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Literature Review On Selection Of Funds

2.1 Introduction

In order to successfully accomplish any research, the key ingredient for its success would be the deep and fine understanding of the concerned subject or topic in consideration. Thus, in this literature review, I would critically review the factors responsible for the performance of a portfolio and also, the key theories related to the performance and evaluation of a portfolio.

In this chapter, I would like to put light on certain key issues related to the diversification of the portfolios. To begin with, I would like to start with the options of selecting funds so as to make a competitive portfolio. Then, the stress would be on the key factors that are capable of measuring the performance of the portfolio like profit, beta, and different portfolio evaluation measures like Sharpe ratio, Jensen ratio and Treynor ratio. In order to start with any portfolio, the benchmark should be in the mind of the investor as to what does he expects out of this investment. Then, I would measure the performance of the portfolio for its regularity and its persistence.

Then, we stress on the main theories of asset allocation that should be followed when a portfolio is to be made. And, once the assets are allocated, the key is to synergize the funds as per the expectations and capabilities of the investor.

The key measures to be kept in mind when investing in the portfolios are correlation, covariance and risk taking ability (i.e. alpha). This might turn out to be quite an interesting theme, since a small change in correlation among the portfolios and the covariance between them can bring in huge change for the returns of the investor. The key to reduce the risk while not compromising on the return is to diversify the portfolio. But, here we have to keep in mind that we don’t over diverse the portfolio since the more the number of stocks in a portfolio, the more is the complexity to deal with the scenario.

According to Markowitz (1991), a portfolio is more than just a list of stocks and bonds, it is a balanced set of investment which keeps in mind the risk seeking capability of the individual without negating the opportunities that are hidden in it and also bringing into notification the threats associated with it. The key to make a portfolio is to make one which suits the individual needs of the investor. This is generally done by analysing the portfolio. The primary information that can be used so as to make an efficient portfolio is the historical performances of the stocks in consideration. Another source of information can be the trust of experienced security analysts in the better performance of the share in future. When the historical performances are kept in mind while choosing the stocks, the outcome is a list of stocks that performed better than others in the past. While, in the latter case, the output is the list with stocks that analysts think would perform better.


Before the funds are to be even considered so as to make an effective portfolio, the key question that the investor faces from the portfolio manager is about his financial stability, motto of his investment and ability to bear risk. A key source about the performance of the stock markets since 1926 up to the present date is Ibbotson Associate’s Yearbook, stocks, bonds, bills and Inflation. This book has covered the overall performance of the stock market during different times such as war, peace, globalization and conservatism to name a few. The main elements that can be included into the portfolio are Fixed Income investments, Equity instruments, Equity derivatives, Futures contract, Investment firms and real estates. (Gibson, R, 2000)

According to Fabozzi (2002), a fixed income security to be put in simple words is the monetary commitment of a firm to the investor so as to pay certain sum of money at some specified pre negotiated contract dates. Some of the main issuers of the U.K. government, local governmental councils and institutions that are huge in structure like IMF and World Bank. It generally falls under two basic categories, i.e. preferred stocks and debt obligations. A preferred stock fixed income security represents a chunk of ownership in the organisation. The repayment to the investor includes both the dividend on the ownership and the original fixed amount. The dividend is the part of the profit’s generated by the organisation. Another kind is Debt obligation fixed income security. In this, the issuer is the borrower while the other half is called as lender. The payment given to the investor consists of interest and a part of the original investment returned.

According to Chorafas (2005), an equity stakeholder is a part owner of the company and anyone can become a part owner of the company since these shares are publicly traded in the market. These common stocks entitle the holder to have a chunk of the profit share of the organisation and this is variable depending upon the performance of the organisation. While, this might turn out to be a fruitful affair, it might even be dangerous if in case the company is liquidated, then these people are the last one’s to get their money back. While, another option of investing is equity derivative, which like common shares entitles the holder to have a claim on the ownership of the organisation. This includes options which give the holder the power to choose as to buy, hold or sell the stock at a specified time and at a specified price. The options included in this are warrants and put & call options. (Francis, J, C, Toy, W, W, Whittaker, J, G, 2000)

Apart from this, other key options in investing are Futures contract which is like a contract where two parties trade a particular asset at a negotiated price at a fixed date. Also, these days, one of the most popular alternatives in investing is to shadow invest some of the popular investment firms which according to their experience and expertise invests in some of the best stocks in the market. These investment firms trade in a very versatile market ranging from money market funds, bond funds, common stock funds to balanced funds, index funds and exchange traded funds. According to Eldred, G (2009), in the current ever developing scenario, an option for investing has popped out by the name of real estate. Since, as the globalization is increasing, it is further leading to steep increase in the prices of real estates as the prices of the property are appreciating. (Brown, K, C, Reilly, F, K, 2009)


