Finanasal varlıkları fiyatlandırma modeli

Abstract

ÖZET Bu çalışmada Finansal Varlıkları Fiyatlandırma Modeli nin tanıtım ve uygulanması amaçlanmıştır. Çalışmaya kısa bir giriş bölümüyle başlanmıştır. Finansal Varlıkları Fiyatlandırma Modeli nin uygulanması için seçilen ve İ.M.K.B'de işlem gören 31 adet firmaya ait hisse senedinin analizlerine geçilmeden önce, uygulama konusunu oluşturan finansal varlıkların incelenmesine geçilmiştir. İkinci bölümde genel olarak finansal varlıkların yatırımcıya sağladığı getirilerden söz edilirken, bu getiriler elde edilirken karşılaşılması muhtemel risklerin neler olduğundan bahsedilmiş ve özellikle yatırımcının dikkat etmesi gerektiği sistematik risk denilen ve beta katsayısı ile gösterilen risk konularına yer verilmiştir. Bir portföyün seçimi ve yönetimi yapılırken, yatırımcı tarafından menkul kıymetler piyasasının işleyişini anlamak üzere gözönüne alınması gereken teoriler ve bu teorilerin doğrultusunda izlenmesi gereken stratejiler vardır. Bu bağlamda karşılaşabileceği olası riskleri dağıtmak amacıyla başvurması gereken yollar, ikinci bölümde kısaca açıklanmıştır. Finansal varlıkları fiyatlandırma modelinin varsayımları ile beklenen getiri ile risk arasındaki bağıntının açıklandığı üçüncü bölümde, hisse senetlerinin regresyon analizleri yapılırken uygulanması gereken istatistiksel yöntemlere yer verilmiştir. Bu bölümde ayrıca, finansal varlıkları fiyatlandırma modelinin çözümlenmesi için yapılan işlemler gösterilmiştir. Çalışmamızın dördüncü bölümünde hisse senetlerinin regresyon analizleri sonucu elde edilen regresyon denklemleri verilmiş ve bu denklemlerin geçerliliğinin saptanabilmesi için gerekli testler yapılmıştır. Bu testler sonucunda saptanan regresyon denklemlerinin yorumlanması ile elde edilen sonuçlara beşinci bölümde yer verilmiştir. Bu çalışma, yararlanılan kaynakların sıralandığı bölümden sonra, tüm hisse senetlerinin veri tabloları ve regresyon analizleri sonuçlarının yer aldığı ekler bölümü ile tamamlanmıştır. XII

