Essay: Risk and expected return

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2.1. Introduction
This chapter presents the theories that have been developed and established to give details about the relationship between risk and expected return .Moreover, it presents the historical development of the asset pricing models, the assumptions and development of CAPM, arbitrage pricing theory, three-factor model, four factor model, and the impact of aggregate volatility risk on asset pricing and the portfolios return.
2.2. The Historical Development of the Asset Pricing Models
Finance was changed through the publication of Harry Markowitz (1952) article on “Portfolio Selection”. Since the days of Bernoulli, it was clear that individuals desire to increase their wealth, and also to minimize the risk related to a potential gain. Nevertheless, could they pool these two criteria? Markowitz studies and rejects the idea that they could construct a portfolio, which gives both the maximum expected return and minimum variance. He explains that, “the portfolio with maximum expected return is not necessarily the one with minimum variance. There is a rate at which the investor can gain expected return by taking on variance, or reduce variance by giving up expected return” (Markowitz, 1952).
The most important contribution of Markowitz study is making a difference between the variability of returns for individual security and the contribution to portfolio risk. He notes that “in trying to make variance small it is not enough to invest in many securities. It is necessary to avoid investing in securities with high covariance among themselves” (Markowitz, 1952). This conception supports most of the papers discussed in this review.
After that a new model had appeared called The Capital Asset Pricing Model (CAPM). It was introduced by Sharpe (1964), Lintner (1965) and Mossin (1966) independently, created from the previous work of Harry Markowitz on modern portfolio theory. Black (1972) has developed another version of the CAPM, called Black CAPM, which suggests the existence of a risk-free asset. This version was stronger against empirical evidence and was influential in the widespread adoption of the CAPM. Then Ross (1976) developed the Arbitrage Pricing Theory (APT) which is considered as one of the most fundamental models in finance. It is a multifactor model that takes into consideration other factors that are not taken in the CAPM. Thereafter, Fama and French (1992) expanded the CAPM by adding two additional factors to it, because the empirical tests show that the market anomalies similar to the size and value effects can not be explained by the CAPM. Then Carhart (1997) has added new factor called the momentum factor to the three-factor model of Fama and French to introduce the four-factor model. The momentum factor indicates that winner (loser) stocks in the last 3-12 months persist in their trend for the coming 3-12 months. This study tries to test the impact of aggregate volatility risk on various asset pricing models.
2.3. The Mean-Variance Models Of Markowitz
In 1952 Harry Markowitz builds the Harry Markowitz model (HM) through his article “Portfolio Selection”, which indicates to select the financial instruments that do not change exactly together. The HM model shows investors how to reduce their risk through diversification. Also, the HM model is called Mean-Variance Model because of the fact that it depends on the standard deviation (variance) and expected returns (mean) of the various portfolios.
Mean-variance model shows the way to allocate assets in a world of risk and return. The investor was expected to know the risks and the returns of all offered investments, nevertheless his or her choices were assumed not to affect the market, neither prices nor uncertainties in the expected returns. Markowitz made the following assumptions to develop the HM model (Kaplan, 1998):
Risk of a portfolio is based on the variability of returns from the said portfolio.
An investor is risk averse.
An investor prefers to increase consumption.
The investor’s utility function is concave and increasing, due to his risk aversion and consumption preference.
Analysis is based on a single period model of investment.
An investor either maximizes his portfolio return for a given level of risk or minimizes his risk for a given level of return.
An investor is rational in nature.
To indicate the best portfolio from a number of likely portfolios, each portfolio would have different risk (variance)and return (mean), two separate decisions are to be made: first the determination of a set of efficient portfolios; Second the selection of the best portfolio out of the efficient set (Rosset al., 2008).
After that, Markowitz developed the so-called Capital Market Line (CML).The CML is the tangent line passing from the risk free rate and tangent the efficient frontier at the market portfolio point. The market portfolio consists of the mixture of all risky securities and the risk-free security, using market value of the securities to control the weights.
