# 5 explain the relationship between financial risk and return

Article (PDF Available) in Journal of Banking & Finance . relationship between expected return and risk. . intertemporal asset pricing model in explaining the cross-sectional variation of expected returns. 6 5 We thank Hui Guo from the Federal Reserve Bank of St. Louis for providing us with these data. The trade-off between risk and return is a key element of effective financial The relationship between risk and required rate of return can be expressed as follows : A number of theories have been advanced to explain the shape of the yield .. 5 Important interview questions techies fumble most · What are avoidable. What is the basic relationship between risk and return and how is this reflected What are the primary differences and/or similarities between financial risk and.

## The risk-return relationship

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.

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. 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.

### 4 Main Sections of Risk and Return Relationship

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.

- 4 Main Sections of Risk and Return Relationship

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.

This is possible by combining securities to hedge out the sensitivity of a portfolio to all but one factor. APT says nothing about either the magnitude or the rings of the factor coefficients or what the factors themselves might be.

## Relationship Between Risk and Return Financial Management

The model does not give us this guidance nor did Ross when he first found this model. The theory does not say anything about how the identity and magnitude of the factors should be determined. It says that by active trading of securities with different sensitivities to the important factors, investors trade away opportunities for excessive gains. Since there are only a few systematic factors affecting returns, many portfolios are close substitutes for each other and thus will have the same value.

Excessive gains come only when, by buying some assets and selling others the investor hedges his portfolio and thereby insulates it from risk without eliminating excess return the return above the risk free rate. These excessive gains are called arbitrage profits. In efficient markets, excess returns are eliminated by trading and investors cannot on average or over time, find opportunities to arbitrage for profits.

A simple example will demonstrate what arbitrage profit is and how an investor can take advantage of it; if it were available. Let us assume a market where there are only three assets, all sensitive to only one factor e. The sensitivities of each of the assets to the common factor, real interest rate and the expected returns are shown in the following table: Since the return that would usually be expected for an asset with sensitivity to interest rate is To take advantage of this excess return and to do so with no risk, an investor can arbitrage among three assets; the investor with Rs.

The results of buying and short selling activities are shown in the following table: The investors earns 1. Inequities offer opportunities to arbitrage. The same situation exists when assets are priced on more than one factor. APT allows for as many factors as are important in the pricing of the assets. The APT thus describes the behaviour of most investors, who are opportunity seekers and believe that opportunities to make profits exist. Such investors however dislike higher levels of risk.

The fact is that there is always a trade-off between risk and return, which is not considered by the APT model. 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.