# Application Of Capm In Measuring Risk And Return Finance Essay

Abstract

Capital asset pricing model (CAPM) is an equilibrium model which uses to show the relationship between the risk and return of an individual asset or portfolio of assets. In other words, CAPM indicates how assets are priced considering their risk. According to the portfolio theory, investors use diversification in order to reduce unsystematic risk. Efficient portfolios will dominate other investments and each investor will select one of the efficient portfolios based on the degree of his risk-aversion.

Previous studies done in Iran or other countries on CAPM, considered the application of the model for individual stocks, portfolios of stocks, specific assets, or the market indexes. Only few studies applied the CAPM model for major real assets of the economy. Considering this gap of research that extended this model to other markets, this study applies the CAPM to measure systematic risk and expected return of selected markets in Iran's economy, the gold market, currency market, stock market and real estate market, for the period from the first quarter of 1995 to the second quarter of 2007.

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The research results showed that negative relationship exist between systematic risk with realized and expected return of the currency market, a negative relationship between risk and expected return rate in the stock market, and a positive linkage between these two variables in the real estate market. On the other hand, there is no significant relationship between risk and realized return in the stock market and the real estate market. Furthermore, lack of significant relationship between risk with realized and expected return is found in Gold market.

Key Words: CAPM, Systematic risk, Financial Assets, Expected Return, Real Return.

## Introduction

CAPM is an equilibrium model used to show the relationship between risk and expected return for individual assets and for portfolios. In other words, CAPM shows how assets are priced considering their risks. CAPM assume that investors use diversification in an attempt to reduce unsystematic risk. According to the portfolio theory, efficient portfolios will dominate other investments and each investor will select one of the efficient portfolios based on the degree of his risk-aversion (Treynor 1961; Sharp 1964; Lintner 1965).

To date, various studies have been done to describe the relationship between risk and expected return of stock market in Iran and other countries. These studies mostly considered stocks of one company, the stocks combination of some companies, specific assets, or the market indexes. They mainly attempt to answer two questions (1) how the risk of assets should be measured, and (2) what relationship exist between risk and expected return of investors (i.e. Basu 1977; Rosenberg, Reid, and Lanstein 1985; Bakhshande 1990; Hamedani and Pirsalehi 1993; Shafizadeh 1995). To answer these two questions, first it is assumed that investors are able to select their preferred portfolio among different portfolios based on the expected return and the variance. Second, all investors agree on investment horizon and distribution of expected returns of assets, and also there are no imperfections in the capital market (Copeland, Weston and Shastri 2005).

On the other hand, the empirical research mostly investigated the asset's return dependence on the market return and also the linear relationship between risk and expected return in each selected stock markets (i.e. Lakonishok and Shapiro 1986; Shafizadeh 1995; Zarif fard and Ghaemi 2003). In general, studies on CAPM model were not limited only to the stock markets, this model was also used in other markets to explain the relationship between risk and return (i.e. Kullmann 2001; NG 2003; Jafari samimi et al., 2006).

Many of research about CAPM in the context of stock markets in one hand and the lack of research to extend this model to other markets in the other hand, provide this opportunity to generalize CAPM to other markets. In other words, this study will apply CAPM to estimate the systematic risk and expected return in four selected markets in the Iranian economy, namely, real estate market, stock market, gold market, and currency market. This study will cover the period from the first quarter of 1995 to the second quarter of 2007.

This study in addition to estimating the systematic risk for these four selected markets of Iran's economy based on CAPM, tried to find out the following (1) Is there a significant relationship between the systematic risk and the corresponding rate of expected return in currency, stock, gold, and real estate markets, (2) Is there a significant relationship between the systematic risk and the realized return in the selected markets, and finally If so, what type of relationship exists?

This paper is organized as follows; Section II discusses the existing empirical literature on the CAPM and its development in other areas. Section III states the theoretical basis pertaining to CAPM. Its applications in measuring the systematic risk and return of four selected markets of Iran are explained in Section IV. The data used in the study and the methodology that examines the testing of unit root and linear regression is explained in Section V, and finally the results and findings of research are concluded in Section VI.

## Literature Review

The CAPM was developed by Sharpe (1964) and Lintner (1965) and it relates the expected rate of return of an individual security to a single index. The sensitivity of the asset return to changes in that index is a measure of the asset systematic risk. In fact, the index may be any variable thought to be the dominant influence on stock returns and need not be a stock index (Jones, 1991).

