Financial Risk Investment - Free Essay Example

Sample details Pages: 23 Words: 6768 Downloads: 1 Date added: 2017/06/26 Category Finance Essay Type Research paper Did you like this example? Investment and Financial Risk Management. A performance analysis of UK based speciality sector funds Abstract Several studies have charted the performance of mutual funds across various styles and investment strategies; this study aims to contribute to previous literature by presenting a performance analysis of a subset within mutual funds known as sector funds; focusing particularly on property, technology and financial funds in the UK market. The study aims to inform investors of this particular style of investment by addressing the risk and returns of this product. Don’t waste time! Our writers will create an original "Financial Risk Investment" essay for you Create order This paper analyses the performance of constructed portfolios of approximately 50 mutual funds per sector over an approximate 10 year period relative to a given benchmark. The study uses established performance measures such as the Sharpe and Treynor ratio, Jensens Alpha, and Carharts multifactor model. The findings of this study are that every portfolio has significantly underperformed relative to its assigned benchmark, the worst performing sector funds were from funds concentrated in the technology industry. Although there was underperformance, on a risk adjusted return level, property funds provide the most stable returns to investors. Sector funds should not be used a stand alone investment strategy but may have a place in a portfolio of funds. Introduction This paper examines the performance of a subset within mutual funds known as sector funds. These are in fact portfolios of stocks with a high weighted concentration invested entirely on a particular industry in which the fund manager believes that the portfolio of selected stocks will provide returns in excess of the industry benchmark. This may also be the view of the investor who may also invest for hedging or speculative purposes. In recent times there have been significant changes in the attitude of investors towards speciality sector funds and the returns that are required. This paper will examine the performance of UK sector funds in order to establish the effectiveness of these types of investments, whether there is any persistence in the returns achieved over a period of time, in order to conclude whether sector funds do outperform the market. For this investigation 50 UK funds will be selected from 3 of the main sectors of investment, namely: Financial Services, Real Estate, and Technology. The data will be collected from Thomson Data Stream and will consist of monthly prices over a period of 15 years. Data will also be collected on the relevant benchmarks for each sector, specifica lly the returns of the FTSE All Share index for each of the aforementioned sectors for the 15 year period. The risk free rate will be calculated from the rate of return from investing in a UK 1 month T-bill. In order to investigate performance of the funds the following models will be implemented: Jensens Alpha, Sharpe Ratio, Treynor Ratio, and Carharts Four Factor model. The data will then be analysed using various statistical methods such as regression analysis and then presented in a way to clearly assess the relative returns over the specified time period. What is a mutual fund? A mutual fund can be described as a financial intermediary or investment vehicle which allows investors to pool together their funds and invest in a diversified portfolio of securities such as stocks and bonds with a predetermined investment objective. In the UK, mutual funds are commonly referred to as Unit Trusts. The investor is in fact investing in a unit or portion of an already diversified po rtfolio and achieves returns through income from the fund and capital appreciation. What are its advantages and disadvantages? One of the primary benefits of investing in a unit trust is diversification. As investors are buying a portion of a portfolio as opposed to an individual stock the volatility of returns on one stock may not have a significant effect to the overall portfolio value; a loss on 1 individual security may be offset against the gain in another. Diversification of unit trusts can also be attributed to the fact that these funds have exposures to several stocks and bonds with different risk profiles, furthermore the weighting of each asset in the portfolio ensure that risk is minimised. There is also the benefit of professional management, securities within funds are bought and sold by a professional fund manager, which means that the investor has no role in selecting the stocks of a particular fund or research into the type of stock that might improve the fund. In other words the professional managers have more money to research stocks than an individual investor; money which is sourced from expense and transaction fees from every investor. These funds are also liquid; funds can be bought or sold in a way similar to stocks however