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# Theory of Corporate Finance FIN 332

Cal State Fullerton

GPA 3.97

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This 26 page Class Notes was uploaded by Mr. April Weber on Wednesday September 30, 2015. The Class Notes belongs to FIN 332 at California State University - Fullerton taught by Staff in Fall. Since its upload, it has received 16 views. For similar materials see /class/217018/fin-332-california-state-university-fullerton in Finance at California State University - Fullerton.

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Date Created: 09/30/15

Chapter 4 Risk and Return The Basics ANSWERS T0 ENDOFCHAPTER QUESTIONS E Fquot 0 3 1 D quot1 Standalone risk is only a part of total risk and pertains to the risk an investor takes by holding only one asset Risk is the chance that some unfavorable event will occur For instance the risk of an asset is essentially the chance that the asset s cash ows will be unfavorable or less than expected A probability distribution is a listing chart or graph of all possible outcomes such as expected rates of return with a probability assigned to each outcome When in graph form the tighter the probability distribution the less uncertain the outcome The expected rate of return 2 is the expected value of a probability distribution of expected returns A continuous probability distribution contains an in nite number of outcomes and is graphed from oo and 00 The standard deviation 6 is a statistical measure of the variability of a set of observations The variance oz of the probability distribution is the sum of the squared deviations about the expected value adjusted for deviation The coefficient of variation CV is equal to the standard deviation divided by the expected return it is a standardized risk measure which allows comparisons between investments having different expected returns and standard deviations A risk averse investor dislikes risk and requires a higher rate of return as an inducement to buy riskier securities A realized return is the actual return an investor receives on their investment It can be quite different than their expected return A risk premium is the difference between the rate of return on a riskfree asset and the expected return on Stock i which has higher risk The market risk premium is the difference between the expected return on the market and the riskfree rate CAPM is a model based upon the proposition that any stock s required rate of return is equal to the risk free rate of retum plus a risk premium re ecting only the risk re maining after diversification Answers and Solutions 4 1 Pquot The expected return on a portfolio ip is simply the weightedaverage expected return of the individual stocks in the portfolio with the weights being the fraction of total portfolio value invested in each stock The market portfolio is a portfolio consisting of all stocks Correlation is the tendency of two variables to move together A correlation coefficient p of 10 means that the two variables move up and down in perfect synchronization while a coefficient of l0 means the variables always move in opposite directions A correlation coefficient of zero suggests that the two variables are not related to one another that is they are independent j Market risk is that part of a security s total risk that cannot be eliminated by diversification It is measured by the beta coefficient Diversifiable risk is also known as company specific risk that part of a security s total risk associated with random events not affecting the market as a whole This risk can be eliminated by proper diversification The relevant risk of a stock is its contribution to the riskiness ofa welldiversified portfolio F The beta coefficient is a measure of a stock s market risk or the extent to which the returns on a given stock move with the stock market The average stock s beta would move on average with the market so it would have a beta of 10 l The security market line SML represents in a graphical form the relationship between the risk of an asset as measured by its beta and the required rates of return for individual securities The SML equation is essentially the CAPM ri rRF birM 1111 m The slope of the SML equation is rM rRF the market risk premium The slope of the SML re ects the degree of risk aversion in the economy The greater the average investors aversion to risk then the steeper the slope the higher the risk premium for all stocks and the higher the required return 39F N s The probability distribution for complete certainty is a vertical line Fquot The probability distribution for total uncertainty is the X axis