In order to make a portfolio performance worthwhile considering, an investor has certain limitations in his mind which guides his/her performance. The mind frame of the investor determines the level of success; he/she is entitled to. Before investing his wealth into the stock market, an investor has certain expectations and limitations that channel his ambition in it. Since, it is well known, that the higher the risk the person is willing to take, the higher the return he would be entitled to. The most important factor that keeps on revolving in every investor’s mind is the profit that he would be entitled to while investing in certain set of stocks. This profit might be in the form of dividends which are distributed to the investors or it might come when the stock is traded in the exchange. This thing is generally resembled in the form of financial health of the company which is easily gauged by the financial ratios of the organisation in comparison to its past and the industry competitors. (Chincarini, L, B, Kim, D, 2006)

Then, another feature guiding an investor is beta. It is termed as a measure of the systematic risk within the set of stocks listed in the portfolio. According to Jacobs, Levy, Anson (2005), beta is defined as risk which is calculated as the covariance among the returns on the asset or set of stocks in a portfolio divided by the variance of market returns. This factor signifies the sensitivity of the price change of the asset in comparison to the market as a whole. It ranges from +1 to -1, where +1 means that the portfolio is in perfect correlation with the market and -1 means that the portfolio is perfectly uncorrelated to the market as a whole. (Ramesh, R, 2000)

According to Vinod and Reagle (2004), the most practical solutions offered for evaluation of a portfolio performance are Sharpe, Jensen and Treynor measures which are most commonly used by the investors to choose a list of stocks in the whole possible list of mutual funds. Sharpe measure is basically used so as to measure the surplus return per unit of risk being taken by the investor. An investor would prefer a portfolio with large Sharpe ratios as it is thought that any rational investor would like to minimise the risk on his investment. (Bernrud, E, Filbeck, G, Upton, T, 2005) Also, Logue and Rader (1997) came forward with the concept that Sharpe measure is the most suitable ratio if the investor would like to adjust risk on his investment. While, Jensen (1969) developed a performance measure which stresses the relevance of relation between market risk and the return on the portfolio. It is measured as the difference between real return on the portfolio and the return on the whole market portfolio. Quite similar to this was Treynor measure, which gave the freedom to interpret the relativity between rewards to risk factor. A high treynor measure is preferred as compared to a smaller one. (Baker, Logue, Rader, 2004)

The last factor for performance measurement that we consider over here is Value at risk. It is defined as the most horrible loss possible within a specified time frame at a given level of confidence. More formally, it is defined as the quantile of the projected distributions over a specified time frame of the gains and losses. It is generally suited for a short trading horizon and massive turnovers. (Jorian, 2000)


When an investor decides of investing his capital in a portfolio, he has certain expectations from that portfolio which he expects to be fulfilled. The portfolio manager is expected to work as per the benchmark set or expected by the investor. This way of managing funds is termed as index managing while the counter parts that are least bothered with the benchmarks are termed as active managers. The manager is expected not to divert much from the benchmark limit set to him.

This step might turn out to be quite an important step as it is through this step that the investor compares an orange with an orange. (Travers, F, 2004)

One of the most simple and traditional methods is ad hoc method where the investment manager selects a portfolio with the same number of stocks in it, with the largest capital in the stock market and then compare with this to be the benchmark according to the weight of each stock in the portfolio. Another popular way is to set the beta of the portfolio equal to 1 or as close as possible to it. This way the manager ensures that the risk level of the portfolio doesn’t cross the limit. (Chincarini, L, Kim, D, 2006)

The traditional way to set the benchmark in a portfolio was to base the performance of the portfolio on the term based alpha. Jensen’s (1968) alpha is the key measurement factor if the case in consideration is a capital asset pricing model which gives the information on excess return on the asset’s average return. Here, information is before hand provided on beta (systematic risk) and the benchmark return set.

Another theory from Chen, Roll, and Ross (1968) where the returns on the asset is calculated on the basis of the external influential factors such as the cash flows, discount rates, Gross national product and inflation. This is useful in case of multi factor models which have a bit different theory than single index models.

Sharpe (1992) gave his own theory which broke down the portfolio return into several key factors which are based on the asset classes chosen like growth, income stocks, and value stocks and high and low yield bonds. On the contrary, Gary and Goetzmann (1986) brought in the theory that the return on the stocks is based on the correlation across managers signifying the role of common strategies among the managers.

