principles of financial analysis week 4: lecture 4 1lecturer: chara charalambous

Lecturer: Chara Charalambous 1

PRINCIPLES OF FINANCIAL ANALYSIS

WEEK 4: LECTURE 4


Learning Objectives

• What is expected rate of return ?• What is risk?• How investment risk should be measured?• Explain the relationship between an investor’s

required rate of return and the riskiness of the investment.


Meaning of RiskRisk refers to the chance that some unfavourable

event will happen. For example, If you engage in skydiving, you are

taking a chance with your life – skydiving is risky. If you bet on the horses, you are risking your

money. Most people view risk as a chance of loss, but in

reality risk occurs when we cannot be certain about the outcome of a particular activity so will not sure what will happen in the future.


Risk and InvestingThe Rules:

– Investing is risky.– Risk is manageable.

Types of Risk:– Diversifiable Risk – Can be eliminated through diversification. Is

not important to informed investors because they can eliminate its effect by ‘diversifying ‘ it away. Diversify means expand, spread, choose more than one alternative. In finance, diversification means reducing risk by investing in a variety of assets. Simply put it: it is foolish to invest all your money in one investment. ‘’Don’t put all your eggs in one basket’’. .

– Nondiversifiable Risk – this is the important risk and is bad in the sense that it cannot be eliminated and if you invest in anything else than riskless assets, like government assets, you will be exposed to it.


http://www.google.com.cy/url?sa=i&rct=j&q=risk+and+rate+of+return&source=images&cd=&cad=rja&docid=ALG5MEsWCZn6DM&tbnid=a2bAAVq13HIsoM:&ved=0CAUQjRw&url=http://www.greekshares.com/investment_profile_1.php&ei=5EUrUbe8DZCMswbikoGwCA&bvm=bv.42768644,d.Yms&psig=AFQjCNEO_804KD5IaeTXVLkooLmS3u1hVg&ust=1361876734692479


Investment returnsThe average rate of return on an investment can be calculated as follows:

(Amount received – Amount invested)

Return = ________________________

Amount invested

For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is:

($1,100 - $1,000) / $1,000 = 10%.


What is investment risk?Investment risk is related to the possibility of earning a low or negative actual return.The greater the chance of lower return than expected or negative returns, the riskier the investment. The greater the range of possible events that can occur, the greater the risk


Illustration of Riskiness of financial assets Supposed you have a large amount of money to invest for one year You could buy a Government security that has an expected return to

6%. The rate of return in this investment can be determined quite accurate because the chance of the government defaulting is small: the outcome is guaranteed which means this is a risk free investment.

OR On the other hand you could buy shares of a newly formed company

which has developed technology that can be used to extract petroleum. This technology is still in the process of proven economically affordable so it is not known what returns the ordinary shareholders will receive in the future. Experts have appreciate that the expected return of such investment will probably be 30% but there is also the possibility-the risk that the company will not survive and so the entire investment will be lost. The return that the investors will receive can not be determined accurately because more than one outcome is possible. This is a risky investment.


THE RETURN EXPECTED FROM AN INVESTMENT IS POSITIVELY RELATED TO THE

INVESTMENT RISK – A HIGHER EXPECTED RETURN REPRESENTS AN INVESTOR’S

COMPENSATION FOR TAKING ON A GREATER RISK!!!


Explanation:• If you buy a bond you expect to receive interest on the bond

(interest payments are the rate of return on your investment). The possible outcomes on this investment are (1) the issuer will make the interest payments (2) ) the issuer will fail to make the interest payments . The higher the probability of default on the interest payments the riskier the bond, and the higher the risk the higher the rate of return you would require to invest in the bond.


Defining and Measuring Risk

We evaluate risk in two different bases:

Stand-Alone Risk is that risk which is associated with an investment which it is held on its own- in one asset.

Portfolio Risk is that risk which is associated with an investment which it is held in combination with other assets/investments.


Probability Distributions

• An event’s probability is defined as the chance that the event will occur.

• For example, a weather forecaster might state: “There is a 40% chance of rain today and a 60% chance that it will not rain.” If all possible events, or outcomes, are listed, and if a probability is assigned to each event, then the listing is called a probability distribution. Keep in mind that the probabilities must sum to 1.0, or 100%.


