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Summary

The study examined the relationship between risk-free rate and equity markets. In five years of monthly data from 2003-2007 time series of Treasury bills and KSE-100 index, the study has found. For data analysis, simple regression model was applied approach. again on the open market has been as dependent variable, while the risk-free interest rate is included as independent variables. In addition, Pearson correlation matrix was obtained by the correlation model. The results suggest that risk-free rate has no effect on the dependent variable has. Furthermore, no correlation between the risk-free rate and stock market performance has found. Therefore, there exist a bivariate relationship between the risk-free rate and equity markets. A multiple regression of the risk-free rate and market return shows a strong correlation, indicating that the stock market performance as a function of variable than the risk-free interest rate.

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1. Introduction:

The risk-free interest rate is the return on security or a portfolio of securities that is free of default risk. Theoretically, the yield of a zero-beta portfolio, the best estimate of the risk-free rate. The CAPM says the risk ratio ship of an asset and its expected return. This relationship is very useful in two ways. First, it creates a baseline to evaluate different investments. Second, it helps us to make an informed guess about the return of an asset that can not be traded so far expected.

Risk rate is calculated increasingly important part of any return on financial assets. The Security Market Line (SML) predicted from a simple linear relationship between expected return and standard deviation while the capital market line (CML), a relationship between the risk-free rate and the straight line contribute risk-free rate (Rf) for a tangent to the Efficient Frontier .

Investors

combine their securities uncorrelated help lesson the risk of a portfolio. You want to know the appropriate level of risk mitigation in their portfolios. Research studies to look at what happens in portfolio risk stocks selected randomly grouped into equally weighted portfolios. If you start with a single stock, portfolio risk is that the standard deviation of a stock. As the number of actions at random from the increased portfolio is selected, the whole portfolio will reduce risk.

The total risk systematic and unsystematic risk risk. Systematic risk management is due to factors that affect the entire market, such as changes in the economy, the global energy situation, the political and economic world at risk. This type of risk is not diversifiable and well-diversified portfolio exposure to that risk. The second component, which is non-systematic risk, unique to the company. It is independent of all factors relating to the systematic risk. Investors always want to be compensated for taking systematic risk. However, you should not expect the market to offer additional compensation for bearing diversifiable avoidable, unsystematic risk. It is this logic that the model of asset pricing (CAPM) is based.

2 Significance of the Study:

The aim of this study, the relationship between risk-free rate (Treasury Bills) and return on the market at Karachi Stock Exchange KSE -100 Index investigate. There was a controversy among investors, there were some that affect the risk-return of the market, while others were in terms of return on equity market is moving positively, regardless of independent risk-free rates

<. solve p> So, this controversy, a study was carried out with the following objectives.

3 Study objectives:

The next objective would be filled during the study:

show • For the quantitative effects of the risk-free return on the free market.

• For training, the correlation between risk-free rate and return on the stock market.

· suggestions and recommendations for investors.

4 Literature Review:

Peter Easton el (July 2000 ) developed an empirical estimate of the expected return on a stock portfolio. They appreciate reversed residual income valuation model, the expected returns of a portfolio of stocks. They used similar approach in estimating the internal rate of return on a link with the market value and coupon payments. They helped by using data on stock prices and accounting for the simultaneous estimation of growth rate and the single implicit internal rate of return. They recommended that the growth rate adjusted for the return of inventory valuation. They showed that the estimated market premium over risk-free interest rate received closer to the historical premium than that of other studies using data for forecasting sales.

Roger G. Ibbotson (July 2002) believes long-term stock returns in the real economy are involved. It decomposes the 1926-2000 historical equity return on supply factors, including inflation, earnings, dividends, price-earnings ratio, dividend payout ratio, book value, return on equity, and GDP per capita. He concluded that the growth in overall productivity, in line with productivity growth in terms of reduced income. The nature of the benefit is for the payment of dividends and earnings, such as inflation and nominal earnings growth. To calculate the additional risk and return the bonds were used as reference.

Christian Lundblad (February 2004) discussed risk-return trade-off is fundamental to the financing. Previous studies have shown weaker relationship between the risk premium of the market portfolio and the variance of return despite the positive relationship. He explained that this weakness is needed on the nature of the limited data available, a large number of time series observations to estimate accurately the relationship. His main objective was the achievement of the data of individual components needed to return / risk analysis, calculated for the theory of finance.

Hui Guo and Robert F. Whitelaw (April 2005 ) is evidence of the intertemporal capital asset pricing model (ICAPM) developed and demonstrated the positive relationship between risk and return in the equity markets and to what extent the volatility in the equity markets move stock prices. They have provided new insights into the risk-reward ratio by estimating a variant of Merton (1973) model of intertemporal capital asset pricing (ICAPM). They identified two components of the expected return on the risk component and the component by the desire for change in the investment opportunities to hedge. They showed that the estimated coefficient of relative risk aversion is positive, statistically significant.