from oo to 00 43 Security A is less risky if held in a diversified portfolio because of its lower beta and negative correlation with other stocks In a singleasset portfolio Security A would be more risky because GA gt GB and CVA gt CVB Answers and Solutions 4 2 4 4 a No it is not riskless The portfolio would be free of default risk and liquidity risk but in ation could erode the portfolio s purchasing power If the actual in ation rate is greater than that expected interest rates in general will rise to incorporate a larger in ation premium IP and the value of the portfolio would decline Fquot No you would be subject to reinvestment rate risk You might expect to roll over the Treasury bills at a constant or even increasing rate of interest but if interest rates fall your investment income will decrease c A US govemmentbacked bond that provided interest with constant purchasing power that is an indexed bond would be close to riskless The risk premium on a high beta stock would increase more RPj Risk Premium for Stock j rM rRFbJ If risk aversion increases the slope of the SML will increase and so will the market risk premium rM 7 rRF The product rM 7 rRFbj is the risk premium of the jth stock If bj is low say 05 then the product will be small RPj will increase by only half the increase in RPM However if bj is large say 20 then its risk premium will rise by twice the increase in RPM According to the Security Market Line SML equation an increase in beta will increase a company s expected return by an amount equal to the market risk premium times the change in beta For example assume that the riskfree rate is 6 percent and the market risk premium is 5 percent If the company s beta doubles from 08 to 16 its expected return increases from 10 percent to 14 percent Therefore in general a company s expected return will not double when its beta doubles Yes ifthe portfolio s beta is equal to zero In practice however it may be impossible to find individual stocks that have a nonpositive beta In this case it would also be impossible to have a stock portfolio with a zero beta Even if such a portfolio could be constructed investors would probably be better off just purchasing Treasury bills or other zero beta investments Answers and Solutions 4 3 SOLUTIONS TO ENDOF CHAPTER PROBLEMS 4 1 2 01 50 02 5 0416 0225 0160 1140 43 4 4 62 50 114020 1 5 1140202 16 1140204 25 1140202 60 1140201 62 71244 6 2669 2669 1140 234 Investment Beta 3 5000 08 40 000 14 Total 71000 350007500008 400007500014 112 rRF 5 RPM 6rM rM 5 6111 rswhenb 12 rs 5 612 122 rRF 6rM13b07rs rs rRF rM rRFb 6 13 607 109 Answers and Solutions 4 4 4 5 a 2m 0315 049 0318 135 103200450312 116 b 6M 10315 1352 049 1352 0318 135212 385 m 10320 1162 045 1162 0312 116212 622 7 385 CV 7 029 c M 135 CV 622 054 116 46 I A I RF I M I RFbA 12 5 10 5bA 12 5 5bA 7 5bA 14 bA E Fquot rA 5 5bA rA 5 52 rA 15 47 a ri rRF rM rRFbi 9 14 913 155 b 1 rRF increases to 10 rM increases by 1 percentage point from 14 to 15 ri rRF rM rmbi 10 15 1013 165 2 rRF decreases to 8 rM decreases by 1 from 14 to 13 ri rRF rM rRFbi 8 13 813 145 c 1 rM increases to 16 ri rRF rM rmbi 9 16 913 181 Answers and Solutions 4 5 2 rM decreases to 13 r rRF rM rmb 9 13 913 142 48 Old portfolio beta 142500 b 7500 100 150000 150000 112 095b 005 107 095b 113 b New portfolio beta 0951 13 005175 116 Alternative Solutions 1 Old portfolio beta 112 005b1 005b2 005b20 112 2b1005 215i 112005 224 New portfolio beta 224 10 17500511575 116 N Zbi excluding the stock with the beta equal to 10 is 224 10 214 so the beta of the portfolio excluding this stock is b 21419 11263 The beta of the new portfolio is 11263095 175005 11575 116 Answers and Solutions 4 6 410 400000 150 4000000 1000000 2000000 4000000 4000000 0115 015 050 025125 05075 015 0075 03125 0375 07625 600000 Portfolio beta 4000000 050 125 075 rp rRF rM rRFxbp 6 14 607625 121 Alternative solution First compute the return for each stock using the CAPM equation rRF rM rRFb and then compute the weighted average of these returns rRF 6 and rM rRF 8 k Investment oc Beta r rRF rM rRFb Weight A 400000 150 18 010 B 600000 050 2 015 C 1000000 125 16 025 D 2 000 000 075 12 M Total 4 000 000 1 00 rp 18010 20151602512050121 First calculate the beta of what remains after selling the stock bp 11 100000200000009 19000002000000bR 11 0045 095bR bR 11105 bN 09511105 00514 1125 We know that bR 150 bs 075 rM 13 rRF 7 ri rRF rM rRFbi 7 13 7bi rR 7 6150 160 rs 7 6075 115 Q Answers and Solutions 4 7 412 The answers to a b c and d are given below rA rB Portfolio 2000 1800 1450 1625 2001 3300 2180 2740 2002 1500 3050 2275 2003 050 760 405 2004 2700 2630 2665 Mean 1130 1130 1130 Std Dev 2079 2078 2013 CV 