FREE online courses on Investment Appraisal - Basic Concepts of Investment Appraisal - Risk

 

Risk and return go hand in hand in investments and finance. One cannot talk about returns without talking about risk, because, investment decisions always involve a trade - off between risk and return. Risk can be defined as the chance that the actual outcome from an investment will differ from the expected return. This means that, the more variable the possible outcomes that can occur (i.e. the broader the range of possible outcomes), the greater the risk.

 

Risk and Expected Rate of Return

 

The width of a probability distribution of rates of return is a measure of risk. The wider the probability distribution, the greater the risk or the greater the variability of return or greater the variance. An investor cannot expect greater returns without being willing to assume greater risks.

 

Sources of Risk

 

• Interest Rate Risk. It is the variability in a security's return from changes in the level of interest rates.
• Market Risk. Market risk refers to the variability of returns due to fluctuations in the securities market.
• Inflation Risk. With rise in inflation there is reduction of purchasing power, hence this is also referred to as purchasing power risk and affects all securities.
• Business Risk. This refers to the risk of doing business in a particular industry or environment and it gets transferred to the investors who invest in  the business or company. It may be caused by a variety of factors like heightened competition, emergence of new technologies, development of substitute products, shifts in consumer preferences, etc.
• Financial Risk. Financial risk arises when companies resort to financial leverage or the use of debt financing. The more the company resorts to debt financing, the greater is the financial risk as it creates fixed interest payments due to debt or fixed dividend payments on preference stock thereby causing the amount of residual earnings available for common stock dividends to be more variable than if no interest payments were required. It is avoidable to the extent that management has the freedom to decide to borrow or not to borrow funds.
• Liquidity Risk. This risk is associated with the secondary market, which the particular security is traded in. A security which can be bought or sold quickly without significant price concession is considered liquid. The greater the uncertainty about the true element and the price concession, the greater the liquidity risk. Securities that have ready markets like treasury bills have lesser liquidity risk.

 

Measurement of Total Risk

 

Risk is associated with the dispersion in the likely outcomes. Dispersion refers to variability. If an asset's return has no variability, it has no risk. An investor analyzing a series of returns on an investment over a period of years needs to know something about the variability of its returns or in other words the asset's total risk.

 

There are different ways to measure variability of returns. The range from the highest possible to lowest possible rate of return is one measure, but the range is based only on two extreme values.

 

A more popular way of measuring variability of returns is standard deviation. The standard deviation is simply the square root of the variance of the rates of return.

                                                         

          where, s   =  standard deviation

                                      P_i   =  probability associated with the ith possible outcome

                                      k_i   =  rate of return from the ith possible outcome

                                      k    =  expected rate of return

                                      n    =  number of outcomes

 

Portfolios and Risk

 

An investment portfolio refers to the group of assets that is owned by an investor. When an investor invests all his funds in a single security, it is more in the nature of speculation than of an investment, because the returns to the investor are based on the future of the single asset, making it a very risky proposition. Generally, in order to reduce risk, investors hold on to a diversified portfolio, which might contain equity capital, bonds, real estate, savings accounts and various other assets. In other words, the investor does not put all his eggs into one basket.

 

Diversifiable and Non-diversifiable Risk

 

The fact that returns on stocks do not move in perfect tandem means that risk can be reduced by diversification. But the fact that there is some positive correlation means that in practice risk can never be reduced to zero. So there is a limit on the amount of risk that can be reduced through diversification. The lower the degree of positive correlation, the greater is the amount of risk reduction that is possible.

 

The amount of risk reduction achieved by diversification also depends on the number of stocks in the portfolio. As the number of stocks in the portfolio increases, the diversifying effect of each additional stock diminishes.

                            

As you can see that the major benefits of diversification are obtained with the first 10 to 12 stocks, provided they are drawn from industries that are not closely related. Increases beyond this point continue to reduce the total risk but the benefits are marginal.

 

It is also apparent that it is the diversifiable risk that is being reduced unlike the non-diversifiable risk, which remains constant whatever your portfolio is.

 

Nondiversifiable risk is that part of total risk (from various sources like interest rate risk, inflation risk, financial risk, etc.) that is related to the general economy or the stock market as a whole and hence cannot be eliminated by diversification. Nondiversifiable risk is also referred to as market risk or systematic risk.

 

Diversifiable risk on the other hand, is that part of total risk that is marginal to the company or industry and hence can be reduced by diversification. Diversifiable risk is also called unsystematic risk or specific risk.

 

Risk of Stocks in a Portfolio

 

A portfolio's standard deviation is a good indicator of the risk of a portfolio, to the extent that if adding a stock to the portfolio increases the portfolio's standard deviation, the stock adds risk to the portfolio. But the risk that a stock adds to a portfolio will depend not only on the stock's total risk, its standard deviation, but on how that risk breaks down into diversifiable and nondiversifiable risk. If an investor holds only one stock, there is no question of diversification, and this risk is therefore the standard deviation of the stock. For a diversified investor, the risk of a stock is only that portion of total risk that cannot be diversified or its nondiversifiable risk. The nondiversifiable risk is generally measured by Beta coefficient. Beta measures the relative risk associated with any individual portfolio as measured in relation to the risk of market portfolio. The market portfolio represents the most diversified portfolio of risky assets an investor could buy since it includes all risky assets.

The relative risk can be expressed as:

Nondiversifiable risk of asset or portfolio

Risk of market portfolio

 

Thus, the Beta coefficient is a measure of the non-diversifiable or systematic risk of an asset relative to that of the market portfolio.

• A Beta of 1.0 indicates an asset of average risk.
• A Beta coefficient greater than 1.0 indicates above-average risk - stocks whose returns tend to be more risky than the market.
• A Beta coefficient less than 1.0 indicates below-average risk, i.e., less riskier than market portfolio.

 

In case of market portfolio all the diversification possible has been done-thus the risk of market is all nondiversifiable which an investor cannot avoid. Similarly, as long as the asset's returns are not perfectly positively with returns from other assets, there will be some way to diversify away its unsystematic risk. As a result beta depends only on non-diversifiable risks.

 

The beta of a portfolio is nothing but the weighted average of betas of the securities that constitute the portfolio, the weights being the proportions of investments in respective securities.

 

Measurement of Beta

 

The systematic relationship between the return on the security or a portfolio and the return on the market can be described using a simple linear regression, identifying the return on a security or portfolio as the dependent variable K_j and the return on market portfolio as the independent variable K_m, in the single-index model or market model developed by William Sharpe.

This can be expressed as:

                                K_j =a_j + f_j K_m + e_j

The Beta parameter b_j in the model represents the slope of the above regression relationship and measures the responsiveness of the security or portfolio to the general market and indicates how extensively the return of the portfolio or security will vary with changes in the market return. The Beta coefficient of a security is defined as the ratio of the security's covariance of return with the market to the variance of the market. This can be calculated as follows:

                                      b_j= Cov(K_j K_m)        

                                                 Var(K_m)

The Alpha parameter "a" is the intercept of the fitted line and indicates what the return of the security or portfolio will be when the market return is zero. For example, a security with an a of +2 % would earn 2 % even when the market return was zero and would earn an additional 2 % at all levels of market return. The converse is true if a security has a of -2 %. The positive a thus represents a sort of bonus return and would be a highly desirable aspect of a portfolio or security while a negative a represents a penalty to the investor.

The third term e_j  is the unexpected return resulting from influences not identified by the model. Frequently referred to as random or residual return, it may take on any value but is generally found to average out to zero.