topic 4 investment analysis

INTRODUCTION

In Topic 3, the discussion of portfolio theory showed how an efficient portfolio was formed using a combination of risky assets. In this topic, we will extend the analysis of portfolio as well as the usage of some tools derived from Topic 3. We will be introduced to risk-free assets and changes observed in the shape of an efficient frontier. Next, we will discuss the concept of equilibrium condition and how assets are being priced in these conditions. As a result, we will derive two equilibrium models, namely the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT).

TTooppiicc

44 Equilibrium

Models and Applications

LEARNING OUTCOMES

By the end of this topic, you should be able to:

1. Explain risk-free asset;

2. Calculate the return and risk of a portfolio;

3. Explain the importance of the Capital Asset Pricing Model (CAPM) ininvestment decision-making;

4. Review the concept of systematic risk or Beta; and

5. Explain the concept of Arbitrage Pricing Theory.

TOPIC 4 EQUILIBRIUM MODELS AND APPLICATIONS

49

RISK-FREE ASSETS

Technically, the asset will provide a return that is equal to its expected return. Thus, there is no variability in the returns. An example of a risk-free asset is a fixed deposit in the bank. If the bank promises to pay a fixed amount of interest within a stated period, then the bank would normally fulfil its promise. Therefore, the investor will neither expect the return to be lower nor expect the bank to increase the return. Since this type of arrangement has no risk, the return offered is normally low.

RISK-FREE AND RISKY ASSETS

An investor can choose to invest 100% in a risk-free asset (RF) or divide his funds into risk-free assets and risky assets. For example, if RF is offering a return of 8% and the expected return of risky Asset A is 10%, what is the expected return from the portfolio? Risky Asset A has a standard deviation of 6% and the investor places 40% of funds in RF . The correlation between the risky asset and risk-free asset is zero, that is AF = 0. From Topic 3, we know that portfolio return (ERp) is:

ERP = wFRF + wAERA. Where:

wF = Weights in RF wA = Weights in Asset A ERA = Expected return of Asset A.

Thus, ER(P) for the above example is:

ER(P) = (0.4 x 8) + (0.6 x 10) = 9.2

The risk (P) of the above portfolio is:

4 4 4 4

4 4 4

4

206 *2+ 208 *8 + 4*206+*208+*2+2*8+ 508

R H H C C H C CH H Cy y y y

Notice that the risk of Asset A made up the whole risk of the portfolio, in proportion to the amount of funds invested in the asset. As mentioned earlier, we

4.2

A rrisk-free asset is an asset with zero variance.

4.1

TOPIC 4 EQUILIBRIUM MODELS AND APPLICATIONS 50

can shift funds from RF to Asset A and build a set of portfolios and a range of returns and risks. Table 4.1 shows the range of portfolio returns and risks when funds are shifted from RF to Asset A. Table 4.1: Calculation of Portfolio Return and Risk between Asset A and Risk-Free Asset

RF = 8 ERA = 10

RF = 0 A = 6

ARF = 0

wRF wA ERp w2RFs2RF w2A2A 2wRFwAPRFARFA 2P P

1.0 0 8.0 0 0 0 0 0

0.9 0 8.2 0 0.36 0 0.36 0.6

0.8 0 8.4 0 1.44 0 1.44 1.2

0.7 0 8.6 0 3.24 0 3.24 1.8

0.6 0 8.8 0 5.76 0 5.76 2.4

0.5 0 9.0 0 9.00 0 9.00 3.0

0.4 0 9.2 0 12.96 0 12.96 3.6

0.3 0 9.4 0 17.64 0 17.64 4.2

0.2 0 9.6 0 23.04 0 23.04 4.8

0.1 0 9.8 0 29.16 0 29.16 5.4

0

1

10.0 0

36.00 0

36.00

6.0

Note: Please refer to Topic 3 for explanation on the calculations and symbols. If the expected return and risk are plotted on a graph, we will get a straight line as shown in Figure 4.1.


