The Use of Mean Variance Analysis in the Economy

Check out more papers on Economy Investment Risk

It is a very important for an investor to analyse the decision of selecting the investment options before actually executing the choice. Also, it is even more imperative to follow the right approach to reach the correct investment option. Harry Markowitz in 1952 introduced the notion of mean variance analysis to quantify the risk before effectively deciding on the portfolio. Again, the idea was to look for the maximum return corresponding to the minimum risk (Markowitz et. al., 2000). This essay focuses on the importance of mean variance analysis while selecting the individual assets for the portfolio. In addition, it will traverse through different aspects of the same. The primary objective of the essay is to understand its importance in the portfolio selection. Also, it will focus on critical issue involved with the analysis in different background. Moreover, it will highlight the limitations and advantages of its use complemented with the brief discussion on the technical issue in between. The essay will start with general discussion describing the asset and its classes and then, will introduce the points for the necessity for its use. It will also highlight the importance of extraordinary events in between along with the small but, critical issues like currency fluctuation. Finally, it will put some light on the advancement in the same area and try to critically analyse the weakness of the mean variance framework in the real world.

Don't use plagiarized sources. Get your custom essay on

“The Use of Mean Variance Analysis in the Economy”

Get custom essay

GENERAL DISCUSSION

For the investors in the developed markets the broadly observed investment are classified as: (1) Stocks/Equity (2) Bonds (debt) (3) cash or cash equivalents and (4) Property/Real Estate. This can be further extended into subcategories depending on the specific needs of particular investor (Fabozzi, F., J., 2009:4-6). Similarly, the assets can be categorised in risky and Risk free assets. For example, stock of a company in the equity market is a risky asset while, 1 year bond of US government is risk free because it is almost sure that the returns on the bond will be materialised in future to a very good certainty (Fabozzi, F., 2009: 15-18).

APPLICATION OF MEAN VARIANCE ANALYSIS

The importance of financial scrutiny of investment options is clear from the fact that, it is an essential part of the investment process to choose the most appropriate from a variety of options. Whether, it is a small scale investment by an investor via any broker in the US equity market or a large scale investment by the large investors in infrastructure bonds of Australia (Brown, C., 2005: 431-438). The investigative approaches used for minimising the financial risk while, choosing the portfolio encourages the analysts to look for the proper economic agents for sharing the risk. Taking mean variance as the bases for studying the portfolio risk and return for the US investors Liu (2010) pointed to the gains made by them while holding the foreign corporate bonds. As the economies are transforming into more globalised ones, the application of such methods is becoming more important. In the light of financial meltdown during the year 2008, the significance of diversifying the portfolio again got highlighted. In brief, pooling of assets from different background is widely practiced approach and so is the utilization of data for the analysis of variety of assets. While studying the US Stock and bond market Chordia et. al. (2005: 92-93) mentioned that returns in assets are affected by lot of factors. The complexities of analysing the return are clear from the details in his work. For Example, time of investment corresponding to the specific circumstances of economic cycle such as recession or boom. Again, aspect of investment like economic vulnerabilities of the potential investment opportunity, external vulnerabilities such as Russian default crises in 1998 especially, when the examined seek after asset is exposed to such external factors determines the final realised return. For this reason, the analysis of returns is requires good amount of statistical and fundamental analysis. Consequently, risk and return is now considered to be a specialised area of work for the finance professionals. Going into more detailed examination of the Mean Variance Analysis for portfolio selection Campbell et. al. (2004:1-3) found that, predictability of return with respect to the time is complex; nonetheless, the shift over a period of time is supposed to be fairly estimated within a band of uncertainty. Though, the exercise of statistical or fundamental testing heavily relies on certain assumptions. For instance, data for the past will almost reflect the same proposition for the future analysis, the probability of unexpected events like collapse of Lehman brothers is rare phenomenon and so on. Despite, all the ambiguity in the analytical work researchers like Samuelson (1969:50-55) argued that, the empirical analysis gives fair degree of plan to the investors while considering the long term or short term investment strategies. As pointed above, the analysis can also be applied in cross country analysis to achieve greater information lead before investing. Following the same CAPM model and optimizing the mean-variance relationship Fidora et.al. (2006:4-10) concluded that, there is significant degree of home biasness occurs in the investment decisions. The currency fluctuation adds additional risk while choosing the foreign assets unless the real foreign currency exchange rate is negatively correlated to the realised returns on foreign assets. This suggests that the risk return analysis points towards greater home biasness for higher degree of volatility in a currency and vice versa. This is endorsed by the study by French et. al. (1991:222-226). They had found that, almost 98 percent of holdings in Japan was by domestic investors similarly, the figure stands at 94 and 82 percent for the US and UK market.

