# Risk and return relationship

### The Risk / Rate-Of-Return Relationship - eXtension

There is generally a close relationship between the level of investment risk and the potential level of growth or investment returns over the long term. Generally speaking, risk and rate-of-return are directly related. As the risk level of an investment increases, the potential return usually. This article throws light upon the four main sections of risk and return relationship . The sections are: 1. Risk and Return of a Single Asset 2. Risk and Return of a.

According to this theory, the effects of one security purchase over the effects of the other security purchase are taken into consideration and then the results are evaluated. Effects of Combining the Securities: Holding more than one security in the portfolio is always less risky than putting all the eggs in one basket. As per Markowitz, given the return, risk can be reduced by diversification of investment into a number of scrips.

The risk of any two scrips is different from the risk of a group of two companies together. Thus, it is possible to reduce the risk of a portfolio by incorporating into it a security whose risk is greater than that of any of scrips held initially. Given two scrips A and B, with B considerably less risky than A, a portfolio composed of some of A and some of B may be less risky than a portfolio composed of only less risky B.

Moreover, when two stocks are taken on portfolio and if they have negative correlation, the risk can be completely reduced, because the gain on one can offset the loss on the other. The effect of two securities can also be studied when one security is more risk as compared to the other security.

### The Relationship between Risk and Return - National Financial Inclusion Taskforce

Interactive Risk through Covariance: When individual securities are held by the investor, the risk involved is measured by standard deviation or variance. But when two securities are held in the portfolio, it is essential to study the covariance between the two.

Covariance of the securities will help in finding out the interactive risk. The covariance between securities is considered to be positive when the rates of return of the two securities move in the same direction.

But if rates of return of the securities are independent, covariance is zero. If rates of return move in the opposite direction, the covariance is said to be negative. Mathematically the covariance, between two securities is calculated with the help of the following formula: The probabilities remaining same and using the figures of the previous example of stocks A and B: The coefficient of correlation is another measure designed to indicate the similarity or dissimilarity in the behaviour of two variables.

Taking the above mentioned stock A and B, coefficient of correlation can be calculated with the following formula: If Y is 1, then perfect positive correlation exists between securities and returns move in the same direction.

Thus, the correlation between two securities depends upon the covariance between the two securities and the standard deviation of each security. Change in Portfolio Proportion: If the amount of proportion of funds, invested in different stocks is changed e. Using the same example, the portfolio standard deviation is calculated for different proportions as follows: Thus, by changing the investment proportions in different securities, the portfolio risk can be brought down to zero.

If advantages of diversification are to be availed of coefficient of correlation has to be taken into consideration. This can be explained graphically also. The graph proves that: Thus, if one is on the curve MN rather than on the straight line MN, one can increase the return without increasing the risk.

Stocks A and B displays the following parameters: There is high degree of risk in combining the two securities. Market and Non-Market Risk and Return: The non-market component of excess return is uncorrelated with the market component. The variance of the sum will thus equal the sum of the variance of the parts: The risk of a security measured by variance can thus, be divided into two parts.

One that is not related to market risk and one that is. Sharpe developed the capital asset pricing model CAPM. He emphasized that the risk factor in portfolio theory is a combination of two risks i. The systematic risk attached to each of the security is the same irrespective of any number of securities in the portfolio. The total risk of portfolio is reduced with increase in the number of stocks, as a result of decrease in the unsystematic risk distributed over number of stocks in the portfolio.

A risk adverse investor prefers to invest in risk free securities. A small investor having few securities in his portfolio has greater risk.

To reduce the unsystematic risk, he must build up a well-diversified portfolio of securities. This is shown in the following figure: The systematic risk of two portfolios remains the same. To the rational investors, it makes no difference that the stocks in one portfolio are individually riskier than other stocks because successive stock price changes are identically distributed, independent of random variables.

An individual is assumed to rank alternatives in his order of preference. However, due to operating constraints e.

As such an individual chooses among the logically possible in the highest on his ranking. In other words an individual acts in a way in which he can maximize the return on his investment under conditions of risk and uncertainty. The CAPM is represented mathematically by the following equation: The CAPM relates a required rate of return to each level of systematic risk.

The following figure portrays it graphically. Point K represents the market portfolio and point R the risk less rate of return. Line RKZ represents the preferred investment strategies, showing alternative combinations of risk and return obtainable by combining the market portfolio with borrowing or lending.

The CAPM suggests a required rate of return that is made up of two separate components: The market price of risk is multiplied by nth assets systematic risk coefficient. The product of this multiplication determines the appropriate risk premium i. This risk premium induces investors to take risk.

## Risk–return spectrum

The Capital Market Line CML defines the relationship between total risk and expected return for portfolios consisting of the risk free asset and the market portfolio.

If all the investors hold the same risky portfolio, then in equilibrium it must be the market portfolio. CML generates a line on which efficient portfolios can lie.