this may take a few days to settle. Funds are traditionally meant to be held for a long term period however this is still down to investor preference. Unit trusts also provide a level of convenience for the investor, with information easily obtainable online or by telephone. Investors also benefit from economies of scale through lower transactions costs; if investors wanted to achieve a level of diversification with equity investment the transaction costs would be much higher due to the lack of volume of securities being bought and sold. The disadvantages associated with investing in unit trusts are expenses, tax, and lack of control over stock selection. Expenses that can occur for a fund include manageme nt fees, transaction costs, annual fees for day to day operation, and even one off fees such as load fees, which charge for the sale of funds and marketing and distribution costs of funds, as well as manager commission. All of these expenses which arent associated with the exchange of individual stocks can often erode the potential return on a fund. There is also the issue of tax on income yield and capital gains of the fund. Another disadvantage is that investors cannot influence what securities the fund manager trades in a particular fund. However sector funds do provide the opportunity for investors to actively manage their portfolios to an extent. What is the purpose of a sector fund? A sector fund is a type of unit trust with a large concentration of securities (at least 25%) in its portfolio limited to only 1 particular sector, for example technology. The reasoning behind this choice of investment fund is that there is a belief that a portfolio of stocks from a particula r industry can outperform the market, providing superior returns to investors, whilst also reducing individual company risk in that same portfolio. Investors have the ability to actively manage their portfolios to an extent by investing in sector funds; they are making an informed choice on the direction of the market in a particular industry. A common strategy used by investors is to have a proportion of their portfolio dedicated for investment in sector funds for better diversification in industries that may be under represented in their portfolio, but to also cater for the potential to achieve superior returns. What are it benefits and risks? Sector funds provide investors with the opportunity to exploit the fact that sectors move in distinct cycles from the market. Particularly when they know that a sector will respond favourably to factors such as government legislation, consumer expenditure or even the commodity market. If used correctly sector funds can be used to add f urther value to investment portfolios, and have the potential to create superior profits and enhance diversification. However sector funds are subject to a high level of risk because of the fact that there are high levels of concentration in one particular sector. There are also various transaction costs, expenses, fees and charges which are likely to affect the investors returns if they both invest in a sector fund but also implement rebalancing strategies. Sector fund strategies Three key strategies which investors could use when investing in sector funds are rotation, targeted growth and diversification. Sector fund rotation involves rebalancing investment portfolios between sectors to take advantage of the fact that some sectors perform better when the economy strengthens, for example Utilities funds which tend to outperform when the economic cycle declines. Targeted growth tends to be the standard strategy where investors have a belief that reforms in an industry will lea d to higher gains in the future, and sector funds allow the investor to capitalise on this. The diversification strategy is a way of stabilising long term returns by investing in sectors which dont necessarily follow the decline of the markets. A new type of investment strategy has also been made available recently through investment companies, one particular example is ProFunds which offers investors inverse sector fund investments; which allow investors to profit from sector declines or even hedge the risk of sector downturns. When should an investor buy a sector fund? Investors should consider investing in a sector fund when they are looking to invest in the long term; Morningstar suggests a period greater than 10 years, as this means that volatility may not matter as much, and further more sector funds can still achieve returns if the fund manager matches the market returns for the sector. Investors should be looking to invest when they think that the industry hasnt achiev ed its best returns, so an approach could be to invest at a point in time where investors are generally fearful for the returns in a particular industry. Investing at that particular time period can be a way investors can identify that they havent bought at the wrong time and can look to benefit in terms of performance from adopting a contrarian attitude. Literature Review Literature regarding the performance of UK sector funds is