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The CAPM predicts that the expected return on an asset above the risk-free rate is linearly related to the non-diversifiable risk, which is measured by the asset's beta. The CAPM is a single-period ex ante model. However, since the ex ante returns are unobservable, researchers usually rely on realized returns in order to test the validity of the CAPM.

However, a growing number of studies found that the cross-sectional variation in average security returns cannot be explained by the market beta alone, and showed that fundamental variables such as size (Banz, 1981), ratio of book-to-market value (Rosenberg et al., 1985; Chan et al., 1991), macroeconomic variables and the price to earnings ratio (Basu, 1983) account for a sizeable portion of the cross-sectional variation in expected returns.

Jagannathan and Wang (1996) show that the lack of empirical support for the CAPM may be due to the inappropriateness of basic assumptions made to facilitate the empirical analysis. For example, most empirical tests of the CAPM assume that the return on broad stock market indices is a good proxy for the return on the market portfolio of all assets in the economy. However, these types of market indexes do not capture all assets in the economy such as human capital.

Basu (1975) investigated the relationship between risk and (E/P) ratio with asset's return in stock market. The research evidence showed that companies with higher (E/P) ratio have high returns. Reinganum and Banz (1981) mentioned that Companies' size has a significant effect on stock return and the ones with a smaller size have a higher return. Benz (1982) found that adding the market value of the firms to the regression between return and stock beta helps to have a better clarification for the average return of company's stock differences. The evidence of Rosenberg, et al. (1985) showed that there is a positive relation between the average stock return of American companies and the book value of common stocks. Lakonishok and Shapiro (1986) investigated on the relationship between the systematic risk and the firm size with stock return; they found that there is a weak relationship between beta with stock return, and a significant relation between market's prices of stock return with stock return.

To conclude, the testing of the CAPM is susceptible to many difficulties. Among those, the problem of finding a suitable market proxy. To overcome this problem, Hou (2003) used a hypothetical market portfolio to proxy the true market portfolio in the CAPM testing. This aggregate market portfolio has GDP as its dividends. As a result, it is supposed to include every factor that contributes to the accumulation of wealth. This approach is particularly relevant to this study since we will test four different markets and no other proxy can serve as a market portfolio for the selected markets.

In Iran, studies done on CAPM, such as Bakhshande (1990), Hamedani et al., (1993) and Shafizadeh (1995) on risk and return in Tehran Stock Market found that there is a linear relationship between systematic risk and return of common stock. The research evidence of Hesami (1998) showed that a correlation between (P/E) ratio and exist, with stock return. Mosavi Kashi (1988) found that there is no linear relation between size and stock return. He also found that (P/E) ratio and rate of return have a weak relationship. The research results of Mirzai (1999) showed that, (B/M) ratio, (E/P) ratio and (C/P) ratio were related to each other during the past years and value strategy can be an appropriate method for investment. (E/P) ratio and (C/P) ratio are highly correlated with the future return of stocks, and through investing in stocks with higher ratios, higher return is expected too. The research evidence of Pourreza (2000) detected that there is a significant relation between stock return, portfolio, macro and monetary factors of the economy. Shafiezadeh (1995) showed that systematic risk and return have significant relation in terms of statistics. He also found that non linear relationship helps to have a better clarification for the relation of systematic risk and stock return in comparison with linear models. Jenani (2003) investigated on the relationship between two indicators, (P/E) and the real stock returns of the industrial nonmetal minerals groups companies. In continue Zarif fard and Ghaemi (2003) mentioned that measuring systematic risk alone can't satisfy the stock return changes. Nosratollahi (2003) used the CAPM model to evaluate the efficiency of Tehran Stock market and pricing mechanism. Although the market efficiency hypothesis of Tehran Stock Exchange was not supported, yet the possibility of over pricing or under pricing securities is not rejected.

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In all studies mentioned above, CAPM were used to analyze the risk and return in stock markets (mainly companies stocks). Studies which studied the applications of CAPM in other economic activities other than the stock market have also been done. The purpose was to prove that CAPM has capabilities to be used for analyzing other assets, especially for assets in the macro economy.