2.4. The Capital Asset Pricing Models Development and Assumptions
1. Sharp (1964) Lintner (1965) and Mossin(1966) had developed the capital asset pricing model.
2. The first model that determines the minimum required rate of return on an investment given its level of systematic risk measured by a factor called beta.
3.The CAPM is the most universally widely used; The CAPM was introduced by Treynor, (1961, 1962) depending on Harry Markowitz model and later on was developed by (Sharpe, 1964; Lintner, 1965; and Mossin, 1966) independently. According to this model, the expected return of a security or a portfolio equals the rate on a risk-free asset plus a risk premium (Market risk premium multiplied by Beta). The CAPM is used in financial decision, such as helps to compute the risk and return on an investment, through the following Formula:
〖E(R〗_(i,t))=R_(f,t)+β_(i,m) 〖(R〗_(m,t) 〖-R〗_(f,t)) ………………..………………… (2.1)
E(Ri,t): is the expected rate of return on a security or portfolio i at the time t.
Rf,t: is the risk free rate of return asset (Return on T-bills) at the time t.
Rm,t: is the expected rate of return from the market portfolio at the time t.
Βi,m: is the slope coefficient (Beta) for asset or portfolio i, can be viewed as a standardized measure of systematic risk (no diversifiable risk).
The development of the model depends on some assumptions. These assumptions are (Blanco, 2012):
It is a static model (one period).
There exists fixed asset supply.
There exists a zero net supply risk free asset (borrowing and lending at same rate r).
The returns follow a normal distribution.
There are homogeneous expectations about investment opportunities set.
The financial markets are competitive markets.
There no transaction costs (taxes, frictions, and so on).
The graphical representation of the CAPM is the SML, which is derived by the CAPM, explaining expected return at different levels of risk (Ross et al., 2008).
The empirical tests of CAPM expose the existence of several problems when it is applied in computing returns for the reason that a number of investigators evaluated the way beta is calculated. For example, Miller and Scholes, (1972) and Jensen et al., (1972) show that various problems in estimating beta came from the change in the risk free rate of return over time, and the expected rate of return on assets is nonlinearly related to beta. Moreover, they reject the formula of the CAPM because of the problem in computing beta.
Fama and French (1993, 1996, and 1998) recommend that return is associated with size (Market capitalization) and value (Book-to-market ratio). It is styled in a multifactor edition of Mertons (1973) intertemporal capital asset pricing model (ICAPM) or Ross (1976) arbitrage pricing theory. The special challenge for asset pricing is the stochastic elements of data generation that can not be controlled (Fama and French, 1993, 1996, and 1998; Mertons, 1973; Ross; 1976).Fame and French (2004) say that “the failure of the CAPM in empirical tests implies that most applications of the model are invalid”. The cross-sectional forms of stock returns are closely related to features like book-to-market ratio (value), market capitalizations (size) and stock return momentum (Fama and French, 1993; Carhart, 1997). Therefore, to overcome the CAPM problems a new model has been established (The arbitrage theory). The following section presents the explanation of this model.
2.5. The Arbitrage Pricing Theory Development and Assumptions
Ross (1976) developed the Arbitrage Pricing Theory (APT) which considered as one of the most important asset pricing models in finance. It is a multi-factor model that takes into account other influences that are not taken in the CAPM.Moreover, the APT basically has two differences from CAPM. First, the fact that the equilibrium relationship is only approximate and is derived based on the assumption of the absence of arbitrage. Second, the model assumes several factors that affect the actual and expected returns on assets, compared with the market portfolio in CAPM. The main assumptions of the APT are:
Efficient markets (perfectly competitive).
Investor expectations are homogeneous.
The stochastic process generating asset returns can be expressed as a linear function of a set of N risk factors.
The theory assumes that the stochastic process generating asset returns can be represented as an N factor model as follows:
〖E(R〗_i)=R_f+β_(j,1) f_1+β_(j,2) f_2+β_(j,3) f_3+⋯+β_(j,N) f_N+ε_(j,t) …….. (2.3)
E(Ri): is the expected rate of return on a security or portfolio i.
