Management Engineering - Finance Lab + Corporate FInance

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Complete course

CHAPTER 1 INTRODUCION TO CORPORATE FINANCE CORPORATE INVESTMENT AND FINANCING DECISIONS The distinction between REAL assets (assets used to produce goods and services) and FINANCIAL assets (claims to the income generated by the firm’s real assets) is nece ssary to identify the main corporate decisions: INVESTMENT DECISIONS, also called capital budgeting , capital expenditure or capex decisions , involve the purchase of real assets. Particularly the decision concerns the investment i n tangible or intangible as sets. F=NANC=NG DEC=S=ONS involve the selling of the firm’s financial assets; shareholders, that are equity investors, contribute to equity financing. Financing can happen through debt or equity; this involves the CAPITAL STRUCT URE decision. ( Capital refe rs to the firm’s sources of long -term financing). WHAT IS A CORPORATION? A corporation is a legal entity characterized by • Separation of ownership and control • Legal personality • Limited liability • Indefinite duration • Freely transfe rable shares Different type s of corporations exist: public or private corporations, listed or not, limited liability corporations (LLC). Other forms of business organizations are sole proprietorships, partnerships, limited liability options ( limited liability refers to the fact tha t owners of the corporation are not personally liable with the corporation’s obligations). FLOW OF CASH BETWEEN FINANCIAL MARKETS AND FIRM’S OPERATIONS The flow of cash starts with an amount of cash provided by inve stors that invest in the financial marke ts, and so buy financial assets (bonds or shares) from issuing companies. The financial manager’s role is the one on an intermediary: he invests the cash raised in the financial market to finance the firm’s operation , making the firm grow and (hopefully) g enerating a positive cash flow through such operations. At this point cash can either be reinvested into the firm (retained earnings) or it can be distributed to the initial investors (in the form of dividends). THE FINANCIAL GOAL OF THE CORORATION Shareh olders want three things: 1. Maximize current wealth (current assets - current liabilities); 2. Transform wealth into the most desirable pattern of consumption; 3. To manage risks and characteristics of the chosen consumption plan. Profit maximization, that could seam as a goal of the shareholders, is instead a not well defined financial objective: • Which year’s profits? Shareholders will not welcome high profits in the short term that damage long term ones. • Companies may increase future profits by cutting a year’s dividend and reinvesting the cash into the firm Not in the company’s best interest if it earns less than the opportunity cost of capital. The investment trade off implies choosing a minimum acceptable rate of re turn on an investment (hurdle rate/cost of c apital). The opportunity cost of capital represents the return you are giving up -in similar risks circumstances - by investing in the project. For this reason the return on a project should always be grater than the opportunity cost of capital (otherwise i nvestors would invest in their own). AGENCY PROBLEMS As noted before, shareholders desire wealth maximization, but the corporation, and so its managers, must also consider the many stakeholders (people that hav e a stake (interest) in the corporation). Co nflicts of interest that might arise when managers act in their own interests rather than in the owners’ ones, are known as agency problems. Agency problems generate agency costs, that involve both costs incurred by preventing the rising of agency problems and the costs incurred to address the problems once that they have already occurred. Other than the relationship between managers and shareholders, also the role of stakeholders is worth mentioning: stakeholder s represent people that have a stake in the business. Should managers care about their many stakeholders’ interest? This argument is much discussed in corporate governance matters; corporate governance aims at aligning shareholders and stakeholders’ intere sts, by providing laws, regulations and inst itutions that protect corporate practices. CHAPTER 2 HOW TO CALCULATE PRESENT VALUES FUTURE VALUES AND PRESENT VALUES The future value is the amount of money to which an investment will grow after earning int erest, the future value of $100 dollars at year t, after earning r of interest is: FV= $100 (1+r) t The present value represents the value today of a future cash flow at t=1: PV= discount factor x C 1 Discount factor= 1/(1+r) t Discount factors can be used to compute the present value of any cash flows. The present value formula has many applications: given any variables in the formula, you can solve for the remaining one. VALUING AN INVESTMENT OPPORTUNITY Step 1: forecast cash