Using an intertemporal multifactor asset pricing model, Doukas, Hall and Lang (1999) tested whether foreign currency exposure is priced in the capital market of Japan. This study relies on the assumption that the currency-risk premium changes through the time in response to changes in business conditions and investors' perception of risk. Their asset pricing model tests showed that the foreign exchange-rate risk premium is a significant component of Japanese stock returns. Specifically, the results suggested that currency-risk exposure controls a significant risk premium for multinational and high-exporting Japanese firms. The currency risk factor is found to be less influential in explaining the behavior of average returns for low-exporting and domestic firms. However, it is shown to exhibit large return volatility that is likely to be perceived by investors, who wish to control portfolio risk, as an important underlying source of risk.

Kullmann (2001) used CAPM to examine whether residential and commercial real estate risks carry positive risk premiums. By using both Fama Macbeth cross-sectional regression techniques and a stochastic discount factor, GMM framework is tested to find whether the cross-sectional explanatory power of well-known asset pricing models can be improved by adding a real estate factor. He found strong evidence for the hypothesis that both residential and commercial real estate risks are priced by the market and therefore have a definite role in empirical asset pricing specifications. The research evidence showed that returns of real estate market are not sensitive to the pricing of the assets.

Ng (2003) investigated the relationship between average return of currency market and the stock market of U.S., Japan, Germany and England. He mentioned that international CAPM has a great potential to be used to analyze risk and return for the two main economic assets in those countries, i.e. the Stock market and foreign exchange market. Jafari samimi et al., (2006) applied the combined method of Markowitz efficient portfolio and capital asset pricing model on petro-chemistry, gas injection, and gas export in Iran. They found optimal portfolios, which derived from various allocations to different gas consumption choices and also create the best value in different risk levels, through the Markowitz efficient portfolio theory. The authors reached to an efficient frontier by combining all of these efficient portfolios. Then through implementing CAPM they found the efficient portfolio. With definite pricing of all possible assets, an efficient market line was achieved. The authors reached to an efficient combination at the tangent point of efficient market line with efficient frontier. Based on this model Jafari samimi et al., (2006) computed the efficient portfolio for alternative combinations of petro-chemistry, gas and gas injection projects in five different scenarios of 100, 200, 300, 400, 500 million cubic meters.

This study will add to the literature in a sense that CAPM will be utilized in new markets for the first time in determining the systematic risk of the four selected markets in Iran.

## Theoretical Basis

The CAPM is an equilibrium model that shows the relationship between risk and return for individual assets. It was developed by Sharpe (1964), Lintner (1965), and later generalized by Black (1972). This model states that expected returns of individual assets should be a linear functions of their systematic risk. The model has been built on five key assumptions. These assumptions include that the investors have homogeneous expectation about asset returns, they are risk- averse individuals who maximize the expected utility of their wealth, they may borrow or lend unlimited amount at risk free rate, all assets are marketable divisible, and there aren't market taxes, regulations, or restrictions on short selling.

The equation of CAPM is as follows;

(1))

Where E (rj), Rf, E (Rm), and are expected return for asset j, risk free return, market portfolio return, and systematic risk respectively.

The systematic risk of an asset is calculated by its beta, which is defined as the covariance of the asset's return with the return of market portfolio, it is normalized by the variance of the market portfolio returns. Coefficient for an asset is calculated as follow (Copeland, Weston and Shastri 2005):

((2(

The easier equations can be used to calculate systematic risk is as follows;

((3(

((4(

((5(

((6(

The beta coefficient is a very important index for CAPM, it defines the sensitiveness of asset's return rate to market return rate. If it becomes equal to (1), the expected return rate will be equal to the market rate of return. If beta coefficient considers as (2), the expected return rate will be higher than the market return rate. Also, if beta coefficient supposed to be 0.5, the expected return rate will be lower than the market return rate.

## Figure 1. The Relation between Risk and Return for Individual Return

Figure (1) explains the relationship between risk and expected return for individual asset and total of assets (the portfolio). It shows that when the risk increase on the capital market line (CML) and the stock market line (SML), the return will rise simultaneously.

## Figure 2. CML in Different Status

As shown in Figure (2), with increasing the correlation coefficient between risk and return, the relationship becomes direct, and with increasing the risk the return also increases. In contrast, when the correlation coefficient decreases, it leads to changing the relationship and even makes it reverse and negative.