Rf: is the risk free rate of return.
βj,1, βj,2, βj,3, and βj,N: are the sensitivity of the asset’s J return to the particular factor.
f1, f2, f3, and fN: are the market prices associated with the particular factor.
εj,t: is the random error term.
2.6. The Three-Factor Model
In 1992 Fama and French published an article entitled “The Cross-Section of Expected Stock Returns”;they show that the small firms seem to provide higher risk-adjusted returns than large firms. In other words, small firms outperform large firms; this is called the size effect .They also show that firms with high B/M ratio outperform low B/M ratio firms; this is called the value effect (Fama, 1991).
Fama and French (1993) have added two factors to the CAPM.They argue that the empirical tests indicate market anomalies such as the size (market capitalization) and value (Book-to-market ratio) effect that can not be explained by the CAPM.Fama and French (1993) show that size and value affects stock returns. The size and value risk factors improve the explanatory power of the CAPM (Fama and French, 1992).The well-known Fama-French Three-Factor Model is as follows;
R_(i,t)=α_i+β_1 〖(R〗_(m,t)-R_(f,t))+β_2 〖SMB〗_t+β_3 〖HML〗_t+ε_(i,t)
Ri,t: is the return of stock i at time t.
(Rm,t-Rf): is the market risk premium.
Rm,t: is the average market return at time t.
Rf,t: is the risk free rate at time t.
HMLt (high minus low): is the difference between the average rates of return on high and low book-to-market equity stocks at time t.
SMBt (small minus big): is the difference between the average rate of return on small and large stocks at time t.
β1, β2, and β3: are the coefficients of the model.
εi,t: is the random error term.
αi: is the constant term for stocki.
2.7. The Four-Factor Model
Carhart (1997) has added a new factor to the Fama-French Three-Factor Model; it is called the momentum factor to formulate his four-factor model. In finance, momentum is the empirically practical tendency for increasing asset prices to increase further, and dropping prices to continue dropping. For example, momentum effect indicates that stocks with good past performance remain outperform the stocks with bad past performance in the following period with an average excess return of around 1% per month (Jegadeesh and Titman, 1993).Carhart (1997) argues that the momentum factor significantly affects the cross section of stock returns. The Carhart four factor model is as follows;
R_(i,t)=α_i+β_1 〖(R〗_(m,t)-R_(f,t))+β_2 〖SMB〗_t+β_3 〖HML〗_t+β_4 〖MOM〗_t+ε_(i,t)
Ri,t: is the return of stock i at time t.
(Rm,t-Rf): is the market risk premium.
Rm,t: is the average market return at time t.
Rf,t: is the risk free rate at time t.
HMLt: (high minus low): is the difference between the average rates of return on high book-to-market equity and low book-to-market equity stocks at time t.
SMBt: (small minus big): is the difference between the average rate of return on small stocks and the average rate of return on big stocks at month t.
MOMt: (the monthly premium on winners minus losers): is the Momentum factor return at time t.
β1, β2, and β3: are the coefficients of the model.
εi,t: is the random error term.
αi: is the constant term for stock i.
2.8. Additional Risk Factors in Asset Pricing Model
There are numerous studies , that have added many factors to asset pricing models in order to improve the ability of the explanation of these models, and in what follows, some of these factors:
1- Liquidity Risk Factor
Financial markets are exposed to different types of risk. But most of the academic literature perceived liquidity risk factor as a normal part of daily processes on the financial markets. It refers to the failure of company assets quickly enough, or the market price to prevent loss and most assets can be converted into cash with the passage of time, but if certain assets should be sold at once. There is a possibility that this could be the high cost of the cheapest (Babies and Urniežius, 2012). Amihud (2002) established a measure of stock illiquidity that is easily and cheaply computed using daily prices and trading volume data, and he found that it is strongly priced in the cross-section of stock returns. This finding has been approved by (Chordia et al., (2009)).