Those which are not efficient will however lie below the line. It is worth mentioning here that CAPM risk return relationship is separate and distinct from risk return relationship of individual securities as represented by CML. In contrast the risk less end R statistics of all portfolios, even the inefficient ones should plot on the CAPM. The CML will never include all points, if efficient portfolios, inefficient portfolios and individual securities are placed together on one graph.

The individual assets and the inefficient portfolios should plot as points below the CML because their total risk includes diversifiable risk. Security Market Line describes the expected return of all assets and portfolios of assets in the economy. The risk of any stock can be divided into systematic risk and Unsystematic risk. Beta b is the index of systematic risks. In case of portfolios involving complete diversification, where the unsystematic risk tends to zero, there is only systematic risk measured by Beta.

Thus, the dimensions of the security which concern us are expected return and Beta. The expected return on any asset or portfolio, whether it is efficient or not can be determined by SML by focusing on Beta of securities.

The higher the Beta for any security the higher must be its equilibrium return. Further the relationship between Beta and expected return is linear. It can be drawn as follows: The SML is an upward sloping straight line with an intercept at the risk free return securities and passes through the market portfolio.

The upward slope of the line indicates that greater expected returns accompany higher levels of Beta. In equilibrium each security or portfolio lies on the SML.

The above figure shows that the return expected from portfolio or investment is a combination of risk free return plus risk premium. An investor will come forward to take risk only if the return on investment also includes risk premium. Thus the expected return on a portfolio E Rm consists of the following: In other words, the investor gets rewarded for bearing systematic risk.

It is not total variance of returns that affects expected returns but only that part of variance in return that cannot be diversified away. If investors can eliminate all non-systematic risk through diversification there is no reason they should not be rewarded in terms of higher return for bearing it. Though the CAPM has been regarded as a useful tool for both analysts of financial securities and financial managers, it is not without critics.

The CAPM has serious limitations in the real world, discussed as follows: Expectations cannot be observed but we do have access to actual returns.

### Risk–return spectrum - Wikipedia

Hence empirical tests and data for practical use tend to be based almost exclusively on historical returns. They may not be reflective of true risk involved. Due to the unstable nature of beta it may not reflect the future volatility of returns although it is based on the post history. Historical evidence of the tests of Beta showed that they are unstable and they are not good estimates of future risk. However, total risk has been found to be more relevant and both types of risk appear to be positively related to returns.

The factors influencing bonds in respect of risk and return are different and the risk of bonds is rated and known to investors. Thus, it can said that the applicability of CAPM is broken by the less practical nature of this model as well as complexity and difficulty of dealing with beta values. Risk Free Rate of Lending or Borrowing: The three factors discussed in CAPM are systematic risk Bthe expected market return and the risk free rate.

The risk free rate is the least discussed of the three factors. It is used only twice in CAPM. It is first used as a minimum rate of return R and it is used to find out the risk premium rm — R. Thus, any error in estimating the risk free rate of return would lead to a wrong estimate of the expected rate of return for an asset or portfolio. In CAPM theory, the risk free asset is one of the two choices available to the investor.

The investor can reduce the risk of the portfolio by increasing the amount of risk free asset in the portfolio or he can increase the risk by reducing the risk free asset position or by borrowing at the risk free rate to further invest. In fact, the risk free rate is the rate that will entice investors to choose between current or future consumption between savings or investment.

The price required to induce an investor to forgo current consumption for a certain future sum, to forgo liquidity, is the price of time or the risk free rate of return. The separation Theorem propounded by James Tobin States that the investors make portfolio choices solely on the basis of risk and return, separating that decision from all other characteristics of the securities. If particular assets are chosen on the basis of other factors, the CAPM is incomplete because it ignores other relevant factors.

Thus, it is implied that each investor will spread his funds among risky securities in the same relative proportion, adding risk free borrowing or lending in order to achieve a personally preferred overall combination of risk and return. Even if the investor commits zero proportion in these securities, the prices of these would eventually fall, thereby causing the expected returns of these securities to rise until the resulting tangency portfolio has a non-zero proportion associated with it.

Ultimately, everything will be balanced out. When all the price adjusting stops the market will be brought into equilibrium. Instead of just a single beta value, there is a whole set of beta values-one for each factor. Arbitrage Pricing Theory out of which APM arises states that the expected return on investment is dependent upon how that investment reacts to a set of individual macro-economic factors the degree of reaction being measured by the betas and the risk premium associated with each of those macro-economic factors.

The APM was developed in by Ross.

This model does not depend critically on the notion of an underlying market portfolio. Instead, it is a model that derives returns from the properties of the process generating stock returns and employs arbitrage pricing theory to define equilibrium. The Arbitrage Theory is based on the following assumptions: The model takes the view that there are underlying factors that give rise to returns on stocks. Examples of these factors might include such variables as real economic growth and inflation or such financial variables as dividend yield and capital structure.

