# DIFFERENT TYPES OF PORTFOLIO THEORY

## Introduction

The word “Portfolio” can be defined as; the totality of decisions determining an individual's future prospects” (Sharpe, 1970). Portfolio can consist of many types of assets such as plant, property, real and financial assets (P.A Bowen, 1984). Portfolio theories propose how rational and prudent investors should use their due diligence to diversify their investments to optimize their portfolios, and how a risky asset should be priced as compared to less risky asset. People have been investing in the different assets class since decades but then they realize the importance of risk and its negative implications, if not treated effectively. Every investor has his own tolerance of risk and investor's defines it in his ability of taking it. The portfolio theories have been derived over time in order to effectively measure the risk and how it can be reduced by diversify in their asset.

## Article 1: “The Legacy of Modern Portfolio Theory”

This article covers the highlights of modern portfolio theory, describing how risk and its effects are measured and how planning and asset allocation can help you do something about it. Modern portfolio theory is the theoretical conflicting of conventional stock picking. It is being put forward by the economists, who try to understand the phenomena of the market as a whole, instead of business analysts, who look for individual investment opportunities. Investments are explained statistically, as how much investor expected long-term return rate and their expected short-term volatility. It measures how much expected return can deviate much worse than average an investment's bad years are likely to be. The goal of the theory is to identify your adequate level of risk tolerance, and then to come up with a portfolio with the maximum expected return for that level of standard deviation (risk).

### The portfolio it assumes that the investment universe consists only of two market securities, the risk free asset and risky assets. But the actual investment universe is much broader than that being put forward. The optimal level of investment is to invest on efficient frontier but doing this would mean to calculate the millions of covariance among the securities. This calculation could make the life of analyst as difficult as one could have ever imagined. To think practically, it's better to put portfolio theory to work means investing in a limited number of index securities rather than a huge number of individual stocks and bonds. Index investing is the point the where portfolio theory starts to rely on the efficient market hypothesis. When you buy an index based portfolio strategy you're allocating your money the same way the whole market is - which is a high-quality thing if you believe the market has a plan and it is efficient. This is why portfolio theory is one of the branches of economics rather than finance: instead of only studying financial statements and different financial ratios, you study the aggregate behavior of investors, some of whom seemingly *have* studied financial statements so that market valuations will reflect their due diligence and prudence.

## Article 2: “Theory of portfolio and risk based on incremental entropy”

The article has used incremental entropy to optimize the portfolios. This novel portfolio theory has been based on incremental entropy that carries on some facet of Markowitz's (1959, 1991) theory, but it highlights that the incremental speed of capital is a more objective criterion for assessing portfolios. The performance of the portfolio just cannot be justified with the returns because we have to keep in mind the risk of achieving those returns. Given the probability forecasts of returns, we can obtain the best possible investment ratio. Combining the new portfolio theory and the general theory of information, we can approach a meaning-explicit measure, which represents the increment of capital-increasing speed after information is provided. The article has used example to make it more clear that as we try to become rich within days there involve high risk of even losing those money which we at-least own at present. The ineffective investment is like a coin toss either you have all the money in your pocket or you end having nothing in your pocket. The same being very risk averse would not help you become rich. You there has to be a balance in selecting the portfolio and this article explain the optimal investment ratio. (pg 1)

Markowitz explains us that an efficient portfolio is either a portfolio that offers the maximum expected return for a given level of risk, or one with the minimum level of risk for a given expected return. There is no objective criterion to define the maximum effectiveness of a portfolio given the expected return and risk level and different expects have different view about it. The Markowitz's efficient portfolio tells us about the indifference curve of the investor and about the market portfolio. It is not the portfolio which we need for the fastest increment of capital. So, this article has derived a new mathematical model.

The model explains that when gain and loss are have equal chance of occurring, if the loss is up to 100 percent, one should not risk more than 50 percent of fund no matter how lofty the possible gain might be. This conclusion has a great importance and significant for risky investments, such as futures, options, etc. Most of the new investors of future markets lose all of their money very fast because the investment ratios are not well controlled and generally too large. we can obtain the optimal ratios of investments in different securities or assets when probability forecasts of returns are given.

#### Comparison with Markowitz's theory

The new theory supports Markowitz's conclusions that investment risk can be reduced by effective portfolio, but there are some obvious differences: The new theory uses geometric mean return as the objective criterion for optimizing portfolio and gives some formulas for optimizing investment ratios; and . The new theory makes use of extent and possibility of gain and loss rather than expectation of return and standard deviation (risk) of the return to explain investment value.