Diversification of Portfolio and Important Issues

According to Martellini et. al. (2007:3-4) standard mean variance technique suffers from several limitations such as, parameter uncertainty and non-normal asset distribution. Hence, the more robust techniques are needed for taking advantage of the diversification. While arguing on the case of mixing the hedge fund with the traditional investment opportunities Terhaar et. al. (2003) shown that volatility or in other words risk get decreased for a particular level of return. Furthermore, the hedge funds found to have low correlation with traditional investment opportunities. Alternatively, going into the technicality of the mean variance practice if, the volatility is minimised in the statistical model then, it is accompanied by a significant amount of increase in extreme risk with fatter tails (Sornette et. al., 2000). Accordingly, in the case of fat tailed return functions, the usability of the mean variance technique does not seems to be optimal solution and consequently leading to significant loss of its utility (Cremers et. al., 2004:1-4,18-19). Furthermore, a number of times it is quite difficult for the researcher to collect the appropriate data for the study. Parameter estimation is tedious task in the absence of data for required period of time. In addition, the difficulty in finding the relevant data for the relevant regularity also adds to the uncertainty in the parameter estimation. This suggests that it is quite difficult to estimate the expected return within a reasonable estimation error in the real world of scarce data (Fung et.al., 1997:375-302). Nonetheless, progress by Black and Litterman (1991:7-18) in the static mean variance setting, to estimate the uncertainty on the return in terms of deviation while analysing the investment opportunities optimized the scrutiny process to an extent. To put it more simply they had simply added the parameter for psychological side of the trading namely, the inclusion of confidence level and individual beliefs on the prior distribution and estimating the joint distribution in the model. The simplicity of his approach has been widely acknowledged and has been used by analysts to decide on the assets while deciding for the portfolio. Idzorek (Jul, 2004: 1-3, 27) confirmed the same in his research and stated that the psychological part in the active asset allocation should weigh significantly. In other words the study summarized the fact that, all the new work on the mean variance framework has fixed the weaknesses like negligence of intuitiveness, unintended portfolio concentration and error estimation.

Extending the Discussion (Parallel Issues)

Taking the conversation to the another plane, many of the quantitative analysts and researchers in finance pointed to the facts that, the accuracy of the mean variance result depends notably on the factors like interest rates and dividend yields (Breen et. al., 1990: 1177-1189). But, the complications of the real world are very difficult to elucidate in simple mean variance practice. There are many issues like currency, tax and transaction which can make the mean variance analysis merely a statistical exercise for active portfolio allocation (Harvey et. al., 1992). Keeping the above points in mind Leon (2008:272) conveyed the similar point in the context of selected emerging market including Greece, Korea, Thailand, Indonesia, Argentina and Brazil. Interestingly, he deducted a very puzzling point that, in these markets the relationship between the future return and dividend is systematically negative. Whereas, the prior studies by Fama et. al. (Nov, 1989:23-49) and others has shown that dividend return is natural variable for predicting the expected return. That implies a direct relationship between the two. On the contrary, Leon (2008:277-278) explained his finding by explaining the reinvestment of the dividend as the main reason; reinvestment of the sizeable amount of dividend reduces the return over the period. Besides this, they had found that, except Thailand the significance of risk focused investment strategies is minimal. Despite this, the timing of decision with respect to the volatility cannot be ruled as irrelevant in the same way. In summary, he inferred that conditional mean based strategies provide better return than conditional variance based ones in case of the emerging markets after leaving the exception of Thailand. As the mean variance framework is incorporated by many of the statistical financial models for example the Capital Asset pricing model and Arbitrage Pricing Theory therefore, examining its effectiveness is a curious case of study. To test the efficiency of the mean variance analysis Kandel et. al. (1986: 61) used a framework involving the correlation between the originally intended portfolio and the proxy portfolio. While going through the tests they concluded that efficiency of the mean variance method can be rejected if the efficiency of any other portfolio containing the subset of the original portfolio is rejected. As a result it can be said that, it is important part of portfolio selection but, its use might not give perfect answer to an investors about the portfolio selection Kandel et. al. (1986:87-88).