limited to an extent as there arent sufficient studies available on such a specific subset within mutual funds for the UK. However literature has been found which incorporates the theories that will be exhibited later in this study. Efficient Market Hypothesis Efficient market hypothesis is a theory which reflects how quickly information can be absorbed into the prices of securities. It forms a considerable argument in concluding that if all investors have the same information, and this information is reflective in the price, no single investor can achieve returns in excess of the market. In addition to this, Fama (1970) went on to identify that there are 3 forms of market efficiency, weak form which states that prices only contain past information. ‘Semi strong which states that all public information is reflected in the price of a security, and the ‘strong form which states prices are reflective of both publicly available information and private information. The implications of the theory are that if a market is experiencing a weak form of market efficiency, trend analysis in predicting future prices of securities is pointless as all past information is already reflected in the market. If the market is semi strong efficient, fundamental analysis is deemed to have no use. The market structure should have some implication as to the investment strategy employed by fund managers; active management of portfolios is considered to be wasted effort as the market is considered to be efficient and that the transaction costs involved of continually changing securities within a portfolio are not justifiable. It is therefore recommended that funds should be passively managed by creating a portfolio of securities that replicate an index in order to achieve returns in line with the market. Performance Measurements In order to effectively examine the performance of sector funds, key methods will be implemented to the data obtained which centre on performance theories such as the Expected Return of an asset as a component of its risk, as defined by the Capital Asset Pricing Model (Markowitz 1952), Jensens Alpha (1968), the Sharpe Ratio (1966) and the Treynor measure (1968). Literature regarding the implementation of these performance measures in examining the returns of mutual funds has produced significant findings which can provide some indication as to the results of this study. One of the major theories on fund performance stems from Jensens Alpha (1968), which measures returns deviating from the expected return as defined in CAPM can produce unreliable results if the incorrect benchmark is used. The effect of alpha is also considered to be insufficient if the number of mutual funds selected for analysis is too few. In previous studies Jensen concluded that mutual funds did not significantly outperform the market if management fees were subtracted from the gains. This was determined through a study of 115 funds for a period of 19 years between 1945 and 1964, the findings were that only 1 fund outperformed the market, 14 underperformed the market, and the rest produced risk adjusted returns as expected by the Capital Asset Pricing Model. Comparisons of Performance Measures Moy (2002) discusses the importance of Sharpe ratios and Jensens alpha in ranking portfolios; by using regression analysis for 4 different select mutual funds in establish the best-fit indices for a fund. In addition Moy ranks these funds according to alpha and the Sharpe ratio using optimal indi ces to assess the differences. The Sharpe ratio measures the additional return per unit of risk for an asset whereas Jensens alpha measure the return for a given level of risk, the deviation of returns from the security market line. Moy found that ranking portfolios based on these measures are dependent on the level of diversification, as the Sharpe ratio uses total risk, and Jensens alpha uses beta or systematic risk. Moy also notes that portfolios with a high alpha value and a low Sharpe ratio would indicate poor diversification, but also proposes that the alphas validity is dependent on the significance of the beta of the portfolio in finding a suitable index as a benchmark. Performance Persistence Performance persistence is the theory that yesterdays winners will continue to be todays winners and also yesterdays losers will continue to be todays losers. Intuitively it conforms to the principle of past performance acting as indicator of future performance, which in efficien t markets would not hold as an investment strategy. Brown and Goetzmann (1995) investigate US equity mutual funds in the period 1976-1988 and found persistence in performance did exist, however funds did exhibit a reversal pattern in 1987, where winners became losers in the previous year and vice versa. They found that this persistence was due to correlation between strategies of investment used by fund managers and that investors could â€Å"beat the pack† but could not outperform the market. Goetzmann also concluded that because of this correlation, chasing winners as an investment strategy was highly