2- The Trend Factor
Han & Zhou (2013) used the moving average prices to create the trend signals and to predict the expected stock returns. Stocks that have high predicted expected returns tend to return higher future returns on average, while stocks that have low predicted expected returns tend to return lower future returns on average. The difference among the highest ranked and lowest ranked quintile portfolios sorted by the predicted expected returns is about 3% each month, even after controlling for the market risk and risks related with the SMB, HML, and momentum factors. The cross-sectional predictability and profitability of the trend signals are strong to various firm and market features, such as book-to-market ratio, size, trading volume, past return, etc.
3- Price-Earnings ratio (P/E) Effect
Basu (1977) examined the relationship between the historical P/E for stocks and their earnings. Some evidence shows that low P/E stocks will outperform the higher P/E stocks of comparable risk. Basu (1983) finds that the P/E ratio has additional power to explain stock return in addition to size and beta. Ball (1978) argues that P/E can serve as a substitute for factors identified in expected returns. The reason is that when stocks have relatively high risks and expected returns their prices tend to be lower relative to income and therefore the P/E is likely to be higher as well.
4- Profitability Factor
Fama and French (2015) examined the relationship between profitability premium and stock return. Theyfound that the profitability premium is higher for small stocks than big stocks;nonetheless the evidence that the expected premium is larger is weak. The average difference between profitability premium and small stocks(RMWS) and profitability premium and big stocks (RMWB) are less than 1.3 standard errors since zero. The average value of profitability premium and big stocks (RMWB) is 1.94 standard errors from zero, nonetheless with the improvement to the premium if by joint controls, the t-statistic rises to 3.47, and the average difference between profitability premium and small stocks (RMWS) and profitability premium and big stocks (RMWB) is only 0.84 standard errors since zero.
5- Investment Factor (Investment premium)
Fama and French (2014) examined the relationship betweeninvestment premium and stock return. Theyfound that the strong evidence that the expected investment premium is higher for small stocks (Size). The average value of investment premium and small stocks (CMAS) is 4.61 to 5.43 standard errors since zero, nonetheless the average value of investment premium and big stocks (CMAB) is only 0.98 to 2.00 standard errors since zero, and it is more than 2.2 standard errors below the average value of investment premium and small CMAS, in other words, the investment premium significantly improves the return on stocks small size.
Aggregate volatility risk has the main role in this study. The next section presents the aggregate volatility risk and the techniques to measure it.
2.8. Aggregate Volatility Risk
In this concern, Barinov (2012) pointed that investors comply with low returns of new issues, since these firms generally make positive abnormal returns in response to surprise increases in expected aggregate volatility. He approached the risk of losses in response to surprise increases in expected aggregate volatility as a separate risk factor in Merton’s (1973) Intertemporal CAPM (ICAPM). Furthermore, Barinov showed that, with the aggregate volatility risk factor, small growth firms and new issues in the ICAPMaccumulate positively on the factor that simulates innovations to aggregate volatility which provides a barrier against increases in aggregate volatility when compared to firms with similar market betas. The ICAPM beginnings of new issues and small growth firms are marginally different from zero. This suggests that the low returns of new issues are more likely to be the evidence of their low cost of capital than the value-destroying behavior of the management.
Significant information about future investment opportunities and future consumptioncan be drawn from changes in expected aggregate volatility. Some studies, such asCampbell’s (1993) and Chen’s (2002),provided versions of the ICAPM, in which aggregate volatility risk is priced. Campbell (1993)suggested that an increase in aggregate volatility causes higher risks and lower consumption in the next period. If expected aggregate volatility surprisingly raises,consumers, wishing to smoothen consumption, have to save and cut current consumption.In addition, Chen (2002) noted that, in response to surprise increases in expected aggregate volatility, consumers will develop precautionary savings and cut current consumption. This is consistent with the persistency of aggregate volatility which will have the same values the future. In both Campbell’s (1993) and Chen’s (2002), stocks with the most negative return correlation with surprise changes in expected aggregate volatility were found to earn a risk premium. The value of these risky stocks drops when consumption has to be cut to increase savings.