Conclusion

The mean variance framework is widely used for making the investment decisions. With the advancement in the theoretical and practical understanding its relevance in the modern day analysis still holds great importance. However, many assumptions have to be made before applying it to find the optimized portfolio; moreover, the difficulty in finding the appropriate data often constraint its use. Many small but significant issues affect the efficiency of obtained result but, it gives fair amount of planning power to the investor. Despite its weaknesses, its importance as a chief risk return analysis tool made many researchers to work on it and to find the solution for the weaknesses. With the advancements in the framework, it is widely used as a statistical basis for making the optimized investment decisions.

Refrences:

Black, F., Litterman, R., (Sep, 1991),”Asset Allocation: Combining Investor Views with Marketing Equilibrium”, Journal of fixed income, Vol 1, No. 2, pp 7-18 [Online Available] https://www.iijournals.com/doi/pdfplus/10.3905/jfi.1991.408013 Accessed on 30-03-2011 Breen, W., Glosten, L. R., Jaganathan, R., (Dec, 1989), “Economic Significance of Predictable Variations in Stock Index Returns” Journal of Finance, Vol. 44, No. 5, pp 1177-1189 [Online Available] https://www.jstor.org/stable/2328638 Accessed on 30-03-2011 Brown, C., (Dec 2005), “Financing Transport Infrastructure: For whom the road tolls” Vol 38, Issue 4, pp 431-438 [Online Availabe] https://onlinelibrary.wiley.com/doi/10.1111/j.1467-8462.2005.00386.x/pdf Accessed on 25-03-2011 Campbell, J. Y., Viceira, L. M., (2004), “Lond-Horizon Mean Variance Analysis: A User Guide”, Global Risk Guard, pp 1-3 [Online Available] https://www.globalriskguard.com/resources/assetman/assetall_0015.pdf Accessed on 21-03-2011 Chordia, T., Sarkat, A., Subramanyan, A., (2005), “An empirical analysis of stock and Bond Market Liquidity”, The Review of Financial Studies, Vol 18, No. 1, Oxford University press, pp 92-93 [Online Available] https://www.jstor.org/stable/3598068?origin=JSTOR-pdf Accessed on 21-03-2011 Cremers, J., H., Krizman, M., Page, S., (Sep, 2004), “Optimal Hedge fund allocations: Do Higher Moments Matter?”, Revere Street Working paper street, Financial Economics 272-13, pp 1-4,18-19 [Online Available] https://ssrn.com/abstract=587384 Accessed on 30-03-2011 Fabozzi, F, J., (2009), “Institutional Investment Management: Equity and Bond Portfolio Strategies and Applications”, Vol 177, Frank J. Fabozzi Series, John Willey and Sons, pp 4-6, [Online Available] https://books.google.co.uk/books?id=GrbnPFmoWAYCHYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”&HYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”printsec=frontcoverHYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”&HYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”dq=mean+variance+analysis+in+equity+and+bond+marketHYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”&HYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”source=blHYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”&HYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”ots=fcQtrZFw2LHYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”&HYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”sig=3_i87Rs7BlNdVU81j4KFvc5qx3QHYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”&HYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”hl=enHYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”&HYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”ei=1b2HTfeDN9C7hAe6t9y1BAHYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”&HYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”sa=XHYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”&HYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”oi=book_resultHYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”&HYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”ct=resultHYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”&HYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”resnum=3HYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”&HYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”ved=0CCsQ6AEwAg#v=onepageHYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”&HYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”q=mean%20variance%20analysis%20in%20equity%20and%20bond%20marketHYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”&HYPERLINK “#v=onepage&q=mean%20variance%20analysis%20in%20equity%20and%20bond%20market&f=false”f=false Accessed on 21-03-2011 Fama, E. F., French, K. R., (Nov, 1989), “Business Conditions and Expected returns on stocks and bonds”, Vol 25, Issue 1, pp 23-49 [Online Available] https://www.sciencedirect.com/science?