Probability Distributions

Probability Distribution: A listing of all possible outcomes with the

possibility of each option-probability indicated.

• For example, a weather forecaster might state “There is a 40 percent chance of rain today and a 60 percent chance that it will not rain”.


Probability Distributions – example 1

Flip a Coin:

Outcome ProbabilityHeads 50%Tails 50%

100%

Chance of Rain:

Outcome ProbabilityRain 40%No Rain 60%

100%

The probabilities must sum 100% to account for all the possible outcomes


Probability Distributions – example 2

• Imagine two firms: Firm A and Firm B and you make an investment of €10,000 in the shares of one of the two. A’s sales rise and fall depending on the situation exist in the economy and also faces high competition. B on the other hand provides an essential service necessary to all and doesn't face competition so its profits are more stable.


Probability Distributions – example 2Firm A and Firm B

Rate of Return on Stock if State of the Economy

Probability of This State Occurring

This State Occurs

Firm A Firm B

Boom 0.2 110% 20%Normal 0.5 22% 16%Recession 0.3 -60% 10%

1.0Firm’s B rate of return fluctuate much more than this of Firm A. The above table shows the possible outcomes for investing in Firm A or B. We can see that the most possible outcome is for the economy to be normal in which A gives a return 22% and B 16%. But other outcomes are also possible so we need to find a measure that takes in account – considers all possible outcomes. This measure is the expected rate of return.


Expected Rate of ReturnThe rate of return expected to be realized from an investmentThe weighted average of the outcomes, where the weights are the probabilities: we multiply each possible outcome by the probability it will occur and then sum the results. We designate the expected rate of return with

n

1iii

nn2211

k

k...kkk̂

Pr

PrPrPr

^

k


Expected Rate of Return

(1) (2) (3) = (4) (5) = (6)Boom 0.2 110% 22% 20% 4%Normal 0.5 22% 11% 16% 8%Recession 0.3 -60% -18% 10% 3%

1.0 k = 15% k = 15%

State of the Economy

Firm A Firm B

Return if This State Occurs (ki)

Product: (2) x (5)

Probability of This State

Occurring (Pr i)

Return if This State

Occurs (ki)Product: (2) x (3)

^ ^

^

k = 0.2(110%)+0.5(22%)+0.3(-60%)=15.0%


Continuous versus Discrete Probability Distributions

We have assumed that only three states of the economy can exist: this is called discrete because there is a limited number of outcomes.

Discrete Probability Distribution:the number of possible outcomes is limited Actually the situation of the economy could range from a deep depression to a fantastic boom and there are an unlimited number of possibilities between.

Continuous Probability Distribution:the number of possible outcomes is unlimited


Discrete Probability Distributions

-60 -45 -30 -15 0 15 22 30 45 60 75 90 110Rate of

Return (%)Expected Rate of Return (15%)

a. Firm AProbability of Occurrence

-10 -5 0 5 10 16 20 25 Rate of Return (%)

Expected Rate of Return (15%)

b. Firm BProbability of Occurrence

0.5 -

0.4 -

0.3 -

0.2 -

0.1 -

0.5 -

0.4 -

0.3 -

0.2 -

0.1 -


• The tighter the probability distribution, the more likely it is that the actual outcome will be close to the expected value, and, consequently, the less likely it is that the actual return will be mush different from the expected return.

Firm B has a relatively tight probability distribution: its actual return is likely to be closer to its 15% expected return than that of Firm A.

A tighter probability distribution is representative of lower risk.


-60 0 15 110Rate of Return (%)

Expected Rate of Return

Firm A

Probability Density

Continuous Probability Distributions

Firm B

0.5 -

Firm B :In previous figure the probability of obtaining exactly 16% was 50%. Here is smaller because there are many possible outcomes instead of just three.

If we consider more probabilities than we id in table of slide 17 and the outcomes would be continuous curves instead of vertical columns


• Risk is a difficult concept to grasp, and a great deal of controversy has surrounded attempts to define and measure it. However, a common definition that is satisfactory for many purposes is stated in terms of probability distributions.

• The tighter the probability distribution of expected future returns, the smaller the risk of a given investment.

Measuring Stand-Alone Risk: The Standard Deviation


Standard deviation 2 k i - ˆ k 2Prii1

n

s ‘sigma’ provides a specific value that represents the “tightness” of the probability distribution.