flows C1, C 2, … , C t Step 2: estimate opportunity cost of capital Cost of Capital = r Step 3: discount future cash flows PV = C 1/ (1+r) Step 4: go ahead if NPV is greater (or equal) to 0 NPV = PV – required investment = C 0 + C 1/(1+r) Net present value rule : accept investments only when the NPV is positive . Rate of retur n rule : accept investments that offer a return in excess to the opportunity cost of capital. The discounted cash flow formula for t > 1 (DCF) is the following: PV = C / (1+r) + … + C t / (1+r) t NPV = C 0 + PV Sometimes there are shortcuts that make it ver y easy to calculate the NPV of an asset that pays - off in different periods. Shortcuts: Perpetuities: financial concept according to which cash is theoretically received forever. Return = cash flow / present value r = C / PV PV of cash flow = cash flow / d iscount rate PV = C / r Annuities: an asset that pays a fixed amount each year for a fixed number of years PV ANNUITY = C x PVAF = C x [(1 / r) – 1 / r(1+r) t] FV ANNUITY = C x [((1+r) t – 1 ) / r] Annuity due: level stream of cash flows starting immediately PV ANNUITY DUE = PV ANNUITY x (1+r) FV ANNUITY DUE = FV ANNUITY x (1+r) Growing Perpetuities: PV 0 = C 1 / (r -g) HOW INTEREST IS PAID AND QUOTED Annual Percentage Rate (APR): interest rate that is annualized using simple interest APR = MR x 12 Effective Annual Percentage Rate (EAR): interest rate that is annualized using compound interest EAR = (1+MR) 12 – 1 CHAPTER 3 VALUING BONDS DEBT AND EQUITY Bonds and stock are financial claims brought by i nvestors, also called debt and equity , respectively. Buyin g a stock is the equivalent of becoming an owner, while buying a bond is the equivalent of becoming a creditor (lending money). The key differences between debt and equity are that the former has a senior claim to company’s income and assets, although bon dholders have no voice in management and the bond expires at a maturity date. The latter instead provides for a voice in management, generally proportional to the amount if shares owned, it has no maturity date but claims in income and assets are subordina te to debt. BOND TERMINOLOGY BOND : (fixed income security) financial claim that obligates the issuer to make specified payments at fixed dates to the bondholder. FACE VALUE: (par value or prin cipal) payment at maturity of the bond. COUPON: the interest p ayment made to the bondholder. COUPON RATE: annual interest payment, as a percentage of face value. Bond issuers are corporations, commercial banks, government, municipalities and so on… Short -term government bonds (bonds that have a maturity date within 1 year from issuance) are called bills (e.g. US Treasury bills, Italian BOTs). These bonds are also called zero coupon bonds since they make no interest payments. Long -term government bonds of ten do carry coupons (Italian BTP, Bunds in Germany). VALUING A BOND The price of a bond equals the present value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return r (rate of return offered by similarly risky bonds) PV = CPN/(1+r) 1 + … + (CPN + FV)/ (1+r )t The value of a bond can also be thought of as an annuity of T years + final payment: PV = CPN [(1/r) – (1/r(1+r) t)] + FV/(1+r) t The value of a bond is inversely related to change s in the investor’s current required rate of return: as interest rates increase the value (price) of the bond decreases (and vice versa) . Given the price of a bond, what is the rate of return if an investor keeps the bond until maturity? We need to find th e variable y that solves: P = CPN/ (1+ y)1 + … + CPN+FV/ (1+ y)t The rate of return y is called yield to maturity (YTM) or just “yield”. The YTM is the discount rate r that sets the present value of the promised bond payments equal to the current market price of the bond. YTM is the annual rate of return if the investor pays i nitial price P 0 for the bond and keeps it until maturity. The YTM is also called the IRR (internal rate of return). Bonds are traded by a network of dealers. Unlike publicly traded stock, there is no central place or exchange for bond trading. The bond mar ket is an OTC, over the counter. The asked price is the price you need to pay the bond to a dealer. The yield is reported as the annual rate. PRICE vs FACE VALUE A bond can be priced above, equal or below face value. 