51

Figure 4.1: Portfolio return and risk of risk-free and asset A

Let us say there is another investment asset, Asset B for our investment consideration. The expected return for Asset B is 11.6% and the standard deviation is 5.3%. What is the portfolio combination of RF and Asset B? Figure 4.2 shows the portfolio combination that can be made between RF and Asset B. The line is derived from the calculations in Table 4.2.

Figure 4.2: Combinations of RFA and RFB


Table 4.2: Portfolio Returns and Risks for Combinations between Risk-Free Asset (RF) and Risky Asset A and Risky Asset B

wRF

ERP1

P1

ERP2 P2

1 8 0 8 0

0.9 8.2 0.6 8.4 0.50.8 8.4 1.2 8.7 1.10.7 8.6 1.8 9.1 1.60.6 8.8 2.4 9.4 2.10.5 9 3 9.8 2.60.4 9.2 3.6 10.2 3.20.3 9.4 4.2 10.5 3.70.2 9.6 4.8 10.9 4.20.1 9.8 5.4 11.24 4.80 10 6 11.6 5.3

RF RF 0

RF RF 6 RE 0

RF RF 5.3 ARF 0

Portfolio P1 is combination of RP and asset A

Portfolio P2 is combination of RP and asset B

If we also plot the portfolio return and risk (risk-free asset and Asset A as in Figure 4.2), you can see that the combination of RF and Asset B are more efficient than the combination of RF and Asset A. At the same risk level (point 2 and point 1), the combination of RF and Asset B offers a higher return compared to the combination of RF and Asset A. In the last topic, it was shown that if all risky assets were to be combined to form portfolios, then an efficient set of portfolios could be found. This efficient set is located on the eefficient frontier. We can combine RF with any portfolios in the efficient set. Figure 4.3 shows the combinations that can exist between RF and the efficient frontier.


53

Figure 4.3: Combinations of RF with any assets on the efficient frontier

Using the previous discussion, the line RFA are portfolios that are less efficient than RFB. We can move upwards until a line is obtained that gives the highest return with a given level of risk. This line just touches the efficient frontier at point P. Asset P is known as the ooptimal portfolio. It is the portfolio that gives the best sets of returns within its specific risk level. It is also the highest line or the line with the greatest slope. An investor now will not want to consider any other portfolios other than P, since combinations of RF and this portfolio give him the best returns and risk compared with any other combination below the line. Therefore, we can ignore any portfolios or assets that are not on the RFP line. The investment selection now shifts from the curve of the efficient frontier to the straight line. Figure 4.4 shows the complete strategies an investor can choose. At point RF, an investor invests 100% in the risk-free asset. At point P, he invests 100% in portfolio P. Between RF and P, he combines RF with P. Any position on the line is where the investor lends some of his funds to RF and also invests some portion in P.


The investor can extend his choice by borrowing and invest in P. This is shown by the extended line PP1. The investor will expect a higher return but the risk will increase. He will also need to pay interest on the borrowed funds. The interest rate is RF.

Figure 4.4: Combinations of RF and optimal portfolio P; lending and borrowing positions


55

Lending

Table 4.3 shows the calculations for the RF PP1 line.

RF = 8 RF = 0 PRF ?" 2 ER P = 16 P = 7

wRF wP ERPortfolio w2Ps2P w2Ps2P 2wRFwPrRFPsRFsP s2Portfolio sPortfolio

1 0 8 0 0 0 0 0 0.9 0.1 8.8 0 0.5 0 0.5 0.7 0.8 0.2 9.6 0 1.9 0 1.9 1.4 0.7 0.3 10.3 0 4.2 0 4.2 2.1 0.6 0.4 11.1 0 7.5 0 7.5 2.7 0.5 0.5 11.9 0 11.8 0 11.8 3.4 0.4 0.6 12.7 0 17.0 0 17.0 4.1 0.3 0.7 13.4 0 23.1 0 23.1 4.8 0.2 0.8 14.2 0 30.2 0 30.2 5.5 0.1 0.9 15.0 0 38.2 0 38.2 6.2 0 1 15.8 0 47.1 0 47.1 7