SUMMARY CAPITAL ASSETS PRICING MODEL The CAPM which is know to be a pricing method for securities, is especially important to all investors brokerage houses, advisory firms since CAPM help to determine the future value of securities. Bonds, one type of securities, provides its holders a fixed interest income for a specified maturity term. Although there are many different types of bonds and its derivates, in this study we will consider only treasury bills and government bonds while using CAPM. Equities which are the most important part of this study is just another form of securities. The main difference between the equity and the bonds is that, equity is a right for ownership, where as bonds provide right for interest income on invested principal for a limited time. Investors seek maximum return on their equity investment. Their main goals is take minimum risk while receiving the maximum return. Also, investors try to minimize their risks by different tools and products available in the market. Investors who do not want to take high risks, will probably chose bonds to secure a fixed income. Total risk is a combination of many different types of risks, such as, interest rate, currency, financial, trade, default, market, inflation, liquidity and a systematic risk. This systematic risk is especially important for equity markets. The systematic risk is indicated by (3 coefficient. Beta is accepted as a measure to asses the relationship between the market and a particular equity. The second coefficient used in the equity markets is called a (Alpha). This represents the price volatility of the equity which occurs as a result of inter-company developments, regardless of market events, a is also called non-systematic risk. Investors decide their policies on a particular security by looking at its 3 figure. XlllPortfolio is a basket of securities which includes bonds, equities and other type of securities. Portfolio management requires expertise. There are two main approaches in managing portfolios. The first approach (Classical portfolio management) requires the diversity of securities in case the investment can not earn the expected return on one security. The second approach (Modern portfolio management) assumes that the information on all factors which effect the prices will be transferred to investors right away. All investors expect to increase their return on their investment to maximum levels. Investment decisions are made according to risk and return relationship. Securities which form the portfolio are separated according to their risk-return levels. Therefore portfolio strategies are developed based on these levels. Distribution of risk levels is the most important thing while forming an investment portfolio. Concentrating in one economic sector or even one single security in an investment portfolio is very dangerous. The best thing to do while forming such a portfolio is to diversify among different industries, companies, bonds and equities. CAMP is based on the following assumptions: 1. All investors expect the highest return on their investments while they try to minimize their risks. 2. All investors should take their investment decisions according to return probabilities of each security. 3. The prices of securities are not effected by individual behaviors since there are many buyers and sellers in the market. 4. All investors can borrow and lend at risk free rate. 5. All transaction costs are assumed to be zero. 6. All assets are marketable and splitable. 7. For all investors maturity term and the holding period is the same. 8. Investors can take advantage of market prices by short selling. 9. Distribution of return probabilities is a normal distribution. Portfolio managers makes certain choices while forming their portfolio. These are: a) Security type. XIVb) Return (expected). c) Capital gain. d) Liquidity. e) Tax It would be hard to equally weigh all above issues in a portfolio. Therefore investors may have to sacrifice some in favor of others. There is a relationship between risk and return of an equity. Securities such as treasury bills and government bonds (which are accepted as risk free) can be bought and sold at requested amount or even be cashed to buy equities. Investors take their decisions on the volatility of the prices of securities. If there were no riskless assets it would be easy to form a portfolio that lies on the border of the effective curve. But if these riskless assets existed, the expected return of the portfolio will lie where the capital/market line meets the effective curve The line which characterizes the relationship between the return of market portfolio and a particular equity is explained by the following equation: Rit = ait + pi RMt + eit (1) The comparison between the return of a market portfolio and a particular equity is defined by beta coefficient. Beta shows the slope of the characteristics line and expanse. How the return of market portfolio effects the expected return of a particular equity. Thus we can see the expected amount of change in the return of the equity for every unit of change in the return of the market portfolio. Beta coefficient is explained as following: Cov(rh rm) Pi = (2) o^r, m Following comments can be made on how the magnitude of beta can effect the change in the value of a particular equity. If p>1 then, the change in the value of a particular equity will be more than the market. This can also be called aggressive p, which means, the value of equity will increase (decrease) more than the value of the market. It is also XVabsorbed that equities which have p>1 also tend to have higher systematic risks. If the p<1 then, the change in the value of a particular equity will be less than the change in the value of the market. Another words, the increase (decrease) on the value of the equity will be less than the market. If the p<0 then, equity acts in the opposite direction of the market changes. If the market goes up the equity will go down. By the market definition of p, expected return of an equity I can be written as the following: E(Ri) = RF + pi[E(RM)-RF] (3) If we assume that the market model is valid, return of a equity can be defined as a linear function of the return of market. Rit = ait + pi Rıvıt + eit (4) The expected return of this equity than can be written as: E(Ri)= ai+piE(RM) (5) E(Ri)-ai-piE(RM) = 0 (6) When we add this last equation numbered (6) to the right side of the equation number (4) we come to: Rit = E(Ri) + Pi [E (RMt) - RM] + eit (7) If we place the CAMP as described in equation number (7) E(Rj) = RF + Pi [E (RM) - Rf] then our model will look like: Rit=RF + Pi(RMt-RF) + eit (8) Between 1954 and 1963 Lintner studied 301 different equity to asses the relationship between the risk and return. The annual return of each of the 301 equities were compared to the annual average return of the total portfolio. By this study Lintner was able to find a P coefficient for each equity and also to show the non-systematic risk, he calculated the error variance. XVIRit = a + pi RMt + eit (9) Rit = Return of the equity in year t. Rmt = Return of the total market. Pi = Estimated Beta coefficient of the equity. In our application of CAMP is used as developed by Black, Jensen and Scholes. According to this: Rit - Rr = oti + pi (RMt - Rr) + eit (1 0) Rit= Monthly return of the equity i. RMt = Monthly return of the market. RFt = Risk free interest rate. Pi = Beta coefficient of the equity. Below is the summary of the studies on the CAPM as outlined above: First, 31 different equity listed at İstanbul Stock Exchange (ISE) was chosen. Special attention was paid to make sure that these 31 equity belonged to different industries. Then these equities were studied under CAMP. The monthly closing prices on these equities for the last five years (September 90-August 95) was collected. Later, dividend payments of these securities and the closing value of ISE index were found on the each December issue of ISE publications between December 90 to December 94. Because this study was completed before December 95 the figures in this study for 95 were estimated based on historical trend. In our model, the variable Y which forms Y = a + bX regression equation, is driven by the difference between the return of the equity and the return of the risk free rate Y = Rj - RF, however the independent variable X is found by the difference between the market return and the risk free rate. After calculation of X and Y, the regression equation and the regression line for each of the 31 equity was found. xvuAfter testing the autocorrelation degrees of the equations, in our study, we tested the reliability of the equation by employing linear regression analysis. As known, one of the measurements in the linear relationship between the two random variables is correlation coefficient. Even though the correlation coefficient may be close to 1. It does not always mean there is a cause- result relationship. If the two variable has a relation to another variable may also cause the correlation coefficient to be high figure. Thus it is necessary to control the H^ px,Y * 0 hypothesis to H0 : px,y = 0 hypothesis. Therefore by using the rx,Y value drived from the sample. Value of t is calculated: rXlY VN - 2 t= (11) Vl-rXlY2 In all calculations in this study, a is taken 0.05 which represents a reasonable assumption. ( 1 1 1 < t table) H0 hypothesis under this assumptions is accepted as (H0 : px,y = 0). In this situation, we can say that there is no linear relationship between the two variables. But, in the case where H0 hypothesis is denied; since the distribution of t statistics is only valid for px,Y = 0, it will be hard to come to a certain conclusion. In this situation, it will be necessary to find out the sample distribution of rx,Y for pX)Y * 0. Although this distribution is not know for sure, with the following equation; 1 1 + rXiY z = n (-1 2) 2 1 - rx,Y The distribution of z statistics which is defined by rx,Y is known to be around normal if the common distribution of X,Y is normal. The parameters of the z sample distribution are; xvm1 1 + Px,y ^ in (13) 2 1 - px,Y az = (14) VN-3 to check if the main correlation coefficient is equal to any given value, (Ho : px,y= Po) hypothesis is controlled by the basis of sample distribution of z statistics. Once the equations were passed these tests, they were subject to a third study. In this last study the values of beta were examined, if it were 0 or close to (Ho : p = 0)? And if it were 1 or close to (H0 : p = 1)? Since Ho : P = 0 hypothesis is the same as H0 : px,y = 0, the first test determines whether the correlation is 0 or not, at the same time it determines if beta is 0 or not. In these two situations, there is no relationship between the two variable. In these cases, where beta is not 0, to help our assessments, we employed a last test to determine if H0 : P = 1 or not. For this: Ho : P = 1 Ho : p * 1 P-P t = (15) A SO) t is calculated and where 1 1 1 < t table, H0 : P = 1 hypothesis is accepted. xix