Rong Huang at el (May 2005) in the study by the BM residual income valuation model at the same time, the relationship between the growth rate estimate in the long term abnormal earnings and cost of capital. They relate to price-earnings (EFF) and to transmit the ratio of book to market in a linear fashion. The slope coefficient on BM is the rate of long-term growth of abnormal earnings (g), and the constant term is the real cost of capital, ie the difference between the cost of capital (r) and growth rate of abnormal profits. To implement this representation, empirical evaluation, forecasts of analysts have taken advantage of one year in advance of the result calculated and dropped EFF, a regression of the difference between the IEC and the risk-free rate (rf) on BM after another, so that the intercept captures the company-specific risk premium (RP) and the slope coefficient of capture firm-specific, long-term growth of abnormal earnings (g). It extracts the risk-free rate of FEP covariance to IEC and the risk-free rate to reflect.

Mika Vaihekoski > (2007) discusses how the risk-free rate of money market instruments calculate, especially for testing the model of asset pricing and case studies. He used U.S. government bonds and CDs for the calculation. He presented two approaches: the interest and compound interest and approach the price difference. He concluded that the approach of the price difference is larger than the mixing method used often. He studies and case series of U.S. government bonds, then used them to calculate the risk-free interest rate.

Tamal Datta Chaudhuri (April 2008) used to return a structural approach to stock market risk-free rate and Capital Asset Pricing Model (CAPM). He developed a structural model showing the correlation between the risk-free rate and stock returns. It offers new structural macro-economics that the price movements in stock form. He used a test of Granger and Sims tests to demonstrate the interdependence of two variables. He suggested instead the values of the exogenous stock returns and risk-free rate, we must use estimated values of these variables in a reduced form equation of the Capital Asset Pricing Model (CAPM). He tested and proved with the data of individual companies.

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5.1 Data Collection

To have been proposed for the current study, all the stock markets of Pakistan conduct, take aim of the study. The stock markets in Pakistan Lahore Stock Exchange were (LSE), the Islamabad Stock Exchange (ISE) and the Karachi Stock Exchange (KSE) with different indices. Among all these KSE-100 index was the biggest and work at the highest level in Pakistan. A hundred top companies in Karachi Stock Exchange KSE-100 Index included. Historical data show that most investors have invested in the KSE-100. The yield of the entire company in Pakistan can be accessed by the movement of KSE-100 index. Without losing sight of the importance of KSE-100 index, a sample indexes (2003-2007) was selected for data collection and was taken as the dependent variable.

Also, T-Bill is an important instrument of monetary policy, operated by the State Bank of Pakistan. Thanks to T-bills, the central bank controls the interest of Pakistan and the economy. The interest rates on Treasury bills were collected by the State Bank of Pakistan for the same period and included as independent variables. Then the data of the software have been supplied as a worksheet.

5.2 hypothesis formulation

Ho: The risk-free interest rate does not affect the market power

Ha. The risk-free interest rate has an impact on the return of the market <. /> P>

To test these assumptions was the simple regression model used in the following form. The regression model was as below:

Y =? +? X1 + €

Where

/ p> values? = Y intercept

? = Slope coefficient

Y = values of the stock market

€ = error term

It is estimated regression equation.

= y

b = slope coefficient intercepted.

x = value of the risk-free rate in the sample.

while

b = slope of the regression equation estimated

X = the risk-free interest rate

Y = values return stock market

= average risk-free interest rate.

= average share price back

n = number of observations in the sample

while

= average stock returns

= average risk-free interest rate

/ p> intercepted =

/ p> b = slope coefficient

.

The coefficient of determination, R2 measures independent variable and explains how the dependent variable, that is, the degree of association between the dependent variable and independent variables.

The model used a dependent variable and explanatory variables. In the current study, the risk-free rate, considered as an explanatory variable, while the market again as the dependent variable.

6 Results and discussion:

The collected data from the years 2003-2008 on a monthly basis by applying simple regression model approach was analyzed form fields.

Y = A + B + X1 €

during <: p>

Y = Return Exchange <: p>

b = coefficient of X1

<= pa

/ p> <€ = errors / p>

6.1

empirical results derived by a regression model approach in the table below.

Table 1

variables

t-stat

<> p>

intercept

0, <0399

/ p <2.782

/ p>

>

/ p>

< / p> / p <0.012

/ p>

test the hypothesis 6.2:

Ho = 0

Ha? 0

The data in Table (1) showed that there was a negative relationship between the risk-free rate and market returns. But this was not statistically significant variable was found. Thus, the null hypothesis was accepted that risk-free rate is not significant predictor. Alternative hypothesis was rejected. Figure (a) also shows that there is no relationship between them.

/ p> It is the most important, how can we measure the extent or strength of the relationship between two variables, dependent and independent variables or otherwise the determination is being developed to be the amount of variation in the dependent variables measure explained by the regression line.

