Portföy yönetimi
Başlık çevirisi mevcut değil.
- Tez No: 55521
- Danışmanlar: Y.DOÇ.DR. CELAL TUNCER
- Tez Türü: Yüksek Lisans
- Konular: Mühendislik Bilimleri, İşletme, Engineering Sciences, Business Administration
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1996
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 73
Özet
ÖZET Bu çalışmada, riskli yatırımlar arasındaki karşılıklı etkileşimlerin dikkate alınıp, bu şekildeki yatırımların teker teker değil de birarada ele alınıp incelenmesi olan portföy kuramı ele alınmıştır. İlk olarak Harry Markowitz tarafından geliştirilen bu kavram, gerek risk analizlerine, gerekse fînansal varlık değerlemelerine yeni bir boyut kazandırmıştır. Portföy yönetiminde uygulanabilecek analitik yaklaşımlar üzerinde durularak, etkin sınır üzerinde yer alan portföyleri saptamaya yönelik çalışmalar araştırılmış, verilen beklenen getiri seviyesi için en küçük portföy riskini taşıyan veya verilen risk seviyesi için en büyük beklenen getiriyi sağlayan portföylerin belirlenmesi amaçlanmıştır. Uygulama olarak da Lineer Programlama probleminin Simpleks Algoritması ile çözümü üzerine bir program geliştirilmiştir. V
Özet (Çeviri)
SUMMARY PORTFOLIO MANAGEMENT The word portfolio simply means the combination of assets invested in and held by an investor, whether an individual or an institution. Technically, a portfolio encompasses the investor's entire set of assets, real and financial. Most people hold portfolios of assets, whether because of planning and knowledge or as a result of unrelated decisions. The study of all aspects of portfolios can be designated portfolio management. This broad term encompasses the concepts of portfolio theory, a very important part of investments. At this work, the classic portfolio theory model developed by Markowitz is analyzed. In the early 1950s, Harry Markowitz originated the basic portfolio model that underlies modern portfolio theory. Before Markowitz, investors dealt loosely with the concepts of return and risk. Although they were familiar with the concept of risk, they usually did not quantify it. Investors have known intuitively for many years that it is smart to diversify, that is, not to“put all of your eggs in one basket”. Markowitz, however, was the first to develop formally the concept of portfolio diversification. He showed quantitatively why, and how, portfolio diversification works to reduce the risk of a portfolio to an investor. Markowitz sought to organize the existing thoughts and practices into a more formal framework and answer a basic question. Is the risk of a portfolio equal to the sum of the risks of the individual securities comprising it ? Markowitz was the first to develop a specific measure of portfolio risk and to derive the expected return and risk characteristics of securities and is, in essence, a theoretical framework for analyzing risk-return choices. Markowitz was also the first to derive the concept of an efficient portfolio, defined as one that has the smallest portfolio risk for a given level of expected return, or the largest expected return for a given level of risk. Investors can identify efficient portfolios by specifiying an expected portfolio return and minimizing the portfolio risk at this level of return. Alternatively, they can specify a portfolio risk level they are willing to assume and maksimize the expected return on the portfolio for this level of risk. Rational investors will seek efficient portfolios because these portfolios promise maksimum expected return. Given their importance, we should know how they are determined. To determine an efficient set of portfolios, it is necessary to determine the expected return and standart deviation of return for each portfolio. To do this we need to understand the Markowitz model. Markowitz made some basic assumptions in developing his model. Investors 1) like return and dislike risk, 2) act rationally in making decisions, and 3) make decisions on the basis of maximizing their expected utility. Thus, investor utility is a function of expected return and risk, the two major parameters of investment decisions. The model itself is based on equations for the expected return and risk of a portfolio. To solve these equations, some values are needed for the relevant variables. VIThe Markowitz analysis generates efficient portfolios based on a set of inputs supplied by an investor. i. The expected return, E, for every security being considered. ii. The standart deviation of returns, a2, as a measure of the risk of each security. iii. The covariance - a measure of relationships - between securities' rates of return. The world is uncertain, security returns are really probability judgements. To calculate the expected returns on security i, an investor needs an estimate of the realistically obtainable returns from the security plus the likehood of occurence (i.e., probabilities) for each possible return. These probabilities sum to 1.0, as they must in a complete probability distribution, because they are exhaustive. The potential