-0.1 1.1 16.6 0 57.0 0 57.0 7.6 -0.2 1.2 17.3 0 67.9 0 67.9 8.2 -0.3 1.3 18.1 0 79.7 0 79.7 8.9 -0.4 1.4 18.9 0 92.4 0 92.4 9.6 -0.5 1.5 19.7 0 106.1 0 106.1 10.3

When the investor has 10% of his investment using borrowed funds, he is investing 110% in P. The return from the portfolio is:

* 203 : + *303 38+

380:

Rqtvhqnkq H H R RGT y T y GT

The risk of the portfolio is:

4 4 4 4

4 4 4

4

203 *2+ 303 *9 + 4* 203+*303+*2+2*9+

909

Rqthqnkq H H R R H r rH H Ry y y y

Borrowing


THE MARKET PORTFOLIO

In the previous section, we discussed optimal portfolio P, the most efficient portfolio. To maximise returns with the best risk level, the investor will not consider any other rrisky assets. All investors would prefer to hold this portfolio P. Therefore, this portfolio must iinclude all risky assets. If not, there would be no demand for that asset and therefore, it would not have any value (price).

A portfolio consists of a combination of assets according to their respective weights. Therefore, in this mmarket portfolio, each asset will be represented by its value in proportion to the total value of the market. Efficiency is an important characteristic of this market portfolio. An efficient portfolio will be a fully diversified portfolio. A fully diversified portfolio is where all unique risks of the individual asset have been diversified away. The remaining risk is the systematic risk of the individual asset. This systematic risk is measured by the covariance of an individual asset with the market portfolio. Take note that a market portfolio is a combination of all risky assets. An individual asset in the market portfolio will therefore have a covariance with every other single asset in the market. In the next section, we will find that this covariance of an asset with the market will become a very significant contribution to an asset return. If we redraw Figure 4.4 and replace portfolio P with market portfolio M, we will obtain Figure 4.5, the Capital Market Line.

4.3

If we consider an equilibrium situation and all assets are included, then the optimal portfolio P is the mmarket portfolio. All assets will be represented in this market.

You have two types of assets to be considered for investment. Asset A is risk-free but only offers a return of 6% while Asset B is a risky asset which offers 10% returns. Which asset would you invest in? Why?

SELF-CHECK 4.1


57

Figure 4.5: Capital market line

The straight line is known as the CCapital Market Line (CML). CML now becomes the relevant eefficient frontier. The vertical and horizontal lines represent the expected returns and risks of portfolios respectively. The CML shows the relationship between the expected returns and risks of portfolios. This relationship, which is a straight line, is shown below:

* +

0O HR H RO

GT TGT T

The risk of the portfolio is: * +

0O H

O

GT T

The above equation shows that expected returns (ERP) will be high when the risks (P) of the portfolio are high. The value of the slope will be the same at any point along the line. This slope represents the price of the risk that an investor will face. The price will increase when the risk increases.

If a portfolio is what an investor has when he divides his fundsand invests in more than one asset, what is a market portfolio?

SELF-CHECK 4.2


THE CAPITAL ASSET PRICING MODEL

In the previous section, the CML provides the return-risk relationship of portfolios. Though there are numerous risky assets in the market portfolio, the most efficient is the market portfolio. There will be numerous risky assets in this market portfolio. Now, we will examine the relationship of an individual asset with this market portfolio. CAPM was derived by using many assumptions. These assumptions are stated below:

(a) There are many investors and they are all price takers. This situation is similar to perfect competition where nobody has any influence on the market.

(b) All investors have one holding period.

(c) All assets are in the market. Investors can borrow or lend any amount at a fixed risk-free rate.

(d) There are no taxes and no transaction costs.

(e) All investors make decisions based on mean and variance.

(f) All investors have homogeneous expectations. Thus, they will behave the same way if faced with the same situation.