The data in Table 1 indicated that the estimated value of R2 0.0123 shows that the strength was the association between the equity markets and risk-free rate is very low in other words, only 1.2% the total variation of stock returns by the independent variable explains.

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6.4 correlation

correlation coefficient is the second measure, describing how a variable can be explained by another variable. If the study is based on a sample date, then the correlation coefficient of marked (r) and is statistically the square root of the sample determination.

correlation coefficient (r) = 2 —————— (b)

If the slope the estimated equation (b) r is positive, the positive square root, but if (b) is negative, negative r, the square root. For instance, the sign of r the direction of the relationship between two variables in the stock market return and risk-free rate.

In the scenario study, the value (s) of determination was

r = -0.11

So the relationship between two variables is negative indicating that settlement is negative. The amount of r is 0.11 indicating that the risk-free rate was weak predictor of stock market development. to see

To reciprocal relationship between two variables, the RTS and the return of the market. Pearson correlation matrix was obtained by analyzing the data using a correlation model.

The results of this analysis are shown in Table 2.

Table 2

correlation

RTS

< / p>

RTS ¹

Sig (2-sided)

<1.000 p

0.403

M ²

Return Pearson correlation

/ p > Sig (2-sided)

<0.403 p

/ p <> / p <>

¹ risk-free interest rate

/ p> Stock Market Return ²

The above table shows 2 that the correlation between risk-free rate and stock market performance negatively. -0.110 Correlation is significant that the P-value 0.403> 0.05.

The data in Table 2 indicated that there was no significant relationship between these two variables, it was found that RTS and return of the market independently with each other

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The correlation coefficient is a statistical measure of standard linear relationship between two variables. A positive correlation means that move the returns of the two assets are typically in the same direction, while a negative correlation means that they usually move in opposite directions. A correlation coefficient of zero implies that this implies that the returns on two securities are uncorrelated;. They show no tendency to vary together either positive or negative linear

the current study, the goal, the relationship between some risk-free rate was determined and results of equity markets. It was found that the risk-reward had no effect on his return to camp. These variables move independently of one another ineffective because it has very low correlation and weak association between two variables. These results are also consistent with the study of trust A. Amadi, (Associate Professor of Finance at Florida A & M University), the study of the relationship between market risk premium and risk-free interest rate performed.

8 Recommendations :

In the current scenario of Pakistan, was the great need for investors to stocks with less correlation, which can be found to diversify their investment portfolios . In volatile markets such as the Karachi Stock Exchange (KSE), the T-Bill is a useful tool for investors want the shuffle and adjust their portfolios. Without losing sight of the findings and conclusions of the current study was proposed and recommended to investors that they can include treasury bills in their investment portfolios in order to save their investments to total collapse. These diversified investments increase yields and reduce the risk relatively more. The regression model also supports this recommendation applied

. References:

2 Stock returns in the long run: in the real economy by Roger G. Ibbotson participate, PhD. 9. July 2002.

3 A structured approach to return to the stock market, risk-free rate and Tamal Datta Chaudhuri CAPM Investment Bank of India, Ltd.. – Books Kolkata Icfai Journal of Applied Finance, vol. 14, No. 4, pages 21 to 31 April 2008

4 The tradeoff risk / reward in the long term .. 1836-2003 Christian Lundblad ¤ October 2004 discovery of the risk-return relation in the stock market, Hui Guo and Robert F. Whitelaw Working Paper 2001-001C in January 2001, revised in April 2005.

5 An Intertemporal Capital Asset Pricing Model by Robert C. Merton, Econometrica, Vol 41, No. 5 (September 1973), p. 867 887.stable URL. Econometrica is currently provided by the Econometric Society

6 published on the calculation of the risk-free rate. Testing asset pricing models * Mika Comments are welcome Vaihekoski 03/01/2007.

7 appreciate BM Company, residual income valuation model, the relationship between the growth rate in the long term abnormal returns and cost of capital. Rong Huang El (2005) Accounting Association, Göteborg

8 Wadhwani, SB (1999) “The U.S. stock market and the global economic crisis,” National Institute Economic Review, 86-105.

9 Bourse risk-return inference, a nonparametric approach unconditional Thomas Mikosch and ° C or ° Alin ST · Aric ¯ a and Danish Research Council grant no 21-01-0546.

10 Bond Portfolio Optimization risk-reward approach of Korn Olaf Christian Koziol and Dr. Olaf Korn Corporate Finance, (March 2002) School of Management Aduatiques, Burg Platz 2, D-56179 Vallendar, Germany Dr. Christian Koziol, Chair of Finance at the University of Mannheim, D-68131 Mannheim, Germany.

11 On the relationship between market risk premium and risk-free interest rate of confidence w. Amadi (Sep 2005) Finance at the University of Florida A & M.

Exchange rate changes