_ob=ArticleURLHYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”_udi=B6VBX-45NHW7H-HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”4HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”_user=10HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”_coverDate=11%2F30%2F1989HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”_rdoc=1HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”_fmt=highHYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”_orig=gatewayHYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”_origin=gatewayHYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”_sort=dHYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”_docanchor=HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”view=cHYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”_searchStrId=1701407420HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”_rerunOrigin=scholar.googleHYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”_acct=C000050221HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”_version=1HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”_urlVersion=0HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”_userid=10HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”md5=3c01deb1a9027017042cb7e6341fe74aHYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”&HYPERLINK “https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBX-45NHW7H-4&_user=10&_coverDate=11/30/1989&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1701407420&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=3c01deb1a9027017042cb7e6341fe74a&searchtype=a”searchtype=a Accessed on 28-03-2011 Fidora, M., Fratzscher, M., Thimann, C., (Oct, 2006), “Home Bias in Global Bond and Equity Markets – The Role of Real exchange rate volatility” European Central Bank, Working Paper No 685 pp 5-10 [Online Available] https://www.ecb.int/pub/pdf/scpwps/ecbwp685.pdf Accessed on 21-03-2011 French, K. R., Poterba, J. M., 1991, “Investor Diversification and International Equity Markets”, American Economic Review, No 81(2), pp 222-226 [Online Available] https://www.nber.org/papers/w3609.pdf Accessed on 25-03-2011 Fung, W., Hsieh, DA., (1997), “Empirical characteristics of dynamic trading strategies: the case of hedge funds”, Rev Finance Stud, Oxford University Press, Vol 10, No. 2, pp 275-302 [Online Available] https://rfs.oxfordjournals.org/content/10/2/275.full.pdf+html Accessed on 30-03-2011 Harvey, C. R., Whaley, R. E., (Aug 1990), “Market Volatility Prediction and the efficiency of the S&P 100 Index Option Market”, Journal of Financial Economics 31, pp 43-74 [Online Available] https://faculty.fuqua.duke.edu/~charvey/Research/Published_Papers/P16_Market_volatility_prediction.pdf Accessed on 29-03-2011 Idzorek, T., M., (Jul, 2004), “A Step-by-step guide to the Black-Litterman Model”, Zephyr Working Document, pp 1-3, 27 [Online Availble] https://www.indiceperu.com/lecturas/paper13.pdf Accessed on 30-03-2011 Kandel, S., Stambaugh, R. F., (May, 1986), “On Correlations and Inferences about mean-variance efficiency”, Journal of Financial Economics 18, Issue 1, pp 61, 87-88 [Online Available] https://www.sciencedirect.com/science?_ob=MImgHYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”&HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”_imagekey=B6VBX-45R2HV6-6-1HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”&HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”_cdi=5938HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”&HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”_user=899436HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”&HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”_pii=0304405X87900614HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”&HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”_origin=gatewayHYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”&HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”_coverDate=03%2F31%2F1987HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”&HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”_sk=999819998HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”&HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”view=cHYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”&HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”wchp=dGLzVlb-zSkzVHYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”&HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”md5=c94a78e9c3c562f44fd66f5f88dbf3e5HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”&HYPERLINK “https://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VBX-45R2HV6-6-1&_cdi=5938&_user=899436&_pii=0304405X87900614&_origin=gateway&_coverDate=03/31/1987&_sk=999819998&view=c&wchp=dGLzVlb-zSkzV&md5=c94a78e9c3c562f44fd66f5f88dbf3e5&ie=/sdarticle.pdf”ie=/sdarticle.pdf Accessed on 30-03-2011 Leon, N. K., (2008), “Mean Variance Predictability and Economic Value in Emerging Equity Markets”, International Research Journal of Finance and Economics, Issue 14, pp 272, 277-278 [Online Available] https://www.eurojournals.com/irjfe%2014%20leon2.pdf Accessed on 21-0-2011 Liu, E, X., (2010), “Essays on International Finance and Risk Sharing”, University of Pennsylvania, Publicly accessible Penn Dissertations, Paper 206, pp [Online Available] https://repository.upenn.edu/edissertations/206/ Accessed on 25-03-2011 Martellini, L., Ziemann, V., (2007), “Extending Black-Litterman Analysis beyond the mean-variance Framework”, EDHEC Risk and Asset Management Research Centre, pp 3-4 [Online Available] https://www.edhec-risk.com/edhec_publications/all_publications/RISKReview.2008-01-22.3332/attachments/EDHEC%20Working%20Paper%20Extending%20Black-Litterman%20Analysis.pdf Accessed on 21-03-2011 Markowitz, H., Todd, G., P., Sharpe, W., F., (2000), “Mean Variance analysis in portfolio choice and capital markets”, Vol. 66, Frank J. Fabozzi Series, John Willey and Sons [Online Available] https://books.google.co.uk/books?hl=enHYPERLINK “#v=onepage&q&f=false”&HYPERLINK “#v=onepage&q&f=false”lr=HYPERLINK “#v=onepage&q&f=false”&HYPERLINK “#v=onepage&q&f=false”id=eJ8QUsgfZ8wCHYPERLINK “#v=onepage&q&f=false”&HYPERLINK “#v=onepage&q&f=false”oi=fndHYPERLINK “#v=onepage&q&f=false”&HYPERLINK “#v=onepage&q&f=false”pg=PR9HYPERLINK “#v=onepage&q&f=false”&HYPERLINK “#v=onepage&q&f=false”dq=mean+variance+analysis+in+equity+and+bond+marketHYPERLINK “#v=onepage&q&f=false”&HYPERLINK “#v=onepage&q&f=false”ots=t3pVVd9pkDHYPERLINK “#v=onepage&q&f=false”&HYPERLINK “#v=onepage&q&f=false”sig=twrWn39x8M5ytqXKhZlLCO9SNDo#v=onepageHYPERLINK “#v=onepage&q&f=false”&HYPERLINK “#v=onepage&q&f=false”qHYPERLINK “#v=onepage&q&f=false”&HYPERLINK “#v=onepage&q&f=false”f=false Accessed on 21-03-2011 Samuelson, P. A., (1969), “Lifetime portfolio selection by dynamic stochastic programming”, Review of Economics and Statistics 50-55 [Online Availabe] https://www.jstor.org/stable/1926559 Accessed on 28-03-2011 Sornette, D., Anderson, J., V., Simonetti, P., (2000), “Portfolio theory for ‘fat tails'”, International Journal of Theoretical and Applied Finance, Vol 3, Issue 3, pp 523-535, [Online Available] https://www.worldscinet.com/ijtaf/03/preserved-docs/0303/S0219024900000504.pdf Accessed on 29-03-2011 Terhaar, K., Staub, R., Singer, B. D., (2003), “Appropriate policy allocation for alternative invesments”, Journal of portfolio management, Vol 29, No 3, pp 101-110 [Online Available] https://www.iijournals.com/doi/abs/10.3905/jpm.2003.319888 Accessed on 29-03-2011

Did you like this example?

Cite this page

The use of Mean Variance Analysis in the economy. (2017, Jun 26). Retrieved June 29, 2022 , from
https://studydriver.com/the-use-of-mean-variance-analysis-in-the-economy/

Save time with Studydriver!

Get in touch with our top writers for a non-plagiarized essays written to satisfy your needs

Get custom essay

Stuck on ideas? Struggling with a concept?

A professional writer will make a clear, mistake-free paper for you!

Get help with your assigment
Leave your email and we will send a sample to you.
Stop wasting your time searching for samples!
You can find a skilled professional who can write any paper for you.
Get unique paper

Hi!
I'm Chatbot Amy :)

I can help you save hours on your homework. Let's start by finding a writer.

Find Writer