In the last topic, we saw how a portfolio risk is determined. Portfolio risk is a combination of individual assets variance and covariance with other assets. As the number of assets in a portfolio increases, the number of covariance also increases. The number of covariance will finally be more than the variance of individual assets. This will indicate that the covariance between assets will be more important than the variance as the number of assets in the portfolio increases. The covariance between assets will contribute a major portion of the portfolio risk. Therefore, the only risk that is relevant is the covariance of an individual asset with other assets in the portfolio. We also have stressed that the only efficient portfolio is the market portfolio. Therefore, the only risk that is relevant to an individual asset (i) in the market portfolio is its covariance with the market portfolio (iM).

4.4

Capital Asset Pricing Model (CAPM) is a model that shows the relationship between returns and risks of individual assets.


59

Again, this return-risk relationship can be interpreted through Figure 4.6. We have used the same format as in Figure 4.5. However, the vertical and horizontal lines have been replaced with expected returns (ERi) and risk (covariance between i and M, iM) of individual assets. The line is known as the SSecurity Market Line (SML).

Figure 4.6: The security market line (SML) representing the capital asset pricing model

Firstly, observe that the covariance of the market with itself is the variance of the market, (MM) = (2M).

The slope of the SML is therefore: 4

* +O H

O

GT T

The equation for the SML is shown below:

4 4

* +qt * +O H kOk H kO k H O H

O O

GT TGT T GT T GT T

Secondly, we can replace the term with a standardised format known as Beta (i) or systematic risk. The equation of the SML can be shown as:

* +0k H k O HGT T GT T


This equation is known as the CCapital Asset Pricing Model (CAPM). It states that the expected return of an individual asset i is related to its systematic risk (i). The investor should demand a reward to incur this risk. The general price of the risk is the market risk premium (ERM RF). This risk premium is the same for all assets. However, the amount of reward for each risky asset is the risk premium multiplied by the systematic risk (i). Note that the amount of reward for each risky asset together with the risk-free rate will determine the total expected return. Notice that if the covariance of the market with itself is the variance of the market, (MM) = (2M), then the Beta of the market is equal to one. Figure 4.6 will then change to Figure 4.7.

Figure 4.7: The capital asset pricing model

ESTIMATING BETA

The systematic risk or Beta can be estimated using the equation below:

kv k k OvT T where: Rit = the return for asset i during period t; RMt = the return of the market portfolio during period t; i = the constant term or the intercept of the regression line; i = the beta of asset; and = the random error for the line.

4.5


61

The above equation is similar to any time series regression model, where the independent variable is RM and the dependent variable is Ri. Ri is assumed to change when RM changes. The amount of change in Ri will be determined by i, with some level of error, . The equation will give you a straight line. In this context, we can call it a ccharacteristic line. Please take note that the above equation is nnot the CAPM. The actual market portfolio cannot be observed since it is impossible to include all risky assets. A complete market will have to include all financial and physical assets as well as human assets, arts, properties, raw materials, natural resources and others. The alternative is to use a pproxy of the market. The accepted procedure is to use a market index. In Malaysia, we can use the Bursa Malaysia Composite Index. Table 4.4 shows an example of how beta is calculated. We have used monthly price data from Yeo Hiap Seng (YHS) and YTL Power (YTLPWR). The prices have to be converted into returns. For example, the return for January 2002 is obtained by taking the price for that month minus the price from December 2001 and divided by the December price. Hence, the return for YHS is

RM2.03 RM2100 1.50

RM2

. Columns four and five as indicated in Table 4.4

are products of two deviations. For YHS, it will be ( )( )KLCI KLCI YHS YHSR R R R for each month. Figure 4.8 shows the scatter plot for returns of YHS against the KLCI. The x-axis represents the returns of the KLCI. Each dot represents the returns of the share against the KLCI on a particular month. A line can be drawn across the dots to show a general relationship between YHS returns against the KLCI. In a regression model, this line is known as the line of best fit. We can call this line the ccharacteristic line. The slope of the line is the measure for Beta. Figure 4.9 shows the line for YTLPWR. Do you notice that the slope for YHS is steeper than YTLPWR? This indicates that the beta (risk) for YHS is higher than YTLPWR.