184 184 178 D A riskaverse investor would choose the portfolio over either Stock A or Stock B alone since the portfolio offers the same expected return but with less risk This result occurs because returns on A and B are not perfectly positively correlated p AB 088 413 a bx 13471 by 06508 6 rx 6 513471127355 ry 6 506508 92540 0 bp 0813471 0206508 12078 rp 6 512078 1204 Alternatively rp 08127355 029254 1204 Stock X is undervalued because its expected return exceeds its required rate of return Answers and Solutions 4 8 SOLUTION TO SPREADSHEET PROBLEM 414 The detailed solution for the spreadsheet problem is available both on the instructor s resource CD ROM in the le Solution for FM11 Ch 04 P14 Build a ModeLxls and on the instructor s side of the textbook s web site httpb139ighamswleamingc0m Answers and Solutions 4 9 MINI CASE Assume that you recently graduated with a major in fmance and you just landed a job as a fmancial planner with Barney Smith Inc a large nancial services corporation Your rst assignment is to invest 100000 for a client Because the funds are to be invested in a business at the end of one year you have been instructed to plan for a one year holding period Further your boss has restricted you to the following investment alternatives shown with their probabilities and associated outcomes Disregard for now the items at the bottom of the data you will fill in the blanks later Returns On Alternative Fstimatequot Rate Of Return State of the T Alta Repo Am Market 2 stock economy prob Inds Men Foam portfolio portfolio Recession 01 80 220 280 100 130 30 Below avg 02 80 20 147 100 10 Average 04 80 200 00 70 150 100 Above avg 02 80 350 100 450 290 Boom Q Q m M m m m r hat G 17 138 150 Std dev 6 00 134 188 153 Coef ofvar cv 79 14 10 beta b 086 068 Note that the estimated returns of American Foam do not always move in the same direction as the overall economy For example when the economy is below average consumers purchase fewer mattresses than they would if the economy was stronger However if the economy is in a at out recession a large number of consumers who were planning to purchase a more expensive inner spring mattress may purchase instead a cheaper foam mattress Under these circumstances we would expect American Foam s stock price to be higher if there is a recession than if the economy was just below average Barney Smith s economic forecasting staff has developed probability estimates for the state of the economy and its security analysts have developed a sophisticated computer program which was used to estimate the rate of return on each alternative under each state of the economy Alta Industries is an electronics firm Repo Men collects past due debts and American Foam manufactures mattresses and other foam products Barney Smith also maintains an index fund which owns a market weighted fraction of all publicly traded stocks you can invest in that fund and thus obtain average stock market results Given the situation as described answer the following questions Mini Case 4 10 What are investment returns What is the return on an investment that costs 1000 and is sold after one year for 1100 Answer Investment return measures the nancial results of an investment They may be expressed in either dollar terms or percentage terms The dollar return is 1100 1000 100 1001000 010 10 The percentage return is p t b Why is the t bill s return independent of the state of the economy Do t bills promise a completely risk free return Answer The 8 percent tbill return does not depend on the state of the economy because the treasury must and will redeem the bills at par regardless of the state of the economy The tbills are riskfree in the default risk sense because the 8 percent return will be realized in all possible economic states However remember that this return is composed of the real riskfree rate say 3 percent plus an in ation premium say 5 percent Since there is uncertainty about in ation it is unlikely that the realized 211 rate of return would equal the expected 3 percent For example if in ation averaged 6 percent over the year then the realized real return would only be 8 6 2 not the expected 3 Thus in terms of purchasing power tbills are not riskless Also if you invested in a portfolio of Tbills and rates then declined your nominal income would fall that is tbills are exposed to reinvestment rate risk So we conclude that there are no truly riskfree securities in the United States If the treasury sold in ationindexed taxexempt bonds they would be truly riskless but all actual securities are exposed to some type of risk Why are Alta Ind s returns expected to move with the economy whereas Repo Men s are