returns must ultimately reflect expectations of the future rather than be merely averages from the past. Given the probability distribution of potential returns for a security, its expected returns, E, can be calculated as the expected value of the probability distributioa E : the expected return on any security i pi : the probability of occurence of each potential rate of return r* : the potential returns for a security N : the number returns for each security N It is always assumed that ^ p; = 1. (2) i=l To measure the risk of any security we use the variance (standart deviation) of the expected returns. Variance, a2 = [2>i-tf -E2] (3) Standart Deviation, ex = f £ p;. r 2 - E2 V2 (4) The expected return on any portfolio is easily calculated as a weighted average of the individual securitie's expected returns. The weights used are the proportions of total investable funds invested in each security. The combined portfolio weights are assumed to sum to 100% of total investable funds. The expected return of a portfolio can be calculated as, Ep=ixi.Ei (5) i=l where, Ep : the expected return on the portfolio X, : the proportion of investable funds placed in security i Ej : the expected return on security i N : number of securities vnIn the Markowitz model, risk is measured by the variance (or standart deviation) of the portfolio's return, just as in the case of each individual security. Although the expected return of a portfolio is a weighted average of the expected returns of the individual securities in the portfolio, the risk is not a weighted average of the risk of the individual securities in the portfolio. Portfolio risk depends on the relationships, or covariances, among the returns on securities in the portfolio. ^=IZX,X,C0vu (6) a p : the variance of the return on the portfolio Xi : the percentage of investable funds invested in security i Covy : the covariance between the returns for securities i and j The covariance is an absolute measure of the degree of association between the returns for a pair of securities. Covariance is defined as the extend to which two variables move together overtime. The covariance can be i. Positive, indicating that the returns on the two securities tend to move in the same direction at the same time; when one increases (decreases), the other tends to the same. ii. Negative, indicating that the returns on the two securities tend to move inversely; when one increases (decreases), the other tends to decrease (increase). iii. Zero, indicating that the returns on the two securities are independent and have no tendency to move in the same or opposite directions together. Cova.b = Z P,. rA.i ? rB.i - E a. EB (?) To account for the effect of the covariations between securities, it is necessary to estimate the correlation coefficient between each pair of securities, i and j. As used in portfolio theory, the correlation coefficient is a statistical measure of the extend to which the returns on any two securities are related; however it denotes only association. It is a relative measure of association that is bounded by +1.0 and -1.0, with, p^g = + 1 Perfect positive correlation Pas~ 0 no correlation pA3= -1 perfect negative correlation With perfect positive correlation, the returns have a perfect direct linear relationship. With perfect negative correlation, the securities' returns have a perfect inverse linear relationship to each other; Therefore, knowing the return on one security provides full knowledge about the return on the second security. With zero correlation, there is no relationship between the returns on the two securities. A knowledge of the return on one security is of no value in predicting the return of the second security. Combining securities with perfect positive correlation provides no reduction in portfolio risk. Combining two securities with zero correlation reduces the risk of the portfolio. Finally, combining two securities with perfect negative correlation could eliminate risk altogether. In the real world, these extreme correlations are rare. Although risk can be reduced, it usually can not be eliminated. The covariance and the correlation coefficient are linked in the following manner: vmCovAS Pkb=- (8) When we draw a diagram, the vertical axis is the expected return and the horizontal axis is the risk. These are the standart axes in portfolio theory. The expected returns and risks of a hypothetical group of securities have been plotted. By combining these securities into various combinations, an infinite number of portfolio alternatives is possible. In the portfolio theory, this area is referred to as the 'attainable set' of portfolios - these portfolios are possible, but not necessarily preferable. The efficient set dominates all interior portfolios because it offers the largest expected return for a given amount of risk, or the smallest risk for a given expected return. Once the efficient set of portfolios is determined, investors must select the portfolio most appropriate for them from the mil set. The