1. A bond that is priced above face val ue in said to sell at a premium . Investors face a capital loss over the life of the bond. 2. A bond that is priced below face value is said to sell at a discount . Investors fac e a capital gain over the life of the bond. 3. A bond that is priced equal to its fa ce value is said to sell at par . The immediate current yield on the investment is Current yield = CPN/P 0 The tradeoff between coupon rate and yield to maturity signals wh ether there will be a capital loss or gain over the life of the bond. 1. If the coup on rate is grater than the yield to maturity, the bond will be sold at a premium: CPN > YTM : P 0 > FV 2. If the coupon rate is smaller than the yield to maturity, the bond will be sold at a discount: CPN < YTM : P 0 < FV 3. If the coupon rate equals the yield to maturity, the bond will be sold at par: CPN = YTM : P 0 = FV SHORT vs LONG TERM INTEREST RATES Generally short -term interest rates are different from long -term interest rates, so it is not appropriate to discount all cash flows by the same rate. The relat ionship between short -term and long -term interest rates is called the term structure of interest rates. To understand the term structure we introduce zero coupon bonds (bonds that do not make interest payments: treasury bills with maturity of one year), ac cording to which the only cash flow that the investor receives is the final face value payment. Obviously, the price of the zero coupon bond will be smaller than the face value of the bond, since investors need to be compensated for the time value of money . The YTM of a zero coupon bond is denoted as r1 and it is called the one year spot (interest) rate . By the law of one price : in competitive markets all one year risk free spot rates must equal r 1. In general the price of a one year strip is given by: P0 = FV/(1+r 1) In words: for every dollar you put in one year bonds, you will earn (1+r 1) dollars next year. Consider a strip maturing in N years, the price of th at strip is: P0 = FV/(1+r N)N Where r N is the N -year spot rate, that is the per period (annual) rate of return for holding the bond from today until date N rN = (FV/P 0)1/N -1 By observing the prices of strips with different maturities, one can compute r 1, r2, … , r N. The list of spot rates traces out the term structure of interest rates. A yield cu rve is a curve that plots the spot rates of strips with different maturities. Knowing r 1, … , r N and the cash flows at t=1, … , t= N, one can compute the presen t value (PV=P 0). Knowing the current price one can compute the YTM. What explains the upwards s loping term structure? If interest rates are expected to be stable over time, the term structure would be flat and investors are indifferent between buying among different strips (two one -year strips = one two - year strip). If investors expect higher future interest rates (at t=1 r 1 increases), they would be better off by investing at t at such rate, and demand for other two, three… years bonds (with lower interest rates) would decrease, and thus the interest rates would increase until a certain level accord ing to which investors will be indifferent between investing in one, two, three etc.. year bonds. If an upward sloping term structure is presented, it means tha t interest rates are expected to increase . If a flat yield curve is presented, then the market expects stable interest rates. REAL AND NOMINAL RATE OFINTEREST Real cash flow at t = (nominal cash flow at t) / (1+inflation) t Nominal rate of return = [(nominal cash at t=1) / (investment at t=0)] - 1 Real rate of return = [(real cash at t=1) / (inv estment at t=0)] – 1 =n the presence of inflation, an investor’s real interest rate is always less than an investor’s nominal interest rate 1 + real rate = (1 + nominal rate) / (1 + inflation rate) rnominal = r real + i + (r real )(i) Given that the prod uct is very small, one can write rreal = r nominal – i The real interest rate is approximately equal to the nominal interest rate minus expected inflation rate. DEFAULT RISK Default (or credit ) risk is the risk that a bond issuer won’t be able to repay the interest and principal payments to the bondholder. Default premium is the additional yield on a bond that investors require for taking the credit risk. =nvestment grade: bonds that are rated Baa or above (by Moody’s) or BBB or above (by Standard’s an d Poor’s) Junk bonds are bonds rated below Baa or BBB. Moody’s Standard & Poor Safety Aaa AAA Strongest rating Aa AA Very strong likelihood of repayment A A Strong ability to repay Baa BBB Adequate capacity to repay Ba BB Considerable uncertainty of ability to repay B B Questionable ability to repay Caa CCC Danger of imminent default Ca CC Default occurring C C Little prospect of interest to ever be repaid BOND PRICES AND INTEREST RATES Interest rates on bonds are quite volatile, and this impl ies also price changes: Bond prices and interest rates move in opposite direction. Bond prices are subject to (1) the passing of time and (2) unpredictable changes of interest rates. 1. The passing of time: Zero coupon bonds tend to converge to the FV as tim e gets close to maturity. If the yield to maturity doesn’t change, the return on the investment equals the yield to maturity even if y ou sell the bond early. 