expected to move counter to the economy Answer Alta Industries returns move with hence are positively correlated with the economy because the rm s sales and hence pro ts will generally experience the same type of ups and downs as the economy If the economy is booming so will Alta On the other hand Repo Men is considered by many investors to be a hedge against both bad times and high in ation so if the stock market crashes investors in this stock should do relatively well Stocks such as Repo Men are thus negatively correlated with move counter to the economy note in actuality it is almost impossible to nd stocks that are expected to move counter to the economy Even Repo Men shares have positive but low correlation with the market Mini Case 4 11 c Calculate the expected rate of return on each alternative and ll in the blanks on the row for 2 in the table above A Answer The expected rate of return r 1s expressed as follows A n r ZPiri i1 Here p is the probability of occurrence of the ith state m is the estimated rate of return for that state and n is the number of states Here is the calculation for Alta Inds 21131quot 01220 0220 04200 02350 01500 174 We use the same formula to calculate r s for the other alternatives 2 Tbills 80 r Repo Men 17 AmFm 138 2M 150 Mini Case 4 12 You should recognize that basing a decision solely on expected returns is only appropriate for risk neutral individuals Since your client like virtually everyone is risk averse the riskiness of each alternative is an important aspect of the decision One possible measure of risk is the standard deviation of returns 1 Calculate this value for each alternative and fill in the blank on the row for 6 in the table above Answer The standard deviation is calculated as follows I n A 2 G ZGFH P i1 6AM 220 174201 20 174202 200 174204 350 174202 500 174201 5 4014 200 Here are the standard deviations for the other alternatives 0 Tbills 00 o Repo 134 039 Ampoam o M 153 d 2 What type of risk is J by the standard deviation Answer The standard deviation is a measure of a security s or a portfolio s standalone risk The larger the standard deviation the higher the probability that actual realized returns will fall far below the expected return and that losses rather than pro ts will be incurred Mini Case 4 13 d 3 Draw a graph which shows roughly the shape of the probability distributions for Alta Inds Am Foam and T bills Answer Probability of Occurrence TBills ALTA INDS AM FOAM 60 45 30 15 0 15 30 45 60 Rate of Return Based on these data Alta Inds is the most risky investment tbills the least risky e Suppose you suddenly remembered that the coefficient of variation CV is generally regarded as being a better measure of stand alone risk than the standard deviation when the alternatives being considered have widely differing expected returns Calculate the missing CVs and ll in the blanks on the row for CV in the table above Does the CV produce the same risk rankings as the standard deviation Mini Case 4 14 Answer The coefficient of variation CV is a standardized measure of dispersion about the expected value it shows the amount of risk per unit of return CV Hgtlq CVTbi11S 0080 00 CVAnaInds 200174 11 CVRepo Men 13417 79 CVAmRmm 188138 14 CVM 153150 10 When we measure risk per unit of return Repo Men with its low expected return becomes the most risky stock The CV is a better measure of an asset s standalone risk than 6 because CV considers both the expected value and the dispersion of a distributiona security with a low expected return and a low standard deviation could have a higher chance of a loss than one with a high 6 but a high f Suppose you created a 2 stock portfolio by investing 50000 in Alta Inds and 50000 in Repo Men 1 Calculate the expected return 2 1 the standard deviation 6p and the coefficient of variation cvp for this portfolio and ll in the appropriate blanks in the table above Mini Case 4 15 Answer To nd the expected rate of return on the twostock portfolio we first calculate the rate of return on the portfolio in each state of the economy Since we have half of our money in each stock the portfolio s return will be a weighted average in each type of economy For a recession we have rp 0522 0528 3 We would do similar calculations for the other states of the economy and get these results State Portfolio Recession 30 Below Average 64 Average 100 Above Average 125 Boom 15 0 Now we can multiply probabilities times outcomes in each state to get the expected return on this twostock portfolio 96 Alternatively we could apply this formula R wi x ri 05174 0517 96 Which finds r as the weighted average of the expected returns of the individual securities in the