volatile due to the fact that the total risk exhibited by portfolios of winning funds was non diversifiable. In addition Phelps and Detzel (1997) investigated 87 mutual funds between 1983 and 1994 continued with the same methodology of Goetzmann (1995) to find that evidence of positive persistence disappears over time when controlling additional risk factors. Furthermore the p ersistence has been attributed to macro persistent factors such as continued performance in broad equity indexes as opposed to micro persistent factors such as manager skill in selecting funds likely to continue with positive performance. Phelps and Detzel advise that chasing winners is an unreliable strategy as on average, fund managers did not outperform the market using this strategy. Carhart (1997) builds on these findings by examining diversified mutual funds from 1962-1993 and concluding that any persistence found was not attributable to the skill or informed decision making of the fund manager. In addition consistent underperformance of worst performing funds was found to be anomalous. Funds following a momentum strategy of investment only achieved superior returns through luck. For the purpose of this study performance persistence of results will not be tested however the implication of the literature to the analysis of sector funds is that while persistence in performance m ay exist it is unrealistic for an investor to simply invest on the basis of the result of good or bad historical performance of the fund, a situation that is significant for technology fund investors. Research on Property Funds It is recognised that there is relatively scarce data on the performance of real estate and property portfolios to test the importance of fund selection skills in achieving superior returns to that of the market. A performance study of 37 UK based property funds in the period 1987 to 1995 using the â€Å"Henriksson and Merton Model† (1981) found that 35 out of 37 of the funds did not outperform the market. The study concluded that there was no evidence of successful market timing in terms of managers increasing risk in when markets rise or decreasing risk when markets fall. It was also found that there was positive selection abilities exhibited by the fund managers. The major conclusion to be drawn from the study is that for property funds in the time period 1987-1995 exhibit opposing characteristics to those suggested by Jensen (1968) who proposed that timing and selection of portfolios need to be assessed simultaneously. From the study it is found that selectivity and market timing appear to be offsetting, in that it was found that managers appear to be good at selection of stock for the fund, but poor at market timing, namely exhibiting a negative relationship. Henriksson (1984) suggests that this may be due to the exclusion of factors responsible for generating excess return. Furthermore Jagannathan and Korajczyk (1986) argue that results will be biased if the fund manager selects a portfolio with lower leverage than the market, market timing is biased downwards, and selectivity is biased upwards. The opposite occurs if the fund manager selects a highly levered portfolio than the market. The study conducted by S. Lee found that the UK property market is negatively levered, with UK property funds exhibiting a systemat ic risk value of 0.882. Market timing ability is reduced if the fund manager selects a portfolio systematic risk is low. The biased nature of the study means that possibility of achieving excess returns in property funds is significantly affected by the leverage of the portfolio relative to the market. Returns are therefore considered to be inconclusive to an extent. Devaney Lee and Young (2007) find that UK property funds between the period 1981 and 2002 exhibit performance persistence, by compiling cross sectional property funds into quartiles they established that if the probability of a funds return remaining in the same quartile was greater than 25% the fund exhibited serial dependence. The study concluded that this persistence may be as a result of valuation bias of properties which artificially create patterns of performance persistence. Furthermore performance persistence was only achieved by the ‘better property funds, which would suggest that investors of property funds would have to rebalance their portfolios in order to capture good performance. Research on Technology Funds The technology boom between 1997 and 2000 saw a large number of technology funds being made available to investors, but the trend of actively seeking to receive returns based on the past successes of these funds during this period was seen to be the investors demise when the technology sector slumped between 2000 and 2003. U.S technology funds between 2000 and 2003 experienced losses ranging from 32.3% to 42.6% respectively, average returns were highly eroded for investors holding technology funds over the period of the technology bubble. Furthermore Israelson (2003) claims that this poor market timing is largely responsible for the collapse in fund