Markowitz model doesn't specify one optimum portfolio. It generates the efficient frontier of portfolios, all of which are optimal portfolios. To select the expected return-risk combination that will satify an individual investor's personal preferences, indifference curves which are assumed to be known for an investor, are used. The optimal portfolio for any investor occurs at the point of tangency between the investor's highest indifference curve and the efficient frontier. Conservative investors would select portfolios on the left end of the efficient frontier because these portfolios have less risk. Conversely, aggressive investors would choose portfolios on the right end of the efficient frontier because these portfolios offer higher expected returns. Capital market theory builds on Markowitz portfolio theory. Each investor is assumed to diversify his portfolio according to Markowitz model, choosing a location on the efficient frontier that matches his return-risk preferences. Capital market theory is positive, describing how assets are priced in a market of investors. A risk-free asset is defined as one with a certain expected return and a variance of return of zero. Since variance is zero, the covariance between the risk-free asset and any risky asset will be zero. Investors can combine this riskless asset with the efficient set of portfolios on the efficient frontier. The standart deviation of a portfolio combining the risk-free asset with a risky asset is simply the weighted standart deviation of the risky portfolio. When a new line drawn tangent to the efficient frontier at point M, the point M can be called the market portfolio and the line referred to as the capital market line The CML indicates the required return for each portfolio risk level. In equilibrium, all risky assets must be in portfolio M because all investors are assumed to to hold the same risky portfolio. If they do, this portfolio must be the the market portfolio consisting of all risky assets. Each investor would choose a point on this line that corresponds to his risk preferences. This would be where the investor's highest indifference curve is tangent to the straight line. More aggresive investors would be closer to point M, representing full investment in a portfolio of risky assets. Investors are able to borrow and lend at the risk-free rate. Borrowing additional ivestable funds and investing them together with the investor's own wealth allows investors to seek higher expected returns while assuming greater risk. The capital market line applies only to efficient portfolios. These portfolios contain only systematic risk and no unsystematic risk. The total risk of a security can be broken down into 1) systematic risk 2) unsystematic risk. As more securities are added the unsystematic risk becomes smaller and smaller, and the total risk for the portfolio approaches its systematic risk. Since diversification can not reduce systematic risk, total portfolio risk can be reduced no lower than the total risk of the market portfolio. The security market line SML depicts the trade-off between risk and required return for all assets, whether individual securities, in Kefficient portfolios, or efficient portfolios. To implement the SML, an investor needs estimates of the return on the risk-free asset, the expected return on the market index, and the beta for an individual security. Each security's contribution to the total risk of the portfolio, as measured by beta. Using beta as the measure of risk, the SML depicts the trade-off between required return and risk for securities. Problems exist in estimating the SML, in particular estimating the betas for securities. The stability of beta is a concern, particularly for individual securities; however, portfolio betas tend to be more stable across time. In my thesis, I discussed a consideration of portfolios simply means the combination of assets invested in and held by an investor. I tried to analyze the classic portfolio theory model developed by Markowitz and a procedure for determining optimal portfolios. My thesis consists of 7 main sections. In the first section Modern Portfolio theory is mentioned. In the second section, a discussion of the different types of risk and their classification, return and their basic properties are examined. In the third section, an introduction to modern portfolio theory, covariance, correlation, portfolio risk and portfolio return, short selling, techniques for calculating the efficient frontier with short selling are mentioned. In the fourth section, utility theory and functions, which are needed for portfolio analyses are discussed in some detail. In the fifth section, efficient portfolios, efficient frontier, lending and borrowing are discussed. In the sixth section, market portfolio, the capital market line, the security market line and beta forecasting are revealed. Finally in the last section, lineer programming and simplex method and a program are examined.
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