezes in during the hot, humid summers, and big dark curtains to keep the sun out during the mornings. I do not have any children currently but hope to have one or two in the future and they would also have bedroom up stairs. I would like their bedrooms to be kid oriented so for example if we have a boy nice blues and clouds or jungle with animals. If its a girl then pinks and pony’s or whatever it is my wife decides. My dream home will have an elegant appearance, be in a convenient location, and be tastefully decorated. I also believe a home like this would be perfect for the holidays or family gathering and would allow me to see my family more. These are all the things that would make my home perfect for my wife and I in addition I look forward to making this dream home a reality.

Financial risk management in the financial institutions Dissertation

Financial risk management in the financial institutions - Dissertation Example Therefore, it is because of this trend there has been need for the risk management practices in the financial institutions. It has also forced the regulatory authorities and the bankers to improve the internal systems such as pricing, risk evaluation and control (Saita, 1999). It has been found that the traditional banking business of making loans and accepting deposits have declined in the United States in the recent years. People are switching from directly held assets to the pension funds and the mutual funds. In light of this issue, the banks are attempting to uphold their position relative to the GDP. They are putting emphasis on switching from their traditional business to fee-producing activities. It has been found that the household investors in the US and the UK bear more risk from their investment in comparison to the investors of Japan, Germany and France. However, according to few researchers it has been argued that intermediaries from Japan, Germany and France may be abl e to manage the risk by holding liquid reserves and intertemporal smoothing. On the other hand, the countries such as the US and the UK are not able to manage their risk because of the competition that they face from the financial markets. With the decline in the financial innovation and traditional banking business that is normally undertaken by the banks in the US, it can be described as a response to the competition that they face from the markets and the decline in the intertemporal smoothing (Allen & Santomero, 2001). Question Two The design in the new security, advances in the theory of finance along with the improvements in the computer and telecommunication technology have resulted in revolutionary changes in the overall structure of the financial markets and the institutions. Hedging versus equity has a role to play in managing the risk (Merton, 2000). The corporate hedging can help in reducing the volatility of the firm value. In this perspective, it is important to unders tand what the term corporate hedging denotes. It generally makes use of the off-balance-sheet instrument such as forwards, swaps, futures and options. For instance, if in case the value of the American manufacturing firm facing competition in the US markets from its foreign manufacturers are inversely linked to the value of the Dollars, then the manufacturing company can hedge the exposure by employing the off-balance sheet instruments. The exchange rate changes or volatility can be hedged in various ways. It can be done by selling the foreign exchange futures on the foreign currency, entering into the currency swaps, buying a put option or by writing a call option on the foreign currency. Therefore, it can be said that by utilising this tools the firm can hedge the risk. On the other hand, the firm can hedge by making use of the on-balance-sheet strategy (Nance & Et. Al., 1993). Credit options can also be used by the bond investors to hedge against the decline in the price of the b ond. The decline may be caused because of the downgrade in the company’s debt. Credit options are a second type of credit derivatives that can be used to hedge the risk of adverse changes brought about in the credit quality. The debt issuers can also make use of the credit-linked note which is a type of the credit derivative in order to hedge against credit risk. Therefore, it is evident that the conventional methods of managing the risk such as bank loan, assets securitisation and diversification can provide only a

Ophthalmic Care Delivery in Saudi Arabia Assignment - 70

Ophthalmic Care Delivery in Saudi Arabia - Assignment Example   Statistics indicate that this institution has considerably decreased the prevalence of blindness and other eye-related health problems, in the elderly, by over 10 percent in the past few decades (Alwadani et al. 2010). However, it has been noted that there are certain regions and communities with relative surpluses in the delivery of quality ophthalmic care and short put of ophthalmologists and ophthalmic subspecialists. These researchers employed written survey to collect data from ophthalmology residence. The written survey contained questions on medical education, demographic information, residency training, and career goals that affect their career choice (Alwadani et al. 2010). The results of this study indicated that the majority of ophthalmology respondents preferred practicing in urban settings (63%) such as Jeddah, Makkah, Riyadh, and Eastern area to rural settings (37%) such as Jizan, Hail, Asir, Madinah, Qassim and Baha (Alwadani et al. 2010). Additionally, 75% and 77% of the respondents were interested in practicing interactive research and surgery respectively (Alwadani et al. 2010). Research results summarize that most respondents are willing to practice in private sectors rather than public institutions. In this context, these authors recommend that the government should make an effort to encourage adoption of the ophthalmic practice in public institutions other than in the private sec tor (Alwadani, 2010). Additionally, training in sidelined ophthalmic subspecialties should be encouraged to ensure optimum ophthalmic care delivery to all Saudi Arabia citizens (Alwadani et al. 2010).