returns experienced by investors, citing that the downward turn of the market coincided with the increase in technology funds being released on the market. The ideal period for investors to significantly gain from the time period was between 1997 and early 2000. Israelson concluded that fund firms who were introducing tech funds into the market should not have â€Å"chased performance† as an investment strategy as they may have inadvertently fuelled the technology bubble. The significance of this particular review is that the technology funds for this study track the return from 2001 onwards, from the point of the slump in the technology sector, and are likely to suffer from poor initial returns; this study will see if there is any level of recovery in the returns of this type of sector fund. Mellon (2002) suggests that technology funds will continue to be an attractive investment achieving significant returns for investors despite the near bust of the technology sector in early 2000s. Mellon (2002) believes that nanotechnology and telecommunications are innovative sources of growth for the technology industry but warns that there will be new risks such as disruptive technologies, where new inventions can seemingly destroy a market overnight. From an investors point of view, the technology sectors growth is expected to be substantial in the future, and demand for technology funds is unlikely to swell despite the technology bubble at the turn of the millennium. Research on Financial Sector Funds Financial sector funds at the turn of the millennium began to grow in popularity particularly because of the belief of fund managers that the major benefactors of the technology boom would be financial institutions; demand for financial services was predicted to rapidly increase particularly because of the fact that the population was ageing and that global markets have become more integrated. Investors would find that financial funds were a key area of investment for their portfolio for the period 2002-2006. However the recent losses in the financial markets, caused by the large scale default of loans in the sub prime market are likely to have a significant impact on financial funds, with major banks and financial firms posting losses relating to bad debt in the sub prime market. Financial services firms such as mortgage companies have been liquidated due to defaults on mortgages and other loans and this has seen funds focussing on this particular sector suffer also. C. Benz (2007) found that the effect of sub prime market crash has been hit and miss with mutual funds focussing on this sector, on an asset allocation level the weighting of exposure to mortgage related activity in a fund has had a bearing on its success under turbulent market conditions. While one financial fund experience a loss of approximately 8% of its value at the end of July 2007, another financial fund gained 2.38%. Although financial funds have experienced good returns in the past there is a level of uncertainty with regards to future performance as a result of the sub prime crisis. Refer to article. The impact of Benzs findings are that there is likely to be significant volatility experienced by financial sector funds from July 2007 onwards and this is likely to change investor attitude to this style of investment. Effect of Transaction Costs Transaction costs for an investor include the cost of researching a funds prospects, performance and other variables but also expenses involved when changing portfolios of securities through buying and selling strategies and also direct costs such as commission on gains. Goldsmith (1976) discussed how transaction costs influence the level of investors wealth when selecting securities in the portfolio. He found that transaction costs can effect significantly the investment decisions depending on the number of securities bought and sold throughout the investment period. Transaction costs can be ignored if there are only 2 shifts in the portfolio, at the beginning and at the end, thus if a portfolio is bought and held to maturity, transaction costs can be dropped as they represent a fixed cost and can be dr opped due to the form of the investors objective functions for risk and return. Survivorship Bias Survivorship bias relates to the idea that studies on fund performance are considered to be overstated due to the fact that poor performing funds may be excluded from tracking indexes or even that poor performing funds have merged with better performing funds, so in essence their past performance is eliminated and to an extent hidden by the better performing fund. This makes it difficult for investors to differentiate fund performance between passively and actively managed funds. Bu and Lacey (2007) studied US Equity funds between 1998 and 2004 by comparing the returns on a portfolio surviving funds and a portfolio incorporate both surviving funds and excluded funds, they and concluded that survivorship bias was confirmed, particularly in markets experiencing prolonged bear or bull conditions. The likelihood is that over a 10 year