In this condition, the relationship between risk and return will be reverse and return rate in negative correlation coefficient declines to be lower than risk free rate of return. When the correlation coefficient between two variables is equal to 1, (, the CML,, will be equal to the stock market line, , due to being equal of and in this situation.

## CAPM applications in the systematic risk of four selected markets in Iran

## A. Extending of the CAPM model to the entire economy

To measure the systematic risk of the four major economic markets (gold, currency, real estate and stock market), first the required variables for the CAPM should be calculated for each of them. Required variables are return for each asset, risk free return, portfolio return (or return of total market).

The calculation of each asset's return and risk free return is no major problem; however the main problem is selecting an appropriate alternative criterion. In the calculation of company's stocks systematic risk, total return of the stock market or total return of the specific industry is considered as an index. But when we look at the selection of appropriate assets from macro approach, the chosen index should indicate the average return of the investments in the entire economy. If an investor is going to invest in one of these four major selected markets, the main assumptions of CAPM should be considered, first: the ability of choosing among the different portfolios based on the investors' desired expected return and the variance. Second, the information about investment horizon and the distribution of asset's return are clearly exist.

Thus for each of the markets the same return will be expected. On the other hand an investor can invest in every other markets of the economy and obtain the same return. The average return of total economy can be a suitable criterion for portfolio return, because the economic growth achieved from average return of all markets' returns in an economy, and one expects that with investing in each of the economy markets obtain an average return equal to the economic growth, and if the obtained return was less than the amount, he gain less than the portfolio return and vice versa. What Hou (2003) says about choosing GDP?? .Following Hou (2003), we choose GDP to proxy the market portfolio.

So the average return of total economy can be a good criterion that a person can consider if he wants to invest in any of these four selected markets. Economic growth indeed can be defined as a return of physical and human capitals exists in an economy in a specific period. In other words, a person with utilizing his human and physical capitals- respect to the production function in the economy- can add to the production flow of the economy.

If K considers as the amount of physical capital of a person, and L considers as the human capital, an investor who utilizes his capital in the economy can obtain certain amount of return. The average expected return depends on the production function of the entire economy. Therefore one can expect Q amount of production in T periods of time through average production function of economy F, with applying his capitals:

(7(

A change in production in each periods of time is due to the changes of human and physical capitals:

(8(

(9(

(10(

(11(

These equations indicate that economic growth in specific period of time is due to the growth of the one's human and physical capitals. If obtained return was less than this amount it means that he gain less than portfolio return and vice versa.

## B. Describe the Method Used to Calculate the Return in the Four Selected Markets

To measure systematic risk for the four selected markets of the economy, gold, currency, real Estate and stock market, first returns for all of these markets were calculated.

In order to find the gold market return, the percentage of changes in gold coin price was used, with the justification that, the owners of the gold coins benefit or lose based on the increase or decrease of its price. For Currency, the percentage of dollar exchange rate in non-official foreign exchange market of Tehran was considered. For Currency, the owner of one dollar note will gain return with the increase in the dollar exchange rate. For Stock market, the percentage change in total index of Tehran Stock Exchange was considered, because it is assumed that one's stock price will be increased in average the same amount as the total stock market increase. Finally, for the real market, total percentage changes of house rental index in large cities and property index, rental fees and business activities as an outcome of housing and real estate is considered.

As for the risk free rate of return, short-term interest rates for deposits has been used. Meanwhile, for the growth rate of GDP, the constant 1996 prices compared with the same quarter at the previous year, as the return criterion was considered.

All data used are quarterly and include the years from 1995 to 2007. All data were gathered from time series data bank of Central Bank of Islamic Republic of Iran [1] .

The expected rate of return is the rate of return when one invest in an asset and expect to gain benefit with the proportional amount of imposed risk in the future.

## Data and Methodology

## Systematic risk of four selected markets in Iran

To measure the systematic risk of each market, first the average rate of return for the market and the portfolio return were calculated. Then variance of the market prices during the selected period was determined using equation (3). Equations (5) and (6) were used to show the market correlation and systematic risk. To calculate expected rate of return equation (1) was utilized. All the results of these calculations and their analyses are as discussed below.

Since the linear regression is applied to test the research hypotheses and the existence of time series for the research variables, each independent and dependent variables should be tested to confirm their stationary by using testing of unit root. If absolute value of ADF statistic is lower than the absolute value of each critical value 1%, 5% and 10%, so hypothesis will be rejected, means that the considered variable is stationary. According to this definitions and result of Table 1, all independent and dependent variables of this research are stationary due to being lower than the absolute value of ADF Statistic relative to each the critical values.