The Priority for Glenmeadie's Innovation Efforts Essay

The Priority for Glenmeadie's Innovation Efforts - Essay Example Marketing experts should be aware that the product is the thing that they’re selling, and innovation in this field is also necessary to build a customer base. The purpose of this essay is to explore how Glenmeadie can balance their innovation efforts between the product and new types of marketing in an effort to impress new customers and build a loyal customer fan base, by using the Ansoff and 8Ps frameworks to provide an illustration on how best to tackle the issues at hand. Glenmeadie The information provided by Nunes & Driggs (2006) paints an outline of Glenmeadie. As a Scotch whiskey distillery, Glenmeadie has won 7 gold medals in one season on a national and international scale, suggesting an upmarket taste and therefore suggesting a target market of whiskey connoisseurs. The marketing campaign led by Bob consists of international efforts to put on Tastemakers events in 25 cities, starting in New York. The aim is to spend $15,000 on each event, offering tastes of various whiskeys and bringing in efforts from an apprentice distiller and buyers from local distributors. Glenmeadie is also trying to give a more personal face to the brand, having interactive websites and creating loyalty card programs. ... Rayport, Stephen Dull and Joe Scafido. Scafiado, a member of the executive council at Dunkin’ brands, raises concerns about the fact that the front- and back-house innovations programs seem to be presented as separate enterprise. This is mainly because they seem to have separate functions in marketing, with product development being considered part of back-room company enterprises and marketing focusing on customer involvement and sales. However, this is a limited perspective on the matter. At Dunkin’ brands, Scafiado brought together the culinary team and the operating specialists into one department, meaning that any culinary development is being innovated simultaneously with efforts on how to present this to the company. Herman, who is president of Lebanon, agrees that Glenmeadie should be focusing efforts on product excellence as well as drawing customers in with these innovative marketing campaigns. After all, it is the product that is being sold, not the marketing scheme. Rayport, founder and chairman of Marketspace, sees things differently. Although Glenmeadie has reported some stress on research and development budgets, Rayport suggests that this can only be a positive thing, even for Ellis, the distiller. Rayport even goes as far to suggest that Ellis’ argument against expansion in marketing efforts is a paradox, as Ellis cannot have the freedom to create and innovate in the distillery without an expanded market and expanded profits. Dull, vice president of strategy at Greensboro, sees things a little differently. Dull suggests that Glenmeadie is a luxury product, as a whiskey, and therefore the aims of the company to branch into mass-marketing are a mistake. Dull suggests that there hasn’t been much of an

Persistent Online Games Essay Example | Topics and Well Written Essays - 250 words

Persistent Online Games - Essay Example Online gaming can involve both technological and social risks, which may cause harm to the subscribers by expending cost as well as time. Various online gaming hazards are related to the computer users, but the users are not aware about the harms caused to the computer. Online gaming raises technological risks such as ‘malicious software’, ‘viruses and worms’, ‘insecure game coding’ and ‘insecure games servers’ among others. In addition, online gaming raises social issues that include ‘identity theft’, ‘virtual mugging’ ‘cyber prostitution’, ‘social engineering’ and ‘virtual sweatshop’ among others (Hayes, 2008). The designers should give some support to the people by the help of general security practices and by gaming specific security practices. The moral responsibility of designers is to ensure the security in terms of privacy and traffic safety. Additionally, the designers are required to ascertain that online gaming violence is not involved in the games. However, the social risks as witnessed by users depend on individual grounds, as playing online games is based on their perceptions and actions (Hayes, 2008; Sicart, 2005). From the above discussion, it can be comprehended that online gaming is popular amid youths. Online gaming is also identified to cause certain harm to the subscribers in relation to technological and social risks. It has been recognized that subscribers have certain moral responsibilities in terms of maintaining privacy and minimizing violence. On social grounds, the users are accountable for their individual responsibility considering health and social

Aluminium Foil ((Corporate Social Responsibility)) & Environmental Assignment

Aluminium Foil ((Corporate Social Responsibility)) & Environmental Impact - Assignment Example The availability of this element is so high that a there is very little chance of demand ever surpassing supply. Producing aluminum is a process that needs a lot of energy; in fact, the commercial growth of this metal in the late nineteenth century was predominantly as a result of the development and accessibility of inexpensive and ample hydroelectric power that has remained the key source of energy for the sector. Energy that is used in the production of aluminum is trapped in the metal, thus if aluminum is re-melted in order to make it new metal, only five percent of the energy that was used initially is needed as ninety five percent of the initial investment in energy will remain in the metal. Since the production of aluminum started, used aluminum has remained a significant source of new metal and based on the industry estimates, almost seventy percent of the aluminum in use will be recycled eventually as it is less costly compared extraction of the metal from its ore. Depending on the previous use of aluminum, the life cycle of aluminum products varies significantly. When aluminum is used in packaging in the form of a foil, it might have a life cycle of approximately a few weeks but when it is utilized as a cladding material in buildings, its life cycle may be approximately a century or even longer. This implies that aluminum has a positive profile in regards to its abundant availability, durability as well as tendency to be recycled at very low costs in terms of energy (Green, 2007, p. 125). Therefore, aluminum foil can make a significant positive contribution towards the conservation of other resources in the environment. Aluminum foil is produced from an alloy of aluminum that contains between ninety-two and ninety nine percent of aluminum, and come in numerous widths and strengths since they can be applied to thousands of applications. Aluminum foil used for manufacturing thermal insulations in the construction