period a level of survivorship bias will affect th e results of this study on sector funds. Data The data source for this study originated from Thomson DataStream and consisted of a selection of monthly price data for 50 sector mutual funds investing in Real Estate, Technology and Financial Services. The data was gathered for a period encompassing approximately 15 years from January 1993 to December 2007, this would therefore encompass a market cycle. However due to a lack of price information, the time period to accurately assess the fund performance has been shortened. In addition to this adjustment 21 funds were excluded from the initial set due to the fact they were either highly illiquid or discontinued over a period of time. The fund details can be found in the appendix. The details of the adjustments for the data set are as follows: 45 Technology funds will be examined between the period June 2001 and December 2007 41 Financial funds will be examined between the period March 2000 and December 2007 43 Property f unds will be examined between the period of October 1997 and December 2007 Furthermore data was collected for the historical price of a 1 month UK Treasury bill to represent the risk free rate over the corresponding time periods, as well as data on corresponding benchmarks to the funds, namely the FTSE All Share Index for Property, Financial Services, and Technology. The data collected represents only monthly price data of the fund and ignores any income received from the fund as well as the effect of transaction costs. Other data that was captured for the purpose of this study was the historical prices for the following indices: FTSE 100, FTSE Small Cap, FTSE 350 Value, FTSE 350 growth, and FTSE All Share for Property, Technology, and Financial Services. The data was collected via Thomson DataStream and Bloomberg over the time period of performance measurement for each set of funds stated earlier. Due to the lack of available data on UK Fama and French factors, it was require d to be manually calculated to find the 1 month lagged returns for each security for the FTSE 350 index constituents so that the appropriate return spreads could be calculated for the Carhart 4 Factor model variable WML, which represents the difference in return between the top 30% of firms and the bottom 30% of firms. When the data was collected it is assumed that the constituents at the present time in the index are constant historically, therefore index rebalancing is ignored. Methodology In order to calculate the various performance measures, fundamental portfolio theory principles were used, together with models for calculating return such as the Capital Asset Pricing model, various performance ratios and multifactor models in order to effectively establish not only the returns achieved by the portfolio but the return in excess of benchmarks, and also their significance. In order to calculate the return from the sector fund on a monthly basis, and also to measure the retu rn from the benchmark index, the following formulae were used: Rpt = Return from price at t Pt+1= Price of fund at month t+1 Pt= Price of fund at month t Pmt+1= Value of index at month t+1 Pmt= Value of index at month t The Natural Log function was used to calculate the returns because it is a more accurate measure of price return for monthly data, particularly for a portfolio where returns are normally distributed. Modern Portfolio theory was also applied in order to construct equally weighted portfolios of sector funds. This will then be compared to the portfolios expected return under CAPM conditions and can therefore aim to determine the performance of the investment over a period of time to determine if the fund outperformed the market; the following formula was used: Portfolio Expected Return: E (Rp) = ?wiE(Ri) For the portfolio of funds, the monthly returns were calculated using the formula above and were converted on an annual basis by finding the av erage monthly return ‘r for the yearly period and applying the arithmetic formula (1+r)^12. The average of these returns were then taken to form analysis for the overall portfolio The risk of the portfolio namely its standard deviation was calculated using the STDEV Excel function, by then applying the arithmetic formula to this standard deviation i.e. STDEV*SQRT(12) the equivalent annual risk for the portfolio was calculated. CAPM and Expected Return The Capital Asset Pricing Model is an extension to the mean-variance model as proposed by Harry Markowitz (1952), the CAPM as developed by William Sharpe (1964), is a model which bound by strict assumptions explains the equilibrium expected return of a security in the market by constructing return as a function of the risk free rate, the risk premium and the beta of the security. The assumptions of the Capital Asset Pricing Model are as follows: The market is perfect i.e. there are no transaction/information costs Investors are price takers with the same investment holding period All investors have the same market expectations. Investors can borrow or lend at the