A lower standard deviation indicates a tighter probability distribution, and therefore the less risk connected with the particular stock.

A tighter probability distribution is representative of lower risk associated with the investment.

A measure of the tightness or variability of a set of outcomes

A measure of stand alone risk

Measuring Stand-Alone Risk: The Standard Deviation


• First we need to Calculate the expected rate of return.• Second deduct the expected rate of return from

each possible outcome to obtain a set of deviations.• Then multiply the deviations by the probability of

occurrence for its related outcome. Sum these products to obtain the variance of the probability distribution:

n

1ii

2

i k̂-k Pr

•Finally, find the square root of the variance to obtain the standard deviation:

n

1ii

2

i2 k̂-k deviation Standard Pr


Thus, the standard deviation is essentially a weighted average of the deviations from the expected value, and it provides an idea of how far above or below the expected value the actual value is likely to be.

Larger standard deviation indicates a greater variation of returns and thus a greater chance that the actual return will turn out to be substantially lower than the expected return. Therefore, is a riskier investment than other investments with lower SD when held alone.


Calculating Firm’s A Standard Deviation

(1) (2) (1) - (2) = (3) (4) (5) (4) x (5) = (6)110% 15% 95 9,025 0.2 1,805.0 22% 15% 7 49 0.5 24.5 -60% 15% -75 5,625 0.3 1,687.5

Payoff

ki(k i - k)2Pr iProbability

Expected Return

kki - k (k i - k)2^

^^ ^

%3.59 517,3 Deviation Standard

0.517,3 Variance

2mm

2


• Firm’s B standard deviation is 3.6%. The larger standard deviation of Firm’s A indicates a greater variation of returns, thus a greater chance that the expected return will not be realized. Therefore Firm A would be consider a riskier investment.


Risk Aversion & Risk Premium

• If you choose the less risky investment, you are risk averse. Most investors are indeed risk averse – this is a well document fact, and certainly the average investor is risk averse.

• Risk-averse investors require higher rates of return to invest in higher risk securities.

• Risk premium – is the difference between the return on a risky asset and less risky asset and serves as compensation for investors to hold riskier securities.


Portfolio Returns

Expected return on a portfolio, kp The weighted average

expected return on the stocks held in the portfolio

^

N

1jjj

NN2211p

k̂w

k̂w...k̂wk̂wk̂W1 is that stocks portion of the portfolio’s dollar value; therefore the sum of the W’s must equal 1.

A portfolio is a combination of two or more securities. Combining securities into a two portfolio reduces risk


Example of PortfolioExpected returns on four large companies:Stocks/ Investments Expected Return1.AT&T 10%2.General Electric 13%3.Microsoft 30%4.Citigroup 16% If we formed a €100,000 portfolio investing €25,000 in

each stock the WEIGHTS OF THE PORTFOLIO ARE: AT&T €25000 WAT&T=25000/100000= 0.25General Electric €25000 … and the same is valid for the otherMicrosoft €25000 investments. Citigroup €25000 €100000


• If we formed a €100,000 portfolio investing €25,000 in each stock the expected portfolio return would be 17.25%:

kp=0.25(10%)+0.25(13%)+0.25(30%)+0.25(16%)=17.25%

Kp or Kj is the same: the expected rate of return on the j or p stock.

^^

33

CAPM: THE RELATIONSHIP BETWEEN RISK AND RATES OF RETURN

• We know that investors demand a premium for bearing risk; that is, the higher the risk of a security, the higher its expected return must be to induce investors to buy (or to hold) it. However, if investors are primarily concerned with the risk of their portfolios rather than the risk of the individual securities in the portfolio, then how should the risk of an individual stock be measured?

• One answer is provided by the Capital Asset Pricing Model (CAPM), an important tool used to analyze the relationship between risk and rates of return.

• The primary conclusion of the CAPM is this: The relevant risk of an individual stock is its contribution to the risk of a well diversified portfolio. A stock might be quite risky if held by itself, but—since about half of its risk can be eliminated by diversification—the stock’s relevant risk is its contribution to the portfolio’s risk, which is much smaller than its stand-alone risk.