Although, Schneeweis and Spurgin (1998) were in the favour of using various standard indexes famous in the financial sector like Goldman Sachs commodity index, the Standard’s and Poor’s 500 stock index, MLM index and Salomon index government bond index. (Gregoriou,G, karavas, V, Lhabitant, F, 2004)


The performance of any portfolio or investment manager is based on the returns he has provided to his client or how close has he matched or maybe over-performed his client’s expectations.

Risk is a familiar term to each and every human being who ever invested or not. It might look a cake walk to define risk but it has different meanings depending on the nature of the human being. Risk is generally measured in terms of loss of capital. Or, it might also be defined in terms of loss of opportunity which is the risk to perform beneath the benchmark.

Basically, risk is the insecurity that goes with the expectations of return of the investor. Like, it is commonly observed that when the horizon of time in consideration is long, then it is risky to invest in small cap equities as they are volatile. While, the large cap equities might give out a small but balanced output. The golden thumb rule in investment is “THE MORE IS THE RISK, THE MORE RETURN CAN BE EXPECTED”.

The key to expect the return would be to measure the risk being taken by the investor. It is generally assessed based on the performance of the past but doesn’t heavily rely on that. The most traditional way to assess risk is on the basis of the histogram that plots the return graph of the concerned stock at a specified time frame. Here, the variation in the returns is observed.

The most preferred way to assess the variability in the returns is standard deviation which is termed as the variation of the results in comparison to the mean i.e. what is the variability in the results of the manager as compared to his expectations. (Lavinio, S, 1999) For the proper utilisation of the data of standard deviation, the time period should be large enough so that no single entry can change the result significantly. In order to get a true and clear figure, the standard deviation should be compared to some benchmark which would further give a clear picture of the performance.

The most common way to put ahead the relation of return and risk is to make a return- risk graph which depicts the performance of the portfolio in relation to the risk taken to achieve it. An investor would like to maximise the returns on the certain risk he can talk. This graph is very helpful as it can easily depict the performance of the portfolio in comparison to any number of benchmarks. There is no certain method to calculate risk and lots of methods can be used alternatively depending on the choice of the investment manager.

The Sharpe measure was the first measures that took in consideration the relation of both risk & return and helped the investor to gauge risk adjusted return. This measure provided the investor the view on the return earned on every unit of risk taken and provided a good view when it was compared to a benchmark. Another method was the one presented by Modigliani’s which showed the performance of any portfolio in comparison to the adjusted risk. This portfolio was adjusted until the volatility of the portfolio is equal to that of a benchmark. If the volatility of the portfolio is less than that of benchmark, then they expanded the portfolio by leveraging it assuming a certain borrowing rate; while, if the volatility is over the benchmark then the portfolio is contracted and some of the money is invested at a certain yield. There theory is that it doesn’t matter whether the organisation is financed by equity or capital, it does not matter. (MacMinn, R, 2005)

Another key ratio used to relate the performance of a portfolio in relation to risk and return is information ratio. It is used to gauge the performance of the investment manager is relation to its benchmark. This ratio is exclusively used to measure the extent to which the portfolio over –performed or under-performed in relation to a benchmark. (Fong, G, 2005) Similar to Sharpe ratio is Treynor ratio where the numerator of both ratios is same but the denominator varies as Treynor ratio is only concerned with systematic risk or non-diversifiable risk (called as beta) and Sharpe ratio is concerned with the total risk (standard deviation) in the system. Beta is termed as the slope of the line in a regression equation. If the value of beta is greater than one, then it is termed as volatile and movement sensitive. While if the value of beta is less than one, then it means that the portfolio is less volatile. And if value of beta is equal to one, it means that the sensitivity of the portfolio is equal to the market index.

Another popular measure is Jensen’s alpha, which is termed as the difference between actual return of the portfolio and the return on the benchmark portfolio with the same level of risk. This ratio tells the performance of the actively managed portfolio in relation to its benchmark. Another risk adjusted measure is Sortino’s ratio, based on the name of its creator, Frank Sortino, which adopts the concept of downside risk rather than the standard deviation. Downside deviation is described as the risk of not getting through to the target return which can be set by any of the returns. (Travers, F, 2004)


The most common and easily understood method to determine the performance of the portfolio is to look at the performance in terms of alpha, i.e. how many weeks has the portfolio experienced positive alpha’s and in how many weeks has it experienced negative values of alpha in a certain time frame. This is a really good measure to gauge the performance of the portfolio in comparison to its benchmark. After assessment of this performance, another question that pops up is whether the performance of portfolio is driven by the investment manager or it is driven by sheer luck of the market, since the results are statistically improbable.