## Table (1). Unit Root Test by Using ADF Test

## Variables

## ADF Statistic

## Critical value

## Stationary/non stationary

## 1%

## 5%

## 10%

Systematic Risk of Currencies

-6.378

-3.6

-2.935

-2.605

Stationary

Systematic Risk of Stock

-4.719

-3.621

-2.943

-2.61

Stationary

Systematic Risk of Housing

-7.345

-3.596

-2.933

-2.604

Stationary

Systematic Risk of Gold

-7.228

-3.6

-2.935

2.605

Stationary

Expected Return of Currency

-5.282

-3.605

-2.936

-2.606

Stationary

Real Return of Currency

-4.84

-3.61

-2.938

-2.607

Stationary

Expected Return of Stock

-7.797

-3.592

-2.931

-2.603

Stationary

Real Return of Stock

-7.404

-3.592

-2.931

-2.603

Stationary

Expected Return of Housing

-8.761

-3.592

-2.931

-2.603

Stationary

Real Return of Housing

-7.702

-3.592

-2.931

-2.603

Stationary

Expected Return of Gold

-11.557

-3.584

-2.928

-2.602

Stationary

Real Return of Gold

-7.003

-3.592

-2.931

-2.603

Stationary

To continue, each of the selected markets will be analyzed in terms of the CAPM assumptions.

## Currency Market

The currency market is considered as a vital substitute market for formal markets in Iran's economy. Risk of this market explains the sensitivity of the expected return fluctuations of investment in currency with the portfolio return. Changes trend of systematic exchange rate risk (Figure 3) indicates it is less than (1) for most of the selected periods. This means that the expected return of investor when invests in the currency market is lower than portfolio return (which is economic growth here). Furthermore, having low systematic risk during research periods explains two points; firstly, in these periods, risk-averse individuals willing to invest in currency market, and secondly, because of low risk of investment, investors' return is also low, so they are not willing to invest in this market. One of the most important reasons might be because of one-rate policy applied for the currency market by government during this period which led to eliminating the arbitrage opportunities in the market.

## Figure 3. Changes Trend of Systematic Risk in Currency Market

Trend of expected return rate changes for the currency market in Figures (4) and (5), indicates that there is an asymmetric changes between systematic risk and return, meaning that when systematic risk increases in one period, investors expect that return increases as well, but actually such changes in expected return rate are not observed in the figures. Especially, this trend between risk and return is observable from the third quarter of (1998) to the end of research period. The reasons of these trends can be implied in controlling policies for the currency markets by central bank of Iran, other markets were more attractive in comparison with currency market in some research periods and also applying one-rate policy to eliminate the arbitrage opportunities in this market after (2001).

Linear regression between systematic risk (independent variable) and expected rate of return (dependent variable) of currency market were used to test whether there is a significant relationship between risk and expected return rate in currency market.

There isn't significant relationship between systematic risk and expected return rate

There is significant relationship between systematic risk and expected return rate

## Figure 4. Changes Trend of Expected Return Rate of Currency Market

Generally, when the regression coefficient is positive it means that there is a positive relationship between risk and return. Therefore, the market will be in equilibrium, and risk and return will change in the same direction, this status is compatible with the concepts of CAPM.

According to the above definitions, the regression results of systematic risk and expected return rate show that return coefficient is significant in the level of first type error (5%), so is rejected and is accepted, it means that there is a significant relationship between risk and expected return rate in Iran's Currency market.

Furthermore, coefficient of independent variable is negative, so the relationship between systematic risk and expected return rate will be negative during research period. This means that investors don't get the return amount coordinated with the corresponding risk, and so the market is not in equilibrium. In addition, significant coefficient () is equal to 38.3% that is acceptable due to existence of only one descriptive variable in regression equation.

## Figure 5. Changes Trend of Expected Return and Systematic Risk of Currency Market

Now to describe the relationship between the risk and return more accurately, another model based on the systematic risk and real return is used. As shown in figure (6), the trend of systematic risk and real return changes are relatively coordinated (Although, low coordination has experienced in some periods). Changes of real return considerably have decreased from the third quarter of (1998) to the second quarter of (1999), and the stable trends for the other research periods can be seen.