• A simple example will help make this point clear. Suppose you are offered the chance to flip a coin. If it comes up heads, you win $20,000, but if it’s tails, you lose $16,000. This is a good bet—the expected return is 0.5($20,000) + 0.5(−$16,000) = $2,000. However, it’s a highly risky proposition because you have a 50% chance of losing $16,000. Thus, you might well refuse to make the bet. Alternatively, suppose that you were to flip 100 coins and that you would win $200 for each head but lose $160 for each tail. It is theoretically possible that you would flip all heads and win $20,000, and it is also theoretically possible that you would flip all tails and lose $16,000, but the chances are very high that you would actually flip about 50 heads and about 50 tails, winning a net of about $2,000. Although each individual flip is a risky bet, collectively you have a low-risk proposition because most of the risk has been diversified away.

• This is the idea behind holding portfolios of stocks rather than just one stock. The difference is that, with stocks, not all of the risk can be eliminated by diversification—those risks related to broad, systematic changes in the stock market will remain.


• Are all stocks equally risky in the sense that adding them to a well-diversified portfolio will have the same effect on the portfolio’s risk? The answer is “no.”

• Different stocks will affect the portfolio differently, so different securities have different degrees of relevant risk. How can the relevant risk of an individual stock be measured? As we have seen, all risk except that related to broad market movements can, and presumably will, be diversified away. After all, why accept risk that can be eliminated easily? The risk that remains after diversifying is called market risk, the risk that is inherent (natural) in the market.


• CAPM is a model that is used to determine the rate of return that investors will require on a stock in order to compensate them for taking the risk.


Beta β


• The primary conclusion reached in the preceding section is that the relevant risk of an individual stock is the amount of risk the stock contributes to a well-diversified portfolio. The benchmark for a well-diversified stock portfolio is the market portfolio, which is a portfolio containing all stocks. Therefore, the relevant risk of an individual stock, which is measured by its beta coefficient, is defined under the CAPM as the amount of risk that the stock contributes to the market portfolio. In CAPM terminology, ρiM is the correlation between Stock i’s return and the market return, σi is the standard deviation of Stock i’s return, and σM is the standard deviation of the market’s return. The beta coefficient of Stock i, denoted by bi, is found as follows:

• bi = σi σM * ρiM


• This tells us that a stock with a high standard deviation, σi, will tend to have a high beta, which means that, other things held constant, the stock contributes a lot of risk to a well-diversified portfolio. This makes sense, because a stock with high stand-alone risk will tend to destabilize the portfolio. Note too that a stock with a high correlation with the market, ρiM, will also tend to have a large beta and hence be risky. This also makes sense, because a high correlation means that diversification is not helping much, with most of the stock’s risk affecting the portfolio’s risk.


Beta β

• A measure of the extent to which the returns on a given stock move with the stock market

β = Covariance of Market Return with Stock Return Variance of Market Return

• β<1: Movement of the asset is generally in the same direction as, but less than the movement of the market

• β = 1 : Movement of the asset is generally in the same direction as, and about the same amount as the movement of the market

• β > 1 : Movement of the asset is generally in the same direction as, but more than the movement of the market


• Suppose correlation coefficient between market and share price of Company P is 0.75; standard deviation (σ) of market is 15% and that of share price is 8%, beta can equals 0.40 (=0.75 × 8%/15%).


The Relationship between Risk and Rates of Return

• kj = expected rate of return on the j stock. • kj = required rate of return on the stock. • k = risk – free rate of return. • βj= beta of the stock. • k = Required rate of return on a portfolio consisting

of all stocks, which is the market portfolio • RP = k - k Market risk premium. This is an

additional return above the risk free rate required to compensate an average investor for an average amount of risk.

^

RF

M

MM RF


The Relationship between Risk and Rates of Return

• Equation of Rate of Return

kj = k + (k -k )βj

Example: A government bond has a rate of return 6% and the portfolio X has a required return 14%. Also beta is 0.5 and the market risk premium is 8%. Find the required return that investors claim.

kx = 6% + ( 14% -6%)*0.5= 10%

RF RFM


• If kj = expected rate of return on the j stock is higher than the kj = required rate of return on the stock then the proposed portfolio is efficient.

Conclusion of CAPM^

principles of financial analysis week 4: lecture 4 1lecturer: chara charalambous

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