Refer to the Bursa Malaysia website at http://www.bursamalaysia. com. Select at least three shares from the same industry listed in the Bursa Malaysia and determine their beta. What can you conclude from the results obtained? You can also obtain the data required for your calculation from the newspapers.

ACTIVITY 4.1


Table 4.4: Beta Calculation for YHS and YTLPOWER

Tgvwtp" *3+*4+?" *3+*5+?"

Fcvg" KLCI YHS YTLPWR RKLCI RYHS RYTLPWR KLCI KLCIR - R *3+ YHS YHSR - R *4+ YTLPWR YTLPWRR - R *5+" *6+" *7+"

Fge/23" 883074" 4" 406" " " " " " " " "

Lcp/24" 8;9033" 4025" 4059" 705:" 3072 /3047" 7078" 5065" /4065" 3;026" /35075"

Hgd/24" 92908:" 4029" 4049" 3074" 30;9 /6044" 308;" 50;2" /7062" 8082" /;037"

Oct/24" 963094" 4026" 407" 60:3" /3067 32035" 60;;" 206:" :0;7" 405:" 66085"

Crt/24" 983064" 4034" 40:;" 4088" 50;4 37082" 40:5" 70:7" 36064" 38079" 620:7"

Oc{/24" 9:;0;5" 4045" 40:9" 5096" 703; /208;" 50;4" 9033" /30::" 490;2" /9058"

Lwp/24" 977043" 30;7" 40::" /6062" /34078 2057" /6044" /32085" /20:6" 660:5" 5074"

Lwn/24" 966084" 30;3" 40:4" /3062" /4027 /402:" /3044" /2035" /5049" 2037" 6022"

Cwi/24" 943087" 30;4" 4097" /502:" 2074 /406:" /40;3" 4067" /5089" /9034" 32088"

Ugr/24" 8;602;" 30:" 4096" /50:4" /8047 /2058" /5086" /6054" /3077" 37097" 7086"

Qev/24" 86402;" 308;" 4077" /906;" /8033 /80;5" /9053" /603;" /:034" 52083" 7;05:"

Pqx/24" 877098" 3095" 4097" 4035" 4059 90:6" 4053" 604;" 8088" ;0;2" 37058"

Fge/24" 83:059" 307" 40:6" /7092" /3504; 5049" /7074" /33059" 402;" 840:2" /33076"

Lcp/25" 848039" 3068" 40:" 3048" /4089 /3063" 3066" /2096" /407;" /3029" /5095"

Hgd/25" 883047" 306:" 40:" 7082" 3059 2022" 709:" 5052" /303:" 3;027" /80:6"

Oct/25" 857088" 3068" 40:" /50:9" /3057 2022" /508;" 2079" /303:" /4034" 6059"

" " " Cxgtcig"T /203:" /30;5 303:" " " Vqvcn," 46704:" 358048"

UF"* + 6054" 7074 70:6" " " " " "Xctkcpeg""*4 + 3:08:" 52069 56035" " " " " "

Eqxctkcpeg"*ko+

" 39074 ;095"" " " " "

Dgvc"*+ " 20;6 2074" " " " " "Cnrjc"*+ " /3098 304:" " " " " "

"Eqnwop"6"ku"eqnwop"4"ownvkrnkgf"ykvj"eqnwop"3""Eqnwop"7"ku"eqnwop"5"ownvkrnkgf"ykvj"eqnwop"3""Vqvcn,"ku"vjg"vqvcn"hqt"vjg"Eqnwop"6"cpf"70""Eqxctkcpeg""?""Vqvcn,"36"*"36"ku"vjg"pwodgt"qh"qdugtxcvkqp"nguu"3."vjcv"ku"37"oqpvju"nguu"3+0"

"Dgvc"ku"*ko 2MNEK +0"Cnrjc"hqt"[JU"ku" * +MNEK[JU [JUT T "cpf"ceeqtfkpin{"hqt"[VNRYT0"


63

Figure 4.8: YHS characteristic line

Figure 4.9: YTLPWR characteristic line


APPLYING THE CAPM

Let us assume that we are able to obtain the following data for a set of shares from an investment analyst:

Stock Beta A 0.8 B 1 C 1.2 D 1.8 E -0.5

Also assume that the investment analyst has predicted that the market is expected to provide a return (ERM) of 10% and the current risk-free rate (RF) of 4%. The market risk premium will be 6%. With this scenario, the expected return (ERi) of each share will be calculated as in Table 4.5.