## Figure 6. Trend of Real Return and Systematic Risk changes in Currency Market

The real return fluctuations decreased from 2001 onwards due to applying the policy of one-rate for currency rate, also the ability of the central bank to control the irregular fluctuations of the currency. This policy considerably led to the decrease of real and expected return for this market, so the market attractiveness severely has declined for risk-loving investors.

The results of regression between systematic risk and real return of currency market are similar to the results of expected rate of return, so that return coefficient is significant for the first type error (5%), and P-Value is equal to (0.001). Therefore, hypothesis rejected and hypothesis is accepted. Furthermore, coefficient of independent variable is negative, means that there is a negative relationship between systematic risk and real return of currency market in the research period. The significant coefficient of regression () also is equal to (18.2%) that is relatively acceptable considering the existence of only one descriptive variable in the regression equation.

## Stock Market

The trend of systematic risk changes for stock market indicates that the risk index is higher than (1) in some periods (i.e. 3th and 4th quarter 1995, 4th quarter 1996 to second quarter 1998), means that investors expect to get higher returns than portfolio return during the cited periods. Therefore, these periods are attractive for less risk averse individuals. In some other periods which the systematic risk is lower than (1), investors expect to get lower returns in comparison with the portfolio return; especially this trend is observable at the end of research period. The positive trend of changes at the first quarter of (2001) and (2003), the third quarter of (2004) and the second quarter of (2005) are due to public culture reinforcing for using stock market as a suitable market to invest, establishing the local stock markets, improving and regulating the controlling laws for stock market, developing broker forums, and investment consulting companies.

As shown in figure (7), the systematic risk is lower than (1) from the third quarter of (2005) to the second quarter of (2007), this trend was simultaneous with the recession periods of Iran's stock market. The main reasons of this recession were the management changes in economy, political shocks resulted by economy sanctions, state structures of Iran's economy and the dependency of many companies to the government which decreases the applicants to finance in stock market.

## Figure 7. Changes Trend of Stock Systematic Risk in Stock Market

Investigations on the trend of expected return rate and systematic risk changes in the stock market (figure 8 and 9), show the coordinated movements between systematic risk and expected rate of return from the first quarter of (1995) to the first quarter (1996), and also from the second quarter (2001) to the second quarter of (2004). In the other periods the relationship between risk and expected return was opposite, so by increasing risk, return decreases and vice versa, and the peak of this trend observed at the end of research period. This status probably is due to existence the political shocks resulted by macro management changes of government, and also economic sanctions.

## Figure 8. Changes Trend of Expected Return Rate of Stock Market

The result of testing the significance of the systematic risk and expected return rate in stock market indicates that the return coefficient is significant in error level of 5%.

In other words, P-Value is equal to (0.0345), so hypothesis is rejected and hypothesis, based on the significant relationship between systematic risk and expected return rate, is accepted. The return coefficient of stock market is negative similar to the currency market (equal to -4.657013) which shows the inverse relationship between risk and expected return during the research period. This result is not compatible with the key principle of CAPM, which is "higher risk higher return". The significant coefficient () of regression also is equal to 0.091 that is very low.

## Figure 9. Changes Trend of Expected Return and Systematic Risk of Stock Market

As shown in the figure (10), the systematic risk and real return rate despite the primary quarters, have coordinated fluctuations at some periods (i.e. the 2th Quarter of 1998 to the first quarter 2000, 2th quarter of 2001 to the 4th quarter 2003, and the 4th quarter 2004 to the end of research period).

The regression results between systematic risk and real return explains accepting of hypothesis in the error level of (5%). It means that P-Value pertaining to this testing is equal (0.15), so hypothesis is accepted. The R-squared (0.043) shows that significant coefficient of the regression is insignificant; meanwhile the slope of equation line with amount of (0.13) is positive. The F statistic is (2.13) that shows the regression is not significant, despite the research sample which detects there is a positive relationship between risk and real return and emphasizes on attractiveness of the market for risk-averse individuals, this linkage is not significant statistically.

## Figure 10. Changes Trend of Real Return and Systematic Risk of Stock Market

## Real Estate Market

The real estate market is perceived as an important market in Iran economy. It is considered as a formal market that attracts the extra funds of investors (especially in recession periods of other markets).