portfolio It is tempting to find the standard deviation of the portfolio as the weighted average of the standard deviations of the individual securities as follows op 2 wioi wjcj 0520 05134 167 However this is not correctit is necessary to use a different formula the one for 6 that we used earlier applied to the twostock portfolio s returns The portfolio s 6 depends jointly on 1 each security s o and 2 the correlation between the securities returns The best way to approach the problem is to estimate the portfolio s risk and return in each state of the economy and then to estimate op with the o formula Given the distribution of returns for the portfolio we can calculate the portfolio s o and CV as shown below op 30 96201 64 96202 100 96204 125 96202 150 962010395 33 CVp 3396 03 Mini Case 4 16 f 2 How does the riskiness of this 2 stock portfolio compare with the riskiness of the individual stocks if they were held in isolation Answer Using either 039 0r CV as our standalone risk measure the standalone risk of the portfolio is signi cantly less than the standalone risk of the individual stocks This is because the two stocks are negatively c0rrelatedwhen Alta Inds is doing poorly Repo Men is doing well and Vice versa Combining the two stocks diversi es away some of the risk inherent in each stock if it were held in isolation ie in a lstock portfolio Suppose an investor starts with a portfolio consisting of one randomly selected stock What would happen 1 to the riskiness and 2 to the expected return of the portfolio as more and more randomly selected stocks were added to the portfolio What is the implication for investors Draw a graph of the two portfolios to illustrate your answer Answer 2 Mini Case 4 17 Density Portfolio of stocks with rp 16 0 1 6 Return The standard deviation gets smaller as more stocks are combined in the portfolio while rp the portfolio s return remains constant Thus by adding stocks to your portfolio which initially started as a lstock portfolio risk has been reduced In the real world stocks are positively correlated with one anotherif the economy does well so do stocks in general and vice versa Correlation coefficients between stocks generally range from 05 to 07 A single stock selected at random would on average have a standard deviation of about 35 percent As additional stocks are added to the portfolio the portfolio s standard deviation decreases because the added stocks are not perfectly positively correlated However as more and more stocks are added each new stock has less of a riskreducing impact and eventually adding additional stocks has virtually no effect on the portfolio s risk as measured by 6 In fact 6 stabilizes at about 204 percent when 40 or more randomly selected stocks are added Thus by combining stocks into welldiversi ed portfolios investors can eliminate almost onehalf the riskiness of holding individual stocks Note it is not completely costless to diversify so even the largest institutional investors hold less than all stocks Even index funds generally hold a smaller portfolio which is highly correlated with an index such as the SampP 500 rather than hold all the stocks in the index The implication is clear investors should hold welldiversi ed portfolios of stocks rather than 39 J39 39J 39 stocks In fact individuals can hold diversi ed portfolios through mutual fund investments By doing so they can eliminate about half of the riskiness inherent in individual stocks Mini Case 4 18 Should portfolio effects impact the way investors think about the riskiness of individual stocks Answer Portfolio diversi cation does affect investors Views of risk A stock s standalone risk as measured by its 6 or CV may be important to an undiversi ed investor but it is not relevant to a welldiversi ed investor A rational riskaverse investor is more interested in the impact that the stock has on the riskiness of his or her portfolio than on the stock s standalone risk Standalone risk is composed of diversi able risk which can be eliminated by holding the stock in a welldiversi ed portfolio and the risk that remains is called market risk because it is present even when the entire market portfolio is held F N If you decided to hold a 1 stock portfolio and consequently were exposed to more risk than diversi ed investors could you expect to be compensated for all of your risk that is could you earn a risk premium on that part of your risk that you could have eliminated by diversifying Answer If you hold a onestock portfolio you will be exposed to a high degree of risk but you won t be compensated for it If the return were high enough to compensate you for your high risk it would be a bargain for