4.6

1. Using a rough sketch, determine the beta for Share A and B.

Year Market Return Return Share A Return Share B

1 3% 16 5

2 -5 20 5

3 1 18 5

4 -20 25 5

5 6 14 5

2. Currently the share price of Fatbody Corp is RM3. The firm is

experiencing a growth rate of 6% annually. Last years EPS (E0) is RM0.40, and the dividend payout ratio is 50%. The risk-free rate is 5% and the market return is 10%. Determine the required return and the beta of Fatbody.

EXERCISE 4.1


65

Table 4.5: Expected Return

Stock Expected Return ERi = Risk-free RF Beta Risk Premium

I (ERM RF) A 8.8% = 4% 0.8 (10% 4%)

B 10% = 4% 1 (10% 4%)

C 11.2% = 4% 1.2 (10% 4%)

D 14.8% = 4% 1.8 (10% 4%)

E 1% = 4% -0.5 (10% 4%) At equilibrium, all the shares should provide the returns as shown in Table 4.5. This will also mean that the returns will depend on the SML. Figure 4.10 depicts this situation. All shares will be in line with their respective betas.

Figure 4.10: Asset returns with their betas

Sometimes, you may face a situation where the expected returns are not in line with the estimated returns. For instance, an investor may have his/her own speculation on the selling price of each share, and this will result in an estimated return that is different from the expected returns. For further elaboration, lets say that the current price is P0 price and the investor expects to sell the shares at P1 prices. The analysis for this scenario is described in Table 4.6.


Table 4.6: Analysis of Prices

Stock Current Price P0

(RM)

Estimated Price P1

(RM)

Estimated Return

(%)

Expected Return ERi (%)

Price Situation

Actual Value

P0"(RM)

A 3.5 3.81 8.8 8.8 Correct 3.50

B 4.6 5.50 19.5 10 Undervalued 5.00

C 2.5 2.61 4.5 11.2 Overvalued 2.35

D 2.1 2.18 4.0 14.8 Overvalued 1.90

E 1.22 1.24 2.0 1 Close 1.23

The estimated return is obtained by taking the percentage change in price

1 0

0

100P P

P

. This estimated return is compared against the expected return

from the CAPM. If the estimated return is equal to the expected return, then the share is in equilibrium. The actual value P0 is the same as the current price, P0. For stock B, the estimated return is higher than the equilibrium or the expected return. Investors might think that the share can offer a higher return than expected. Thus, there will be an increase in demand, since in equilibrium all investors will have the same information and behaviour. The increase in demand will increase the current price P0. As we can see, the current price, P0 of RM4.60 is considered undervalued. The actual value P0 is RM5.00. With this increase, the estimated return will converge to the expected return. The situation for shares C and D is in reverse. In this case, investors estimate returns that are below expectations. They are unlikely to hold these shares and probably try to sell them if they are holding them. This will create less demand and over supply of those shares. As a result, the price will decrease. Share D, for example, is overpriced at P0 RM2.1. The actual value is only RM1.90. With the decrease, the estimated return will converge to the expected return. Figure 4.10 shows the relationship of the estimated return against the expected return. The expected returns lie on the SML. All shares with estimated returns above the SML are considered undervalued. The reverse is true for the overvalued shares.


67

ARBITRAGE PRICING THEORY

Arbitrage Pricing Theory (APT) is another model that shows returns are also related to risks. However, the model uses different assumptions and techniques.

