RISK AND RETURNS:

RISK Risk refers to deviation from an expected outcome. Financial risk has generally been defined as the

variance or standard deviation of returns. Risk in holding securities is generally associated with the

possibilities that realized returns will be less than the returns that were. It was also associated with the

departure of the market value of the firm from its intrinsic value and uncertainty faced by the firm in

earning adequate post-tax profits for paying reasonable dividends to shareholders. There are two forces

that contribute to variations in returns in terms of price or dividend, namely systematic and unsystematic

risk.

Systematic and unsystematic risk

Total risk=Systematic risk + Unsystematic risk

Systematic risk (market risk) expected

Systematic risk is also known as undiversifiable risk. Systemic risk refers the one where the company-

specific or industry-specific risk in a portfolio, which is uncorrelated with aggregate market, returns.

It cannot be controlled or influenced by a business, and affect a large number of businesses. For

instance, consider an individual investor who purchases 1,000,000 of stock in 10 companies. If

unforeseen events cause a catastrophic setback and one or two companies' stock prices drop, the

investor incurs a loss. On the other hand, an investor who purchases 1,000,000 in a single company

would incur ten times the loss from such an event. The second investor's portfolio has more

unsystematic risk than the diversified portfolio. Finally, if the setback were to affect the entire

industry instead, the investors would incur similar losses, due to systematic risk. It cannot be

controlled or influenced by a business, and affect a large number of businesses. The variability in return is

caused by factors affecting the prices of all securities such as, economic change, political change, interest rate

change and fluctuations of foreign exchange. Their effect is to cause prices of nearly all individuals’

investments to move together in the same direction. Some stock and portfolios tend to be very sensitive to

market movement, while others are very stable. About 50 percent of the total risk in an average common

stock is systematic risk supply. The relative sensitivity or volatility to market moves can be estimated on the

basis of the past record (popularly known as beta). Examples of systematic risk are: purchasing/inflation risk,

interest rate risk, market risk, political risk etc

Unsystematic risk is that part of the total risk that is unique to a firm or industry above and beyond that affecting

securities market in general. In short, unsystematic risk refers to the risk of price change due to the unique

circumstances of a specific security, as opposed to the overall market. This risk can be virtually

eliminated from a portfolio through diversification. This kind of risk is influenced by factors such as

management capability, consumer preferences, labor strike, advertising campaigns and lawsuits. The uncertainty

surrounding the ability of the business firm to issues or make payments on securities originate from two

sources .This can be as a result of operating environment of the business or the financing of the firm. e.g. business

risk, financial risk, and liquidity risk.

Business risk is a function of the operating conditions faced by a firm and the variability these operating conditions

inject into operating income and expected dividends. Internal business risk is associated with the efficiency within

which a firm conducts its operations within the broader operating environment imposed upon it. Each firm has its

own set of internal risks and the degree to which it is successful in coping with them is reflected in its leadership to

mitigate risks exposed to the firm.

Risk and returns

There are several theories that can be used to describe the relationship between risk and returns. They

include:

A).Modern portfolios theory

b).The capital-asset pricing model- (used in investment)

Modern portfolios theory:

It begins with the premises that all investors are risk averse. The modern portfolio theory was the

work done by Markowitz in 1951. He observed that most investors invest their money in several

securities rather than just one, and therefore must have some benefits when money is invested in

several securities. They want high returns and guaranteed outcomes. The theory tells investors how

to combine stocks in their portfolios’ to give them the least risk possible, consistence with the return

they seek. It stated that though risk cannot be fully eliminated, it can be reduced through investing in

a diversified portfolio

Portfolios’ diversification should depend on having stocks that are not all dependant on the same economic

variables. Wise investors will diversify their portfolios’ not by name or industries but by the determinants that

influence the fluctuations of various securities.

Use illustration shown separately:

The returns of securities A and B in different securities is as shown below.

Scenarios prob RA RB

Recession o.2 5 20% 5%

Mild growth 0.35 11% 10%

Boom 0.4 2% 15%

Required

(a). Expected returns of individual securities.

