# The risk and return relationship part 1

Brown has tested the risk-return relationship of portfolios tage returns of all common stocks registered on the NYSE from 1/ to 6/ . part of the study. One of the major objectives of investment is to earn and maximize the return. .. The risk of a security measured by variance can thus, be divided into two parts. The risk-return relationship is explained in two separate back-to-back articles in this month's issue. This approach has been taken as the risk-return story is.

They use the money to run their operations. In turn, you get back a set amount of interest once or twice a year. If you hold bonds until the maturity date, you will get all your money back as well. As a shareholderShareholder A person or organization that owns shares in a corporation. May also be called a investor. But if the company is successful, you could see higher dividends and a rising shareShare A piece of ownership in a company. But it does let you get a share of profits if the company pays dividends.

Some investments, such as those sold on the exempt market are highly speculative and very risky. They should only be purchased by investors who can afford to lose all of the money they have invested. DiversificationDiversification A way of spreading investment risk by by choosing a mix of investments.

The idea is that some investments will do well at times when others are not. May include stocks, bonds and mutual funds. The equity premium Treasury bills issued by the Canadian government are so safe that they are considered to be virtually risk-free. The government is unlikely to default on its debtDebt Money that you have borrowed.

You must repay the loan, with interest, by a set date. At the other extreme, common shares are very risky because they have no guarantees and shareholders are paid last if the company is in trouble or goes bankrupt.

Investors must be paid a premium, in the form of a higher average return, to compensate them for the higher risk of owning shares.

Creditworthiness of the issuer viii. Maturity period or length of investment ix.

## The risk-return relationship

Terms of lending x. National and International factors xi. Risk and Return of a Portfolio: Portfolio analysis deals with the determination of future risk and return in holding various combinations of individual securities.

The portfolio expected return is the weighted average of the expected returns, from each of the individual securities, with weights representing the proportionate share of the security in the total investment.

### The risk-return relationship | Understanding risk | yogaua.info

The portfolio expected variance, in contrast, can be something less than a weighted average of security variances. Therefore, an investor can sometimes reduce risk by adding another security with greater individual risk compared to any other individual security in the portfolio. This strange result occurs because risk depends greatly on the covariance among returns of individual securities.

Why does an investor has so many securities in his portfolio? If anyone security, let us say, security X, gives the maximum return, why not to invest all the funds in that security and thus, to maximise the returns?

Answer to this query lies in risk attached to investments, objective of investment, safety, capital growth, liquidity and hedge against decline in the value of money etc.

The concept of diversification deals with this question. Diversification aims at reduction or even elimination of non- systematic risk and achieving the specific objectives of investors. An investor can even estimate his expected return and expected risk level of a given portfolio of assets from proper diversification.

Therefore, it is essential that each security be viewed in a portfolio context. Each security in a portfolio contributes returns in the proportion of its investment in security. It is but natural that the expected return of a portfolio should depend on the expected return of each of the security contained in the portfolio. It is also important that amounts invested in each security should be logically decided.

Assuming that the investor puts his funds in five securities, the holding period return of the portfolio is described in the table given below: The above table describes the simple calculation of the weighted average return of a portfolio for the holding period. Risk on a Portfolio: Risk on a portfolio is not the same as risk on individual securities. The risk on the portfolio is reflected in the variability of returns from zero to infinity.

The expected return from portfolio depends on the probability of the returns and their weighted contribution to the risk of the portfolio. Two measures of risk are used in this context-the average or mean absolute deviation and the standard deviation. The following table shows how the absolute deviation can be calculated: First of all the expected return is determined in this case it is Next, all possible outcomes are analysed to determine the amount by which the value deviates from the expected amount.

These figures shown in column 5 include both positive and negative values. As shown in column 6, a weighted average using probabilities as weights will equal zero. This constitutes the First measure of likely deviation. Another measure is standard deviation and variance. It is slightly more complex but preferably analytical measures. In this the deviations are squared, making all the values positive.

Then the weighted average of these amounts is taken, using the probabilities as weights. The result is termed the variance. It is converted to the original units by taking the square root. The result is termed as the standard deviation. Although both these measures are used interchangeably, the standard deviation is generally preferred for investment analysis.

The reason is that the standard deviation of a portfolio can be determined from the standard deviation of the returns of its component securities, no matter what the distributions. No such relationship of comparable simplicity exists for the average absolute deviations. If an investor holds only one stock, there is no question of diversification and his risk is, therefore, the standard deviation of the stock.

For a diversified investor, the risk of a stock is only that portion of the total risk that cannot be diversified away or its non-diversifiable risk.

The non-diversifiable risk is generally measured by Beta b coefficient. Beta measures the relative risk associated with any individual portfolio as measured in relation to the risk of the market portfolio.

The market portfolio represents the most diversified portfolio of risky assets an investor can buy since it includes all risky assets. This relative risk can be expressed as: A Beta of 1. A Beta coefficient greater than 1.

One important point to be noted is that in the case of a market portfolio, all the diversification has been done, thus the risk of the portfolio is all non-diversifiable risk which cannot be avoided. We can thus say that Beta depends upon only non-diversifiable risk. The Beta of a security portfolio is nothing but the weighted average of the Betas of the securities that constitute the portfolio, the weights being the proportions of investments in the respective securities as shown in the following table.

The systematic relationship between the return on the security or a portfolio and the return in the market can be described by using a simple linear regression identifying the return on a security or portfolio as the dependent variable and the return on market portfolio as the independent variable: Risks involved in investment and portfolio management can be reduced through a technique called diversification.

Diversification may take any of the following forms: Shares, Debentures, Bonds, etc. Textiles, IT, Pharmaceuticals, etc. Some accepted methods of effecting diversification are as follows: Randomness is a statistical technique which involves placing of companies in any order and picking them up in random manner. The probability of choosing wrong companies will come down due to randomness and the probability of reducing risk will be more.

Some experts have suggested that diversification at random does not bring the expected return results. Diversification should, therefore, be related to industries which are not related to each other.

The investor should try to find the optimum number of companies in which to invest the money. If the number of companies is too small, risk cannot be reduced adequately and if the number of companies is too large, there will be diseconomies of scale.

More supervision and monitoring will be required and analysis will be more difficult, which will increase the risk again. An intelligent investor has to choose not only the optimum number of securities but the right kind of securities also.

Otherwise, even if there are a large number of companies, the risk may not be reduced adequately if the companies are positively correlated with each other and the market. In such a case, all of them will move in the same direction and many risks will increase instead of being reduced.

Markowitz theory is also based on diversification. 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. 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. 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.

## 4 Main Sections of Risk and Return Relationship

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.