## Article 3: “On the competitive theory and practice of portfolio selection”

To select an optimal level of portfolio has always been a basic and fundamental problem in the field of computation finance. There are lots of securities are available including the cash and the basic online problem is to agree on a portfolio for the ith trading period based on the series of price for the scheduled i-1 trading period. There has been increasing interest but also mounting uncertainty relating to the value of competitive theory of online portfolio selection algorithms. Competitive analysis is based on the worst and most unexpected case scenarios and viewpoint; such a point of view is conflicting with the most widely used analysis and theories being adopted by the investors based on the statistical models and assumptions. Surprisingly in some of the initial experiments result shows that some algorithms which have enjoyed a highly regarded repute seems to outperform the historical sequence of data when seen in relation to competitive worst case scenarios. The emerging competitive theory and the algorithms are directly related to the studies in information theory and computational learning theory, in fact some of the algorithms have been the broken new ground and set new standards within the information and computational theory learning based communities. The one of the primary goal and objective of this paper is understand the extent to which competitive portfolio algorithms are in reality learning and are they really contributing to the welfare of the investor. In order to find out so they have used set of different strategies this can be adapted to data sequence. This is being presented in a mixture of both strong theoretical and experimental results. It has also been compared with the performance of existing and new algorithms and respects to standard series of the historical sequence data and it also present the experiments from other three data sequence. It is being concluded that there is huge potential for selecting portfolio through algorithms that are being derived from competitive force and as well as derived from the statistical properties of data.

## Article 4: “International property Portfolio Strategies”

The article talks about the investment decisions regarding real estate, and try to put in the Markowitz mean variance formula to analyze the real estate market. They are not confined only to local real estate diversification but they are also including international diversification. Markowitz mean variance continuum and graph is useful in analyzing the efficient securities, and they help in the selection of an optimal portfolio on envelope curve taking into account the risk preferences of an investor. But when analysts try to incorporate real estate market to the Markowitz theory the major problems regarding liquidity, heterogeneity, indivisibility and information are faced by them which restrict them from further optimal analysis.

Many investors have tried to support the theory to make a portfolio by considering property as asset like equity and bond investments; although there are a lot of differences among the characteristics of assets discussed above, but one can diversify its portfolio by investing in real assets, analysts argue. The discussion was dominated by the concept of international diversification of assets including real estate. To support the analysis in UK the (Sweeney , 1988-1989) work in cited most of the times, he came up with the famous model of real estate to come up with efficient diversification strategy, he used rental value of for different countries and came up with the model of risk return theory; after that a lot of analysts including: [Baum and Schofield (1991), Brühl and Lizieri (1994), Gordon (1991), Hartzell et al. (1993), Johnson (1993), Sweeney (1993), Vo(1993) and Wurtzebach (1990)], have come up with analysis to support international diversification; but the result was somehow was not justifying the inculcation of real estate to portfolio theory, because those assets were not correlated at all when inspected for the risk return behavior during last decade or so. This can be attributed to the failure of mean variance model to produce results, the main problems facing would be regarding data collection, technicalities, omitted categories, and ex post analysis.

This is almost irrational and impossible to find the most efficient way to diversify a portfolio by including real asset as a separate asset, because of area problems, different locality, pricing conditions, economic conditions, liquidity differences, and data collection problems. As real estate market is highly uncorrelated even within the industry so the data sets are very difficult to find for analysis because of lack of empirical data on this market.

## Article 5: “Different risk measures: different portfolio compositions?”

Choosing the suitable portfolio of assets in which to invest is an essential component of fund management. A large percentage of portfolio selection decisions were based on a qualitative basis, however quantitative approaches to selection are increasingly being employed. Markowitz (1952) established a quantitative framework for asset selection into a portfolio that is now well known. The measure of risk used in portfolio optimization models is the variance. Variance calculates how much deviation could be expected from the set of portfolio. The alternative methods of risk have their own theoretical and practical advantages and it is atypical that they are not used widely by investors. One of the reason may be because of the difficulty and complexity of understanding such models and then practically implementing those models and to decide in which measure of risk is best and gives the most realistic and useful results. It is important to identify the common risk measure and without doing so any attempt to measure the risk would be useless exercise. In order to cope with this, another approach is considered that is to comparing the portfolio holdings produced by different risk measures, rather than the traditional risk return trade-off. It is than being observed that whether the risk measures used produce asset allocations that are essentially the same or very different. In order to probe this concern this study tested the proposition that different measures of risk produce minimum risk portfolios that are essentially the same in terms of asset allocations, using monthly data over the period January 1987 to December 2002. The results show that the optimal portfolio compositions formed by different risk measures vary quite noticeably from measure to measure. These finding are very useful and have a practical implication for the investors because it recommend that the choice of risk model depends entirely on the individual's attitude to risk rather than any theoretical or practical advantages of one model over another. It has been concluded that different investors have they indifference curve different from other and some of them like to take more risk as compare to other who are happy at earning low but safe returns.

## Conclusion

It is being concluded that risk is more of a subjective term and different analysts and investor measures and perceive it in their own way. In today's word not even a single person can underestimate the importance of risk in selecting a security and emphasized is been given to diversification through proper portfolio selection process and everyone tries to optimize their returns given a certain level of risk. In order to do so they are using different statistical measures those have been derived over time to calculate risk. So selection of such method is limited to the understanding of a certain method to a certain investor and their effectiveness of results as compare to other methods.

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