The objective of security analysis is to identify these factors in the economy and the sensitivities of security return to movements in these factors. A formal statement of such a relationship is termed as a factor model of security returns. According to this model the asset price depends on a single factor, say Gross National Product or Industrial production or interest rates, money supply, interest rates and so on.

In general, a single factor model can be represented in equation form as follows: Empirical work suggests that a number of variables should be taken into account for asset pricing. The above mentioned equation can, thus be expanded to: But the basic question is what are these factors? They are the underlying economic forces that are the primary influences on the stock market.

Several factors appear to have been identified as being important. Some of these factors, such as inflation and money supply, industrial production and personal consumption do have aspects of being interrelated. In particular, the researchers have identified the following factors: Changes in the level of industrial production in the economy ii.

Changes in the shape of the yield curve iii. Changes in the default-risk premium i. Changes in the inflation rate v. Changes in the real interest rate vi. The level of personal consumption vii. The level of money supply in the economy Deriving the Arbitrage Pricing Theory: With the help of APM, investment strategies of many types can be selected if there are many securities to be selected and a fixed amount to be invested the investor can choose in a manner that he can aim at zero non-factor risk.

## The risk-return relationship

According to the expectations theory, current and expected future interest rates are dependent on expectations about future rates of inflation. Many economic and political conditions can cause expected future inflation and interest rates to rise or fall.

These conditions include expected future government deficits or surpluseschanges in Federal Reserve monetary policy that is, the rate of growth of the money supplyand cyclical business conditions. The liquidity or maturity premium theory of the yield curve holds that required returns on long-term securities tend to be greater the longer the time to maturity. The maturity premium reflects a preference by many lenders for shorter maturities because the interest rate risk associated with these securities is less than with longer-term securities.

As we shall see in Chapter, the value of a bond tends to vary more as interest rates change, the longer the term to maturity.

Thus, if interest rates rise, the holder of a long-term bond will find that the value of the investment has declined substantially more than that of the holder of a short-term bond. In addition, the short-term bondholder has the option of holding the bond for the short time remaining to maturity and then reinvesting the proceeds from that bond at the new higher interest rate.

The long-term bondholder must wait much longer before this opportunity is available. Accordingly, it is argued that whatever the shape of the yield curve, a liquidity or maturity premium is reflected in it. The liquidity premium is larger for long-term bonds than for short-term bonds. Finally, according to the market segmentation theory, the securities markets are segmented by maturity.

If strong borrower demand exists for long-term funds and these funds are in short supply, the yield curve will be upward sloping.

Conversely, if strong borrower demand exists for short-term funds and these funds are in short supply, the yield curve will be downward sloping. Several factors limit the choice of maturities by lenders. One such factor is the legal regulations that limit the types of investments commercial banks, savings and loan associations, insurance companies, and other financial institutions are permitted to make.

Another limitation faced by lenders is the desire or need to match the maturity structure of their liabilities with assets of equivalent maturity. For example, insurance companies and pension funds, because of the long-term nature of their contractual obligations to clients, are interested primarily in making long-term investments.

Commercial banks and money market funds, in contrast, are primarily short-term lenders because a large proportion of their liabilities is in the form of deposits that can be withdrawn on demand.

At any point in time, the term structure of interest rates is the result of the interaction of the factors just described. All three theories are useful in explaining the shape of the yield curve. The Default Risk Premium U. In contrast, corporate bonds are subject to varying degrees of default risk. Investors require higher rates of return on securities subject to default risk. Over time, the spread between the required returns on bonds having various levels of default risk varies, reflecting the economic prospects and the resulting probability of default.

For example, during the relative prosperity ofthe yield on Baa-rated corporate bonds was approximately. By lateas the U. In mid, the spread narrowed to 0. The spread expanded to 0. Seniority Risk Premium Corporations issue many different types of securities.

A partial listing of these securities, from the least senior that is, from the security having the lowest priority claim on cash flows and assets to the most senior, includes the following: Generally, the less senior the claims of the security holder, the greater the required rate of return demanded by investors in that security.

For example, the holders of bonds issued by ExxonMobil are assured that they will receive interest and principal payments on these bonds except in the highly unlikely event that the company faces bankruptcy.

In contrast, ExxonMobil common stockholders have no such assurance regarding dividend payments. Also, in the case of bankruptcy, all senior claim holders must be paid before common stockholders receive any proceeds from the liquidation of the firm. For example, there is very little marketability risk for the shares of stock of most companies that are traded on the New York or American Stock Exchange or listed on the NASDAQ system for over the counter stocks.

For these securities, there is an active market. Trades can be executed almost instantaneously with low transaction costs at the current market price. In contrast, if you own shares in a rural Nebraska bank, you might find it difficult to locate a buyer for those shares unless you owned a controlling interest in the bank. When a buyer is found,that buyer may not be willing to pay the price that you could get for similar shares of a largerbank listed on the New York Stock Exchange.