(b). Risk of the individual securities.

© .Expected returns of the portfolios made-up of 60% of A and 40% of B.

(d).The risk of the portfolios.

ER= (Probability X Returns)

SD = ∑ P (CF – EMV)²

(1)

Scenario Probability RA RB ERA ERB

1 0.25 2 5 0.25(2) =0.5 0.25(5) = 1.25

2 0.35 15 10 0.35(15) =5.25 0.35(10) = 3.5

3 0.40 30 25 0.4(30) =12 0.4(25) = 10 EMV = 17.75 EMV = 14.75

EMV =17.75 14.75

(2) RA RB

Scenario Probability RA RB P (CF – emf) ² P (cf – emf)²

1 0.25 2 5 62.016 23.77

2 0.35 15 10 2.647 7.896

3 0.4 30 25 60.025 42.025

124.688 73.691

√124.688 √73.691

Risk = SDA = 11.166 = 8.58

(3) Portfolio

Expected return of portfolio i.e. weighted average of the expected returns

ERp = 60% (17.75) + 40% (14.75)

10.65 + 5.9 = 16.55

ERp = 16.55

(4) Risk of portfolio SD√∑P (Rp – ERp)²

Scenario Probability RA RB Rp P(Rp – ER)²

1 0.25 2 5 60(2) + 40(5) = 3.2 44.556

2 0.35 15 10 60(15) + 40(10) = 13 4.410

3 0.4 30 25 60(30) + 40(25) = 28 52.441

101.407

Risk = SD √101.407

= 10.070

Modeling risk/capital asset pricing model (CAPM)

Focus directly on what part of security risk could be eliminated by diversification and what part

could not.

The theory classifies the source of variability of an individual stock into two:

Systematic and unsystematic risks.

Draw a graph indicating risk and returns

Risk according to Capital-Asset Pricing Model.

Rate of Returns=risk free rate + beta (return from market-risk free rate)

Assumption of CAPM

i. Investors make decisions based on risk and return assessment

ii. The purchases or sale of a security can be undertaken in infinitely divisible units

iii. Investors can short sell any amount of share without limit

iv. Purchases or sale of securities is done in the absence of personal income taxes

v. The investors can borrow or lend nay amount of fund desired at an identical risk-less

rate

vi. Investors share identical expectations with regard to the relevant decision period, the

necessary decision inputs, their form and size

vii. Aim to maximize economic utilities.

viii. Are broadly diversified across a range of investments.

ix. Are price takers, i.e., they cannot influence prices.

x. Trade without transaction or taxation costs.

xi. Assume all information is available at the same time to all investors.

Relevance of CAPM to Kenya capital market

i. Diversification reduce risk

ii. The riskiness of a security when held in isolation is irrelevant

iii. The importance of beta as a measure of risk The notion of dominant portifolio

Problems of CAPM

The model assumes that either asset returns are (jointly) normally distributed random variables

or that active or potential shareholders employ a quadratic form of utility. It is, however,

frequently observed that returns in equity and other markets are not normally distributed. As a

result, large swings occur in the market more frequently than the normal distribution

assumption would expect.

The market portfolio should in theory include all types of assets that are held by anyone as an

investment (including works of art, real estate, human capital) In practice, such a market

portfolio is unobservable and people usually substitute a stock index as a proxy for the true

market portfolio. Unfortunately, it has been shown that this substitution is not innocuous and

can lead to false inferences as to the validity of the CAPM, and it has been said that due to the

inobservability of the true market portfolio, the CAPM might not be empirically testable.

The model assumes that there are no taxes or transaction costs, although this assumption may

be relaxed with more complicated versions of the model.

The model assumes that given a certain expected return, active and potential shareholders will

prefer lower risk (lower variance) to higher risk and conversely given a certain level of risk will

prefer higher returns to lower ones. It does not allow for active and potential shareholders who

will accept lower returns for higher risk. Casino gamblers pay to take on more risk, and it is

possible that some stock traders will pay for risk as well