2. Changes of the interest rates: Bond prices also change due to unpredictable changes in the inter est rates. If you buy a bond and sell it before maturity, the rate of return on your investment depends on the market conditions at th e selling time t inf, PV = 0 In practice, r is noisy and future dividends are hard to predict Suppose dividends are expected to grow at a constant (stable) rate g forever (g mkt cap (r) , positive NPV ) W hen ROE = mk t cap. rate , the sh are has the same price as in a no growth policy , th us the firm ’s investment will make no contribution to the firm value. The PVGO captures a ll the NPVs ge nerated by the additional investments at time t. VALUING A BUSINESS The balance sheet lists the firm ’s ass ets and liabilities • assets: inventory, propert y, plant , equipment and other investments the company has made ; • liabilities: current liabilities / noncurrent liabiliti es, they represent firms ’ obligations to creditors • stockholder ’s equit y: difference betwee n firm ’s assets and li abilities (accounting measure of the firm ’s net worth). ASSETS = LIABILITIES + STOCKHOLDERS ’ EQUITY The book value o f equity if a valid assessment of the true value of e quity M arket value of equity = share s outstanding x market price per share ENTERPRISE VALUE = MARKET VALUE OF EQUITY + DEBT The enterprise value is what i t would cost to buy all the firm ’s equity and pay off its debts ; it give s us the value of the underlying business assets, unencumbered b y debt. To estimate the value of the firm ’s equity , we computed the present value of the firm ’s total payouts to equity holders ( dividends ). To estimate a firm ’s enterpri se value , we compute the present value of th e free cash flow to th e firm (FCF) , that the firm has available to pay all investors, both debt and equity holders. Free Cash Flo ws ( FCF ) is the amount of cash that the firm can pay to investors after paying all investments necessary for growth. The value of an enterprise (or pr oject ) is usuall y computed as the discounted value of the free cash flows ( FCF ) out to a valuation horizon (H) plus the present value of the business at H . the horizon value is sometimes called the terminal value : PV = [FCF 1 / ( 1+r )1] + [FCF 2 / (1+r )2] + … + [FCF H / ( 1+r )H] + [PV H / ( 1+r )H] The method of comparable s offer s an alte rnative way of valuing a business. Rather than valuing the cash flow of a business directly , we estimate t he value of the firm based on the value of other co mparable firms or investments. CHA PTER 5 NET PRESENT VALUE A ND OTHER INVESTMENT CRITERIA Three point s to remember about NPV: 1. a dollar today is wo rth more than a dolla r tomorrow ; 2. net pres ent value depend s solely on the forecasted cash flows and the opportunity cost of capital ; 3. because all p resent values are measured in present dollars, you can add them up NPV ( A + B ) = NPV (A) + NPV ( B) Book rate of return : ave rage income divided by average book value over the project ’s life. Also called the accounting rate of return Book rate of return = book income / book assets M anagers rarely use this measurement to make decision s: the components reflect taxes and accounting figures , not market value s or cash flows. The payback period of a project is the number of years it takes before the c umulative f orecasted cash flow equals the initial outlay; the payback rule says to only accept projects that “pay ba ck ” in the desired time frame. This method is flawed , primarily because it ignores later years cash flows and the present value of future cash flows. Discounted Pa yback: how many years does it take for the pro ject for it to make sense in term s of NPV? INTERNAL OR DISCOUN TED RATE OF RETU RN • internal rate of return (IRR ) • discount rate at which NPV = 0 • internal ra te of return rule • invest in any project tha t offers a r ate of return higher than the opportuni ty cost of capital Rate of Return = (payoff / inv estment) -1 PITFALLS Pit fall 1 : lending o r borrowing? W ith some cash flows , the NPV of the project increases as the discount rate increases . This is con trary to the normal relationship betwee n NPV and discou nt rates. Pitfall 2: multiple rates of retu rn Certain cash flows generat e NPV = 0 at more tha n one discount rate. It is also possib le to have a zero IRR and a positive NP V. Pitfall 3: mu tually ex clu sive projects IRR som etimes ignores the magnitude of the project . (hig her IRR for one project but higher NPV for the other), how do we overcome such problem? W e look at the IRR of the incremental cash flow s: 1. look at the smallest project in terms of NPV . Is the IRR > opportunity cost of capital? o Yes : project is acceptable. o No: project is unaccep table. 