This question can be answered by the use of Hurst exponent which is applied to the profits made by the portfolio and alphas experienced by it. Hurst exponent was developed by the British hydrologist, H. E. Hurst, when he was asked to calculate the best storage capacity of the reservoirs of River Nile, since the area was experiencing frequent floods. It provides the information on the variability and repeatability of a certain event without making any assumptions on the distribution of the data. (Lavinio, S, 1999) Lots of techniques are available for estimating Hurst’s exponent, but the real issue to deal with is its accuracy. But, there is no exact value of Hurst’s exponent as time is an unbound phenomenon, which further leads to changing values of factor H. The value of H rotates between 0 and 1, where higher values indicate that the trend is less volatile and smooth with few roughness patches. (Mandelbrot, B, 2004) A value of H=0.5 indicates the random walk movement, generally referred to as Brownian time series. In such a case, there is no probability or we can say equal probability of each event to occur and nothing can be predicted. Generally, most mature markets have Hurst’s exponent close to 0.5 suggesting that they are more balanced than their emerging counter parts. The main drawback of Hurst’s exponent is that it indicates only a number and not the direction of performance, thus its interpretation can be a tough job. Since the value can be close to 1 if the investment manager is doing a great job or he has been consistently performing poor. Thus, to negate the drawback of Hurst’s exponent, it is used in combination with D-Stat test.

This test is the absolute value of the summation of alphas or profits in consideration of the certain portfolio divided by the fixed value of alphas or profits. Thus, it would help the analyst in judging whether the performance which was described without direction in Hurst’s exponent is a good performance or poor performance. But, all of these tests stand justified on the basis of past performance and would not help in judging the future performance. Their effectiveness was tested in a series of tests in 1997 and 2002 whereby it was concluded that it could identify the regular over performers as compared to their benchmarks. (De Souza, C, Gokcan, S, 2004)


The markets have been changing at a very rapid pace in the past few decades, leading to the evolution of the term asset allocation. The conventional theory of diversification was to avoid putting all eggs in a single basket which meant that investing in a single share would either lead to a great win or a big lose, but if the investment is properly spread out then it leads to less risk as not all investments can fail at the same time. The investment manager’s role was to add value to the portfolio with his immaculate timings and finer equity selection.

In an article published in 1952, by Markowitz, H, he described a model to reduce the volatility in a portfolio by combining securities which had different patterns of results. This was the theory that forced the analysts to think on the inter-relation of returns among stocks. With the ever changing world, the traditional view of putting a long list of stocks in a portfolio is an old tale. Developing a portfolio is done in a sequence of steps.

Choosing which asset classes to be included in the portfolio

Setting the target return in long term horizon to each of the asset classes

Setting a range in each asset class to exploit the market conditions and over performing over other assets

Choosing securities in each of the asset classes

(Gibson, R, 2000)

The key concept that evolved was the concept of Modern Portfolio theory which stated the concept of taking less risk and maximising return by selecting the right number of securities from each asset class. Here, the key to selecting the security is to lower the factor of correlation among the assets selected. Thus, the idea is to find numerous asset classes with a low correlation factor. While, efficient market theory stated that the movement in the prices of stocks is like a random walk factor. The strong form of EMT asserts that the prices of stocks reflect all the publicly and privately available information from the past, present and forecasts of the future. While, the semi strong form of EMT emphasizes that the prices of the stocks only reflect the publicly available information from the past, present and future forecasts. The last form of EMT, i.e., weak form of EMT emphasizes that the prices of stocks only reflect publicly available past information and nothin else. (Ferri, R, A, 2002)

The main concepts that affect the factor of asset allocation are divided into economic, statistical and financial concepts. The first fundamental is to relate the reaction of market to the information which is described by the concepts of Modern Portfolio theory and Efficient Market theory. Then comes the concept of grouping the returns on the assets based on their averages which is explained by Normal Probability distribution, standard deviation of distribution, variance and semi variance of distribution, Mean of distribution and its z-score. Once, the returns are grouped, then their interrelation is checked by the theories of covariance of returns, correlation of returns and R squared coefficient of determination.

After checking the returns and its relations among each others, the key to portfolio theory and every theory in this field comes i.e. to maximise the return and minimising the risk at the same time. This is done by setting up an efficient frontier and using risk adjusting measures like Sharpe ratio, Sortino ratio, treynor ratio and mean variance optimization technique. Since, the returns are maximised at the current levels of risk, now the theories that secede are on justifying the optimal return on the risk that was being taken by the investor. The theories that explain this concept are Capital Asset pricing model, Capital market line, security market line and Alpha & beta factors. (Darst, D, H, 2008)


All the concepts and theories of Portfolio management, diversification or observation rotate around some key factors that should be clearly understood. Some of them are standard deviation, covariance, correlation, alpha, beta, and variance.