As shown in figure (11), estate market has been faced to the systematic risk higher than (1) in many quarters such as the second quarter of (1995), the first and third quarter of (1996), the first quarter of (1998), and so on. This means that if investors invest in this market, they expect to get higher returns than portfolio return during the mentioned periods, so they willingly accept the higher risk for getting higher returns. Furthermore, the research results show that the systematic risk is lower than portfolio return (lower than 1) in some other periods, especially during (2006) and (2007) which are simultaneous with the recession of the estate market.

In fact, when the systematic risk is low it decreases the individuals interest to invest in this market because they know they will gain less return, and the decrease in investments in this market will lead to the recession of estate market.

## Figure 11. Changes Trend of Stock Systematic Risk in Estate Market

The trend of expected rate of return and systematic risk is shown in Figure (12). It indicates that except for some quarters (1995, 1996 and 1997), estate market is completely in equilibrium, and the coordination between risk and expected return is very high. But coordination between these two variables relatively declines at other periods, especially at the end of research periods. In other word, investors expect to increase their expected return rate with increasing the systematic risk and vice versa, but it actually doesn't happen at some periods.

## Figure 12. Changes Trend of Expected Return and Systematic Risk of Estate Market

The linear regression is applied in order to do more precise investigations on the relationship between risk and expected return. The result of regression test shows that return coefficient is significant in error level of 5% and P-Value is equal to 0.000, so hypothesis is rejected and against hypothesis is accepted, (the hypothesis related to the existence of the positive relationship between expected return and systematic risk is accepted because the systematic risk coefficient for this market is positive).

In other worlds, if individuals invest their extra funds to get return, they will get higher returns according to the higher risk and vice versa. The regression significant coefficient is equal to (0.32) that relatively is acceptable considering the existence of only one descriptive variable in the regression equations.

## Figure 13. Changes Trend of Real Return and Systematic Risk of Estate Market

Figure (13) shows the different fluctuations during research period, the positive changes was experienced from the first the periods to the first quarter of (1996), then uncoordinated trends started till the first quarter of (2006), this trend then has improved from (2006) to the end of research period. Furthermore, changes of risk and real return in some of period show that positive return has been faced to negative risk (insignificant risk close to zero). The least amounts of real return are in the second quarter of (2005) and (2006) which are the recession periods of estate market in Iran. After this period, the real return has increased from the 4th quarter of (2006), it was coincident with the price increase of this market's assets.

The regression results of real rate of return and systematic risk in Iran's estate market shows that slope of the line is positive, and the P-Value is (0.843) in error level of (%5), so hypothesis is accepted. Furthermore, significant coefficient () is equal to (0.0008) that is very insignificant. So there is no significant relationship between real return and systematic risk in Iran's estate market during this research period.

## Gold Market

In Iran economy, the gold market is an important substitute for formal markets, so that recession of other markets directs the extra funds toward this market. The changes trend of systematic risk (figure 14) shows the considerable fluctuations which are mainly close to (1), meaning that if individuals invest the extra funds to the market, they will expect to get the same return as the portfolio return. This trend almost continued to the most of the quarters, but it was stopped from the second quarter of (2005) onwards with intense fluctuations. The most important reason might be the changes in oil price, policies of central bank to issue money (open market purchase), and management changes in macro levels of the economy.

The changes trend of expected return rate indicates the coordination of returns with the corresponding risks in gold market.

## Figure 14. Changes Trend of Systematic Risk in Gold Market

Figure (15) detects this market is relatively in equilibrium and there is a logical relationship between risk and return.

## Figure 15. Changes Trend of Real Return and Systematic Risk of Gold Market

The results of the regression shows that P-Value is equal to (0.3), so the hypothesis is accepted, means that there is no significant relationship between systematic risk and expected return rate in Iran's gold market.

Investigation on the relationship between risk and real return in this market also shows similar results, the P-Value of the regression is equal to (0.21), and hypothesis is accepted (the real return doesn't have any logical or significant relationship with systematic risk in Iran's gold market).