2. If the answer is YES, we must ask whether i t is wo rth to make the additional investment , so we calculate the NPV and IRR of the incremental cash flows (diff erence). If the resulting IRR : o IRR > opportunity cost of capital , invest the additional money . o IRR < opportunity cost of capital , invest only in the first project. Pitfall 4: what happens when there is m ore than one opportunity cost of capital? Term struc ture as sumption : we assume discount rate are sta ble over the term of the proj ect. This assumption implies that all funds are reinvested at the IRR . This is a fals e assumption. CHOOS ING CAPITAL INVESTMENTS WHEN RESOURCES ARE LIMITED • Capital Rationing o Lim it set on the funds available for the investment • Soft Rationing o Limit set on avai lable funds imposed by management • Hard Rationing o Limits imposed on availa ble funds by t he unavailability of fun ds in the ca pit al mar ket W hen resources are limited , the profi tability index PI provides a tool for selecting among various combin ations and alternatives. A set of limited projects can yield var ious com binations . The highest weighted average PI can indicate which projects to select. Profitability Index = PI = NPV / investment CHAPTER 6 MAKING INVESTMENT DECISIONS WITH THE NPV RULE Rule 1: discount cash flow s, not profits o Capital expenses o Record capital expenditures when they occur o To determine cash flow s from income add back depreciation and subtract capital expenditure o W orking capital o Difference between the company ’s short term assets and liabilities Rule 2: discount incremental cash flows o Include all incidental effects o Do not confuse average with incremental payoffs o Forecast product s ales today but also recognize after sales cash flows o Include opportunity costs o Forget sunk costs o Beware of a llocated o verhead costs o Reme mber sa vage value Rule 3: treat inflation consistently Be co nsistent with how you treat inflation: o Use nominal int erest rate s to discount nominal cash flows o Use real interest rates to discount real cash flows You will get the same results, whet her you use nominal or real figures. Real Discount Rate = [(1 + nominal discount rate ) / (1 + inflation rate )] – 1 Rule 4: se parate financing and investment decision s Suppose you finance a project partly with debt. How should you treat the proceeds from th e debt issue and the interest and princ ipal payments on the debt/ You should neither sub tract the debt p roceed s from the re quired investment nor recognize the principal and interest payments in the debt as cash outflows . Rule 5: remembe r to deduct taxes Cash flows should be estimated on after tax basis : sub tract cash outflows for taxes from pre tax cashflows and discount net amount. Be careful to sub tract cash taxes. Cash taxes are generally different from taxes reported on the income statement. THE THREE ELEMENTS OF A PROJECT ’S CASH FLOW Total cash flow = cash flow from capital investment + operating cash flow + cash flow from changes in working c apital o Capital investment : up front investment in plant, equipment , research and other startup costs . o Operating cash flow: net increase in sales revenue from the ne w project, less outlays. o Investment in working ca pital: represents a negat ive cash flow. Problem 1: THE INVESTMENT TIMING DECISION Some projects are more valuable if undertaken in the future : o Examine start dates ( t) for investments and calculate the net fu ture value for each date. o Discount net values bac k to the presen t Problem 2: CHOICE BETWEEN SHORT - AND LONG -LIVED EQUIPMENT Equi valent annual cash flo w: the cash flow per period with the sam e present value as the actual cash flow of the project. Equivalent annual cost ( annuity ) = PV of cash flow / annuity factor Pro blem 3: WHEN TO REPLACE AN OLD MACHINE In practice , the p oint at which to replace an old machine reflects econ omics, not physical collapse. Probl em 4: COST OF EXCESS CAPACITY Any firm with a centralized information system encounters many proposals for us ing it. Pare nthesis on accelerated depreciation Depreciation is a noncash expense : it is important only be ca use it reduces taxable income. It provides an annual tax shield equ al to the pro du ct of depreciation and marginal tax rate: ANNUAL TAX SHIELD = depreciation x tax rate CHAPTER 7 INTRODUCTION TO RISK AND RETURN EXPECTED RETURN AND RISK Given the probability distribution of returns, on e can compute the exp ected return by computing the weighted average of th e possible returns , where the w eighs correspond to probabilities. E(r) = p1r1 + p 2r2 + … + pNrN Where the sum p 1 + … + p N = 1 Two common me asures of the risk and probab ility distribution are its variance and standard deviation. o The variance is the expected squared deviation from its m ean . The variance is a measure of how spread out the distribution of th e return is. VAR (r) = E( (r – E (r) )2) VAR (r) = p 1 (r – E(r))2 + … + p N (r – E(r))2 o If the retu rn is risk free, and so never devi ates from its mean, then the var iance is equa l to zero ; o Other wi se, the v ariance incr eases w ith the deviations from the mean , so as r isk increases. o The stand ard deviation is the square root of the variance In general, investors are risk adverse : they would not choose to hold