Recently, Ang et al. (2006) confirmed the hypotheses of Campbell (1993) and Chen (2002). They used the CBOE VIX index, which is defined as the implied volatility of S&P 100 options, to proxy for expected aggregate volatility. They found that firms with more negative return sensitivity to the VIX index changes actually have higher expected returns than firms with less negative sensitivity to VIX changes.
On the other hand, Barinov (2012) identified the firms that are the least exposed to aggregate volatility risk .He found that small growth firms and new issues usually have abundant growth options and high idiosyncratic volatility. This indicates that the more growth options and idiosyncratic volatility a firm has, the less it is exposed to aggregate volatility risk.
Two reasons are behind the fact that an increase in idiosyncratic volatility leads to an increase in the value of growth stocks with high idiosyncratic volatility. One is that because option delta decreases in volatility,the risk exposure of growth options declines when idiosyncratic volatility increases. Generally, in recessions,the decreased risk exposure of growth options leads to a smaller increase in expected returns when both idiosyncratic and aggregate volatility increase, and a 2 smaller drop in price 1. The second reason is that, as Grullon et al. (2012) have shown,an increase in the value of growth options goes along with an increase in idiosyncratic volatility. The ultimate conclusion was that growth stocks with high idiosyncratic volatility relate positively to changes in aggregate volatility, which makes them a barrier against aggregate volatility risk. (Barinov, 2012).
2.9. Overview about Amman Stock Exchange (ASE)
The ASE was established on March.1999, as a result of the reorganization process of the Jordan Capital Market. The three institutions established include the ASE, Jordan Securities Commission (JSC) in addition to the Securities Depository Center (SDC). In other word, the Jordanian government accepted a complete capital market improving policy, which aimed at structure on the previous 20 years’ knowledge, improving the private sector, increasing and spreading the national economy, and improving regulation of the securities market to reach universal standards. Between the most important structures of the new location were institutional changes in the capital market, use of universal electronic trading, clearing and approval systems, elimination of problems to investment, and establishment capital market supervision to reach optimal transparency and safe trading in securities, in line with globalization and openness to the outside world (
The enactment of the Temporary Securities Law, No. 23 of the year 1997; really, it was a qualitative leap and a turn-off point for the Jordanian capital market. Its aim was to reorganize and control the Jordanian capital market, and to complete its organization in consistence with universal standards, so as to secure transparency and safe exchange in securities. The central feature of this reorganization effort was the separation of the supervisory and governmental role from the executive role of the capital market. The latter was left to the private sector, whereby Amman Stock Exchange (ASE) and the Securities Depository Center (SDC) played the decision-making role, and the controlling and governmental role was entrusted to Jordan Securities Commission (JSC). The Law provided for creation three new organizations to replace AFM, specifically (
Amman Stock Exchange (ASE):
It is a non-profit legal unit, with financial and managerial independence, and it is authorized to performance as an organized market for trading in securities in the Kingdom. Its association is made up of financial brokers, and it is accomplished by the private sector. It has started its processes on March, 1999 (
Jordan Securities Commission (JSC):
It aims at controlling the issuance of traded securities, regulating and monitoring the actions and processes of those organs dropping below its control. It moreover purposes at modifiable and controlling the disclosure of information associated to issuers, securities, major shareholders and insider trading (
Securities Depository Center (SDC)
The aim of ensuring safe custody of ownership of securities; registration and transferring ownership of securities traded on ASE; and settling the prices of securities between brokers. It is a nonprofit legal unit, with financial and organizational independence, and it is managed by the private sector (
Table (2.1) shows the main indicators of the ASE from 2005 to 2014. It shows that the number of listed companies in 2005, has increased from 201 firms to 236 ones in 2014. Market capitalization decreased by 32.2% compared to 2005. All other indicators showed a decline in 2014 compared with 2005, such as: value traded decreased by 86.58%, No. of traded shares decreased by 10.10%, turnover ratio decreased by 65.13%, ASE general free float weighted price index decreased by 49.16%, net investment of non-Jordanian decreased by 105.38%, market capitalization / GDP decreased by 76.81%.

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