risk free rate. The formal equation of CAPM is shown below and shows that the Expected Return of a security is the risk free rate added to the risk premium of the security multiplied by the systematic risk of the security. The systematic risk or beta is reflective of how much the returns of the market move in with respect to the returns of the market, and is found using the regression analysis function in Excel: According to the Capital Asset Pricing Model the fund return should lie exactly on the Security Market Line, if above the line the fund is said to be undervalued, if below the line the fund is said to be overvalued relative to the market. In essence if the markets are assumed to be efficient, a buy and hold strategy would suffice as investors cannot beat the market, but instead try to achieve returns in lin e with the market. Jensens Alpha Jensens Alpha, which was developed by Michael Jensen in 1968 measures the return in excess of market, to some extent it changes the underlying foundations of CAPM in that by investing in a security the Expected Return should conform to the CAPM equation shown previously, in effect if the markets are efficient alpha should in fact be zero. Alpha is the difference in the funds expected return and its actual return. If the value is positive the fund is said to exhibit positive alpha and outperforms the market, and if the opposite occurs the fund is said to exhibit negative alpha and underperforms relative to the market. This result can be particularly important to the fund managers strategies when rebalancing portfolios in times when the market is bullish or bearish. Rp= Actual Return of the fund Rf= Risk Free Rate ?p= Beta or systematic risk Rm= Market Return To assess the statistical significance of alpha the t- statistic â€Å"? /a2† is examined using regression analysis, with the portfolio risk premium as the dependent variable and the market risk premium as the independent variable. The null hypothesis is H0: ? =0 and is tested at the 95% significance level at n-2 degrees of freedom. The alpha is deemed to be insignificant if the null hypothesis is accepted, i.e. that the p-value is greater than 0.05. The alpha is significant when the null hypothesis is rejected, where H1: ? ? 0, this occurs when the p value is less than 0.05. Criticism of the CAPM model The CAPM model outlined for this study does have issues regarding its efficacy. The CAPM model is limited by the fact it has poor predictive powers largely because of one of its central assumptions of a single risk factor, the beta, to explain expected returns. The case, more often than not, are that realised returns are often different from the returns calculated through CAPM, a fact that is verified with the existence of alpha. The lack of explanatory power of the CAPM has seen the development of multifactor models such as the Fama and French 3 factor model and Carharts 4 factor model. The addition of more company specific risk variables has resulted in better explanation of an assets return, particularly in terms of isolating return due to particular risk exposures. The Sharpe Ratio The Sharpe Ratio developed by William Sharpe in 1966 measures the reward to variability of each of the funds. As this ratio is calculated from the standard deviation it incorporates both systematic and unsystematic risk of the security. The ratio is in fact the slope of the funds individual Capital Market Line and is measured against the slope of the traditional Capital Market Line, the higher the value of the ratio the better the risk return profile of the fund, relative to the markets performance. Rp= Return of the Fund Rf= Risk free rate ?p= Standard Deviation of the fund For an investor a positive Sharpe ratio would indicate good risk return characteristics and would indicate investment, a negative Sharpe ratio would mean that the asset experienced a loss and would therefore not be considered by the investor. A problem may occur with the existing Sharpe ratio if the Risk Premium is negative, making it difficult to accurately rank portfolios according to their risk return profiles. However, an adjustment can be made to the existing Sharpe Ratio in order to rank portfolios that may exhibit negative performance by adding an exponent to the standard deviation function of â€Å"Risk Premium/Absolute Risk Premium†. The Treynor Ratio The Treynor Ratio measures the Reward to Volatility of each sector fund. It has similar criteria to the Sharpe Ratio in that the highest value is the best performing one. However the key difference for this ratio is that it assumes the fund is well diversified, with the excess return being measured relative to the systematic risk level. The ratio is in fact the slope of the funds individual Security Market Line and is measured against the slope of the traditional Security Market Line. Rp= Return of the Fund Rf= Risk free rate ?p= Standard Deviation of the fund Carharts 4 Factor Model The 4 factor model as developed by Carhart in 1997 is an extension to the Fama and French 3 factor model developed in 1993, as it incorporates