## Table 2. The Regression Result of Research Hypotheses

## Markets

## Variables

## A. Dependent: Expected Return

## B. Dependent: Real Return

## Coeff.

## T-Stat

## Coeff.

## T-Stat

Currency

Constant

0.984176

0.376558

1.418029

2.208317

Beta

-4.410126

-5.405238

-0.68593

-3.421866

Stock

Constant

46.39972

1.310915

5.458832

3.568757

Beta

-4.657013

-2.177657

0.134883

1.459475

Estate

Constant

6.862992

1.377581

9.531631

16.63853

Beta

3.635603

4.797015

0.017340

0.198971

Gold

Constant

14.57965

1.046970

2.492337

2.651270

Beta

1.536802

1.030885

0.125544

1.247523

According to the results of Table (2), it seems that only currency market has consistent results, and the risk is significant in both situations.

Estate market, stock market and gold market are not significant just when the real return is used as dependent variable, although the gold market is not significant at all even when the expected return is considered as a dependent variable.

Numerous reasons can explain the un-equilibrium of Gold market in the two situations, which are categorized in the three following statues;

Investors can easily enter this market in comparison with other markets, (especially stock market). Going to this sensitive market needs low funds, and also low investment knowledge, so stagnancy of other markets will cause to move the extra funds to the Gold market. As a result, fluctuations of any other market rapidly affect its transactions and impose the instantaneous shocks on this market.

On the other hand, intense dependence exist between fluctuations of oil price and the gold price in international markets (generally) and Iran's market (particularly). Since the oil price mainly changes in seconds, it rapidly affects the gold market and will make this market un-equilibrium.

Inefficient monetary policies of central bank of Iran to control the instantaneous shocks resulted by fluctuations of oil price, and also entering irregularly funds from other market (at condition of their recession) to this market.

## Section VI: Conclusion

In this study, the relationship between systematic risk and return in four selected markets of Iran economy were analyzed utilizing the capital asset pricing model (CAPM).

To measure the systematic risk of these four selected markets (Gold, Currency, Real Estate and Stock market), first the required variables for the CAPM model were collected. Required variables were rate of return for each market, risk free return, and market index.

In the calculation of company's stocks systematic risk, total return of the stock market or total return of the specific industry is considered as an index. Here also the calculation of each asset's return and risk free return was no major problem, the main problem was selecting an appropriate index, because when we look at the selection of an appropriate index form the macro approach, the chosen index should indicates the average return of the investments in the entire economy.

In this case, for each of the four markets the same return will be expected, also an investor can invest in every other markets of the economy and obtain the certain return. Thus, the average return of total economy could be a suitable proxy for market index, because the economic growth achieved from average return of all markets' returns in an economy, and one expects that with investing in each of the economy markets obtain an average return equal to the economic growth.

After calculating the systematic risk and analyzing its trend, this study found that in all four selected markets systematic risk fluctuations increase considerably from (1995) to (2007). These results might be because of uncertain situations of the country during sanctions, changes of management teams at decision making levels in Iran and also inefficient policies of central bank to control the price fluctuations in these markets.

Trend of expected return changes in the currency market indicates that there is no positive relationship between risk and return, and also found that changes of risk and return toward each other is not in tandem (despite the CAPM concept). Some reasons might be because of control policies applied from central bank of Iran to the currency market or attractiveness of other markets in some periods to the investors, single pricing policy of currency, and no opportunity for arbitrage after 2001.

Changes trend of systematic risk in the stock market indicated the mentioned risk from the first quarter (1999) to the end of research period, except in six quarters, were lower than (1), which means the stock market was attractive for risk-averse investors during that period. The graph was negative or close to zero at the most mentioned periods, the peak was from (2005) onwards which are corresponding to the recession periods of stock market. In other world, this trend is consistent with stock market recession from (2005).

Respect to the analyzes of the relationship between the systematic risk and the real return in the Currency market and Stock market, this study found that in each of these two markets there is a negative relationship among systematic risk and expected return and also the real return (except the relationship between risk and real return in stock market) In other words, this pattern in these two markets is not consistent with CAPM.

Although regressions done for investigating those relationships in Estate market and the gold market shows that positive relation exists between systematic risk and expected return, but between systematic risk and the real return in these two markets no significant relationships were found (except the relationship between risk and expected return in Estate market).

So this study concludes that in the financial markets of Iran economy, (Currency and Stock markets), taking more systematic risks do not guarantee the higher returns, but this expectation exists in physical assets markets (Estate and Gold market). Therefore CAPM forecasts are not compatible in the financial markets of Iran economy. It might be because the financial markets of Iran are not developed very well, or investors are not quite familiar with the market. Also the higher returns of physical markets encourage people to invest in Estate and Gold market instead of financial markets.

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