However, in reality this situation is unlikely to occur. Firstly, in an equilibrium market condition, there will be no such opportunity. Therefore, returns will always be related to risk and some capital investment is needed before returns can be obtained. If such a situation did arise, market forces will react quickly to restore equilibrium. Secondly, according to the APT, returns will be generated from the following process: where:

kT = The expected return of security i

I1Ij = The value of index or factors that can influence security i. = The expected value of the index or factor. ei = A random error that resembles the portion of returns from an

unsystematic risk. bi1.bij = The sensitivities of the security to each of the index. This is

similar to Beta in the CAPM. In CAPM, the factor is the market. However, in APT, we have not specified the nature of the factor.

Thirdly, in order for APT to take effect, we need a large number of assets in the market. The investor can then find a combination of assets that can eliminate

According to APT, an opportunity exists when the investor is able to generate profit without any risk and uses no capital.

4.7

1. We often hear that investors speculations can affect the price of shares listed in the share market. How do speculations affect the price? Explain.

2. Visit the Bursa Malaysias website at http://www.bursamalaysia. com to review some of the share prices available. And also review business analysis in the newspapers to get input about why speculations happened and how it affects share prices.

ACTIVITY 4.2


risks. These risks include all systematic risks measured by betas (b1..bj) and unsystematic risks. Then, the investor is able to combine assets in such a way that he/she does not have to use any capital. (The details and exact processes are available from any advance book in finance and investment listed at the back of this module.) As mentioned earlier, in an equilibrium situation, the above condition cannot exist because the investor will then obtain zero returns. Take note that a relationship exists between expected returns and risks where an investment with zero risk should provide zero returns. At this point, the investor will not even earn the risk-free rate because he did not invest any capital. Since unsystematic risks can be diversified away, investors will only need to be compensated from systematic risks or the beta of the factors. As the factors are general factors and will affect all assets, the price of risks for each factor will be the same. The amount of this price for each asset will be determined by the value beta related to that factor. If we let the price of this risk be , then APT can be generalised into the following.

2 3 3 4 4 00000000000000000k k k kl lGT Where:

ERi = the expected return of asset i. i1, i2 ij = the systematic risks for each factor 1 to j; 0 = the risk-free rate; and 1, 2 j = the price of risk or risk premium that is required by investors

to bear the risk from factors 1 to j. Different assets will have different returns based on their level of betas for each factor. For example, lets assume there are two general factors and investors perceive factor one should have a risk premium 1 of 5% and factor two 2 with 10% and the risk-free rate is 4%. Then, the APT model will look like this:

3 46 7 32k k kGT Asset A with 1 which is equal to 0.5 and 2 which is equal to 0.8 will have an expected return of 14.5%. Asset B with 1 which is equal to 2 and 2 which is equal to 0.5 will have an expected return of 19%. The APT did not specify the number of factors and the nature of these factors. Previous empirical tests have found several economic variables to be significant. Among them are index of industrial production, default risk premium (the difference between the yield of AAA and BBB bonds), difference in yield curve


69

(the difference between short-term and long-term rates of government bonds) and unanticipated inflation.

Efficiency is an important characteristic of a market portfolio. An efficient portfolio will be a fully diversified portfolio where all unique risks of the individual have been diversified away.

CAPM is a model that shows the relationship between returns and risks of individual assets. It states that the expected return of an individual asset is related to its systematic risk (beta).

According to APT, an opportunity exists when the investor is able to generate profit, without any risk and uses no capital.

1. Your analyst has provided the following information. The expectedmarket return is 12% while the risk-free rate is 4%. The standarddeviation of the market is 8%. You are required to draw the capitalmarket line and the security market line.

2. Using the information from Question 1, what will happen to ashare with a beta of 1, if it is offering a return of 14%?

3. Assume that the risk=free rate is 6% and the expected rate of returnof the market is 16%. A share that sells for RM5.00 today isexpected to pay a dividend of RM0.60 per share at the end of theyear. Its beta is 1.2. At what price do investors expect to sell at theend of the year?

EXERCISE 4.2

topic 4 investment analysis

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