a momentum factor into the equation responsible for security returns. It is a multifactor model extending the explanation of security returns to other factors other than systematic risk effect on the risk premium. The Carhart 4 factor model takes into account performance persistence of the funds, the equation is defines as: Carharts 4 Factor Model Rpt rft= ? p + ?pm (Rmt rft) + ?SML SMLt + ?HML HMLt + ?WMLWMLt + ?pt Rpt=Actual Return of the fund, Rmt= Market Return Rft= Risk Free Rate, ßpm= Beta or systematic risk SMLt=Small Cap Large Cap (FTSE 100 FTSE Small Cap) HMLt= High Book Value Low Book Value (FTSE 350 Value FTSE 350 Growth) WMLt=Winner Returns Loser Returns (FTSE 350 Index) The alpha represented by the Carhart equation represents the return after taking into account a multitude of factors including small cap, value and momentum performance. Small cap and value (or securities with high book to value ratios) are included because these classes of security have tended to outperform the market in the long term. These factors are calculated by subtracting the returns of the aforementioned indices, however for the WML variable, the returns of each constituent in the given index are ranked into best and worst performing, with the weighted average of the top 30% of returns beings subtracted with the bottom 30% of returns. The alpha calculated by Carhart provides more explanatory power to Jensens alpha, by determining more precisely the factors responsible for returns in excess of the market. The significance of the alpha for each portfolio is tested using regression analysis and conforms to the same rule as detailed for the significance for Jensens alpha. For the regression the independent variable was the alpha as defined by Carhart, and the dependent variable was the alpha as defined by Jensen. Empirical Analysis and Findings Technology Fund Returns Summary vs. FTSE All Share Technology Examination of Jensens Alpha and evidence of out performance Examination of Sharpe and Treynor Ratios vs. Market Examination of Carharts Alpha and significance Property Fund Returns Summary vs. FTSE All Share Property Examination of Jensens Alpha and evidence of out performance Examination of Sharpe and Treynor Ratios vs. Market Examination of Carharts Alpha and significance Financial Fund Returns vs. FTSE All Share Financial Services Examination of Jensens Alpha and evidence of out performance Examination of Sharpe and Treynor Ratios vs. Market Examination of Carharts Alpha and significance Peer Analysis of Risk Adjusted Performance Conclusion and Final Remarks References Literature Sources â€Å"Investments, 6th Edition†, Bodie/Kane/Marcus, McGraw-Hill, 2005 â€Å"Performance Measurement in Finance: Firms, Funds, and Managers†, Knight and Satchell, Butterworth-Heinemann, 2002 â€Å"Searching for Alpha: The question for exceptional investment performance†, B. 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Detzel Internet Sources https://personal.fidelity.com/products/funds/content/WhatYouCanBuy/sector_funds.shtml.cvsr https://www.smartmoney.com/university/investing101/funds/index.cfm?story=sector https://news.morningstar.com/classroom2/course.asp?docId=3000CN=COMpage=1 https://articles.moneycentral.msn.com/Investing/JubaksJournal/5SectorFundsYoullNeedIn2007.aspx https://www.alphaprofit.com/Recent-Articles/Sectorfunds0519-2004.html https://www.open-ira.com/Education_Center/4Fund_Advantages.htm https://www.rediff.com/money/1999/nov/17mrev.htm https://home.ubalt.edu/ntsbschr/Financial%20Formulae/ff_portfolio_calculations.htm https://www.telegraph.co.uk/money/main.jhtml?xml=/money/2001/01/31/cmfin31.xml Appendices Excluded Funds Funds excluded from calculations due to insufficient price data or discontinued status. Excluded Financial Funds Code Fund Name 302543(P) DRES.RCM GLB.INVS.FTSE PRTF. 302889(P) CAPITA FINL.BERKLEY UK UNSUPPORTED 671820(P) CAPITA FINL.GHC UK EQ.A UNSUPPORTED 888489(P) CAPITA FINL.JAMES BREARLEY HI.INC. 697136(P) CAPITA FINL.ST ANDREWS GW.FD. 870781(P) ABDN.STLG.FINLS.BD.AC. 888947(P) CAPITA FINL.STOODLEY UNSUPPORTED 888947(P) CAPITA FINL.STOODLEY UNSUPPORTED 270873(P) CAPITA FINL.GHC ACTIVE UNSUPPORTED 270874(P) CAPITA FINL.GHC ACTIVE UNSUPPORTED Excluded Technology Funds Code Name 684979(P) TECH. AND INCOME TRUST INC. 684978(P) TECH. AND INCOME TRUST ORD. 299468(P) FRANK.TMPLETON BIOTECH. 260547(P) HSBC INTERNATIONAL TECHNOLOGY I 13795Q(P) RLSK.LF.EUR.ABDN.EURO TECH. Excluded Property Funds Code Name 137705(P) LIONBROOK PR.PTSHP.PR. FD. 359856(P) NPI PN.PR.INIT.2 UNSUPPORTED 681304(P) FALCON PR.TST.FALCON PR. 679062(P) ROCKSPRING HANOVER PR. INC UNSUPPORTED 906079(P) HERMES PROPERTY UT 138257(P) PDFM UM.PR.PTSHP.FD.ACT. 138258(P) PDFM UM.PR.TST.INC. Property Fund Portfolio Return vs. Expected Return Regression of Beta, Jensens Alpha, Carhart Variables, and Carharts Alpha Technology Fund Portfolio Return vs. Expected Return Regression of Beta, Jensens Alpha, Carhart Variables, and Carharts Alpha Financial Fund Portfolio Return vs. Expected Return Regression of Beta, Jensens Alpha, Carhart Variables, and Carharts Alpha