more rational diversi ed investors They would start buying it and these buy orders would drive the price up and the return down Thus you simply could not nd stocks in the market with returns high enough to compensate you for the stock s diversi able risk How is market risk measured for individual securities How are beta coefficients calculated Answer Market risk which is relevant for stocks held in welldiversi ed portfolios is de ned as the contribution of a security to the overall riskiness of the portfolio It is measured by a stock s beta coef cient which measures the stock s volatility relative to the market Run a regression with returns on the stock in question plotted on the y axis and returns on the market portfolio plotted on the x axis The slope of the regression line which measures relative volatility is de ned as the stock s beta coef cient or b Mini Case 4 19 j Suppose you have the following historical returns for the stock market and for another company PQ Unlimited Explain how to calculate beta and use the historical stock returns to calculate the beta for PQU Interpret your results YEAR MARKET Pg 2U 1 257 400 2 80 150 3 110 150 4 150 350 5 325 100 6 137 300 7 400 420 8 100 100 9 108 250 10 13 1 250 Answer Betas are calculated as the slope of the characteristic line which is the regression line showing the relationship between a given stock and the general stock market O O O 20 6 WI 40 20 0 o O 20 40 O O 2 400 rpQu 083m 003 R2 036 Mini Case 4 20 Show the graph with the regression results Point out that the beta is the slope coeeficient which is 083 State that an average stock by de nition moves with the market Beta coefficients measure the relative volatility of a given stock relative to the stock market The average stock s beta is 10 Most stocks have betas in the range of 05 to 15 Theoretically betas can be negative but in the real world they are generally positive In practice 4 or 5 years of monthly data with 60 observations would generally be used Some analysts use 52 weeks of weekly data Point out that the r2 of 036 is slightly higher than the typical value of about 029 A portfolio would have an r2 greater than 09 k The expected rates of return and the beta coefficients of the alternatives as supplied by bamey smith s computer program are as follows Security Return 1 2 Risk Beta Alta Inds 174 129 Market 150 100 Am Foam 138 068 T Bills 80 000 Repo Men 17 086 1 Do the expected returns appear to be related to each alternative s market risk 2 Is it possible to choose among the alternatives 0n the basis of the information developed thus far Answer The expected returns are related to each altemative s market riskthat is the higher the altemative s rate of return the higher its beta Also note that tbills have 0 risk We do not yet have enough information to choose among the various alternatives We need to know the required rates of return on these alternatives and compare them with their expected returns Mini Case 4 21 l 1 Write out the security market line SML equation use it to calculate the required rate of return on each alternative and then graph the relationship between the expected and required rates of return Answer Here is the SML equation ri rf rm rrfbi If we use the tbill yield as a proxy for the riskfree rate then rRF 8 Further our estimate of rm A m is 15 Thus the required rates of return for the alternatives are as follows Alta Inds 8 15 8129 1703 m 170 Market 815 8100 150 Am Foam 8 15 8068 1276 m 128 TBills 8 15 8129 1703 m 170 Repo Men 8 15 8086 198 m 2 l N How do the expected rates of return compare with the required rates of return Answer We have the following relationships Expected Required Return Return SECURITY 2 g r CONDITION Alta Inds 174 170 Undervalued gt R Market 150 150 Fairly Valued Market Equilibrium Am Foam 138 128 Undervalued gt R TBills 80 80 Fairly Valued Repo Men 17 20 Overvalued R gt 2 Mini Case 4 22 SML ri ru R34 bi Required and Expected Ratwof 7 1 25 20 Alta Inds 15 Return 10 5 0 Repo Men 5 10 3 2 1 0 1 2 3 Beta Note the plot looks somewhat unusual in that the x axis extends to the left of zero We have a negative beta stock hence a required return that is less than the riskfree rate The tbills and market portfolio plot on the SML Alta Inds And Am Foam plot above it and Repo Men plots below it Thus the tbills and the market portfolio promise a fair return Alta Inds and Am Foam are good deals because they have expected returns above their required returns and Repo Men has an expected return below its required return Equot Does the fact that Repo Men has an expected return which is less than the t bill rate make any sense Answer Repo Men is an interesting stock