Risks are categorized under two headings of systematic risk and unsystematic risk. Systematic risk is the un-diversifiable risk which is beyond the range of investor to disperse but unsystematic risk shows the diversifiable risk which has the possibility of being diversified away with carefully monitoring and adding the stocks in the list.

Standard deviation is defined as the measure of scattering of data around the mean or average. If the value of standard deviation is low, then it means that most of the values in consideration are around the average or benchmark as it is called. But, if the value of standard deviation is high, then it means that most of the values are not close to the benchmark and thus representing volatility in the system. A portfolio with high standard deviation is considered risky.

Where: = standard deviation

= value of x from the set of observation

= mean value or benchmark

It is basically used to symbolize the risk adjoining the security or a portfolio. Risk is an important factor in consideration as it helps the investor in assessing the means to reduce the risk in his portfolio of securities. It helps in gauging the variability of the returns in the portfolio which is explained by Mean variance optimization. The basic theory still remains the same as the more is the risk that the investor is bearing, the more return, he/she is entitled to. (Ghahramani, S, 2000)

According to Darst (2008), if the standard deviation is high, then it means that the chances of the actual return as compared to the expected one’s being different are quite high. This condition represents the state of risk, uncertainty and doubt.

While, this method is termed as highly relevant in the field of statistics and finance, albeit even it has certain limitations. Firstly, this method is relevant only in gauging the symmetrical patterns of distribution, where the risks are equal on both the sides, i.e. upside risk and downside risk. Thus, this method would fallback if the distribution is not normally distributed like in asset classes, such as Options and Portfolio Insurance strategies. Another limitation is that, due to the statistical nature of this phenomenon, the standard deviation is incapable in imitating behavioural aspects of investing. Also, this method disregards the mean-return concept as the one showing the risk in the investment. Another limitation of this technique is that, since the distribution in the real world is not normally distributed (i.e. probability distribution curve), it is required to be calculated every time for a different time period. (Ramesh, 2000)

Another key term is Variance, which is defined as the expected mean value of the square of the deviation of the variable from its mean. This led to the birth of Mean variance analysis which is the base of Modern Portfolio Theory. The work on this classical phenomenon was given by Markowitz in 1952 and was further improved upon in 1987. The benefit on any portfolio is determined by the return that can be expected from it. The variance of any portfolio return is used to explain the concept of diversification, i.e. the higher the variance is, the lower is the diversification intensity.

The key phenomenon’s guiding the Mean variance analysis is to find the portfolios with low variance based on the low bound expected performance. And, if the level of diversification is upper bound, then to find the ones with greatest expected returns. ()

Another aspect of seeing the risk discovered in Post Modern Portfolio Theory era is Upside risk and Downside risk, where it was found that an investor prefers upside risk rather than downside risk utilising semi-standard deviation. Semi-standard deviation calculates the inconsistency of performance under the target rate or benchmark. In the calculation of downside risk, all the positive returns are marked as zero. Or, a curve can be fitted to show the probability of returns that under-perform (Sortino and Satchell, 2001)

The risk that is measured by the Variance in the portfolio is categorized under two sub headings: 1) systematic risk, related to the correlation of returns among the securities and 2) Unsystematic risk, related with individual securities. If the returns on the assets in the portfolio are not correlated with each other, then the variance of the portfolio moves towards zero, indicating that the portfolio is well diversified. The general tendency while adding the securities in the portfolio is to diversify the portfolio in such a way so as to reduce the specific risk associated with it. While, systematic risk remains unaffected by diversification. Most investors would like to prefer a portfolio with the minimum variance at a specified mean. These investors are termed as risk averring investors as they like to play safe. In the same way, at a given standard deviation, most investors would choose the highest mean. An efficient combination would be the set of achievable mean-standard deviation blend. Such a set would be termed as efficient frontier and the portfolio as efficient portfolio.

If we imagine that the market portfolio is a portfolio consisting of all the risky assets, then the efficient frontier would be a line starting from the risk-less point and hitting the market portfolio. This line is termed as Capital Market line which depicts the relation between the expected rate of return and the risk. The prices of the stocks should be adjusted in such a manner that all the efficient portfolios fall on the efficient frontier. This is the basis of the theory called Capital Asset Pricing Model depending on the basis of risk adjusted returns. (Lyuu, Y, 2001)

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