Its negative beta indicates negative market risk including it in a portfolio of normal stocks will lower the portfolio s risk Therefore its required rate of return is below the riskfree rate Basically this means that Repo Men is a valuable security to rational welldiversified investors To see why consider this question would any rational investor ever make an investment which has a negative expected return The answer is yes just think of the purchase of a life or fire insurance policy The fire insurance policy has a negative expected return because of commissions and insurance company pro ts but businesses buy fire insurance because they pay off at a time when normal operations are in bad shape Life insurance is similarit has a high return when work income ceases A negative beta stock is conceptually similar to an insurance policy Mini Case 4 23 l 4 What would be the market risk and the required return of a 50 50 portfolio of Alta Inds and Repo Men Of Alta Inds and Am Foam Answer Note that the beta of a portfolio is simply the weighted average of the betas 0f the stocks in the portfolio Thus the beta of a portfolio with 50 percent Alta Inds and 50 percent Repo Men is bp Wibi 11 bp 05bAha 05bRepo 05129 05086 0215 rp rRF rM rRFbp 80 150 800215 80 70215 951 m 95 For a portfolio consisting of 50 Alta Inds plus 50 Am Foam the required return would be 149 bp 05129 05068 0985 rp 80 70985 149 Mini Case 4 24 m 1 Suppose investors raised their in ation expectations by 3 percentage points over current estimates as re ected in the 8 percent t bill rate What effect would higher in ation have on the SML and on the returns required on high and low risk securities Answer Required and Expected Rates of Return 40 7 35 7 Increased Risk Aversion 30 7 Increased Inflation 25 7 20 7 15 Original Situation 10 5 7 I I I I Beta 0 0 050 100 150 200 Here we have plotted the SML for betas ranging from 0 to 20 The base case SML is based on rRF 8 and rM 15 If in ation expectations increase by 3 percentage points with no change in risk aversion then the entire SML is shifted upward parallel to the base case SML by 3 percentage points Now rm ll rM 18 and all securities required returns rise by 3 percentage points Note that the market risk premium rm rRF remains at 7 percentage points m 2 Suppose instead that investors risk aversion increased enough to cause the market risk premium to increase by 3 percentage points in ation remains constant What effect would this have on the SML and on returns of high and low risk securities Answer When investors risk aversion increases the SML is rotated upward about the y intercept rRF rRF remains at 8 percent but now rM increases to 18 percent so the market risk premium increases to 10 percent The required rate of return will rise sharply on highrisk highbeta stocks but not much on lowbeta securities Mini Case 4 25 Optional question cover if time is available Financial managers are more concerned with investment decisions relating to real assets such as plant and equipment than with investments in nancial assets such as securities How does the analysis that we have gone through relate to real asset investment decisions especially corporate capital budgeting decisions Answer There is a great deal of similarity between your nancial asset decisions and a rm s capital budgeting decisions Here is the linkage l N E A company may be thought of as a portfolio of assets If the company diversi es its assets and especially if it invests in some projects that tend to do well when others are doing badly it can lower the variability of its returns Companies obtain their investment funds from investors who buy the rm s stocks and bonds When investors buy these securities they require a risk premium which is based on the company s risk as they investors see it Further since investors in general hold welldiversi ed portfolios of stocks and bonds the risk that is relevant to them is the security s market risk not its standalone risk Thus investors View the risk of the rm from a market risk perspective Therefore when a manager makes a decision to build a new plant the riskiness of the investment in the plant that is relevant to the rm s investors its owners is its market risk not its standalone risk Accordingly managers need to know how physical asset investment decisions affect their rm s beta coef cient A particular asset may look quite risky when viewed in isolation but if its returns are negatively correlated with returns on most other stocks the asset may really have low risk We will discuss all this in more detail in our capital budgeting discussions Mini Case 4 26

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