a port folio that is more volatile (risky) unless they expected to be compensa ted through a hi gher rate of return. PORTOFOLIO RISK Consider a port folio made of two stocks, in whi ch x 1 represents the proportion of stock 1 in the portfolio , and x2 = 1 – x1 the prop ortion of stock 2; then the expected port folio retu rn is Exp ected port folio return = x 1 E(r1) + x 2 E(r 2) The ex pected port folio return is simply a weighted average of the expected returns on individual stocks. In gen al the standard deviation of a portf olio is NOT a simple w eighted average of the standard deviations of e ach stock. The variance of a p ortfolio is : Variance of portfolio = x 12 VAR (r1) + x 22 VAR (r2) + 2 x 1 x2 Cov (r1 , r2) o Covariance describes how the two varia bles are related : it is the expected product of th e deviation s of two returns from their means Cov (r1 , r2) = E [( r 1 – E(r1)) (r 2 – E(r2))] Cov = sd 1 x sd 2 x co rr(1,2 ) o Variables are positively related (Cov > 0) , if they move in the same direction : the returns will tend to move above or below average at the same time ; o Variables are negatively re lated (Cov < 0) , if they move in opposite direction : the returns will tend to move one abov e and the other below the average at the same time ; o Corre lation between two stocks has the same sign as the covariance , so it has similar interpretation Corr (r1 , r2) = Co v(r1 , r2) / (sd (r1) x sd (r 2)) Correl ation is always between -1 and 1 o W hen corr > 1 , the gain from diversification decreases; o W hen co rr < 1 , the gain from diversification i ncreases ; o W hen corr = 1, portf olio does no t reduce risk: standard deviation is just an average of the two standard deviations ; Diversification is a strategy designed to reduce risk by spreading th e port folio among many investmen ts. The risk of holdi ng a stock is that dividends and f ina l stock pri ce may be higher or lower than expected, which makes the re alized return risky. W here does the reduced ri sk come from? Stock prices and dividends fluctu ate d ue t o: 1. Firm specific news : good or bad new s about the company itself . Stock flu ctuations due to fir m specific news are called independent risks . These are unre lat ed across stocks. This risk is calle d firm -specific , idiosyncratic, unique or diver sifiable risk . This risk can be eliminated through diversification . 2. M arket wide news: about the economy as a w hole . Stock fluct uations due to m arket wide new s re present common risk . All stocks are affected simultaneously . This type of risk is called systematic, und iversifi able or market risk. This risk cannot be eliminate d through diversification . When evaluating the risk of a stock , an investor will care about systema tic ( market) risk since it cannot be eliminated through diversification. One must determine how much of the var iability of the stock ’s return is due to systemati c versus firm specific risk. To determi ne how much a stock is sensible to systematic risk , we can look at the average change in its return for each 1% change in the return of a port folio that fluctu ates solely due to systematic risk. Thus the first ste p is to find a port folio that co ntains on ly the systematic risk: since diversification improves with the number of stocks held into the port folio, a natural candidate is the mkt portfolio of all securities traded in the capital markets. (it is common practice to use the S&P 500 por tfolio as an appr oximation of the market portfolio). Changes in the value of the market portfolio represent systematic shocks t o the economy. W e can measure the systematic risk of a security by calculatin g the sensitivity of the secu rity ’s return to the return of the marke t port folio. This measure is known as beta. ➢ Beta : sen sit ivity of a stock ’s return to t he retu rn on the market portfolio . It is the expected % change in the stock ’s return given a 1% change in the return of the market portfolio. o Key point: the contribution of a stock to the risk o f a well diversified portfolio , is not the standard deviation, but its market risk (how sensitive it is to the market risk): i ts beta. Stock s in cyclical industries are more sen sitive to syste matic risk and so have betas > 1; stocks of non cyclical firm s tend to have betas < 1. Utili ties tend to be stable and highly regulated, and thus are ins ensitive to market fluctuations in the overall market . Drug and food companies are also very insen sitive. Technology corporations tend to have very high betas . Gold has had in so me periods, negative betas. The beta of as asset Bi = Cov( ri , rm) / Var ( rm) Contribution of stock i to market port folio is increasin g with th e covariance of that stock to the market portfolio. CHAPTER 8 PORTOFOLIO THEORY AND TH E CAPITAL ASSET PR ICING MODEL Consider a por tfolio made of two stocks , x 1is the proportion of stock 1 in the port folio and 1 – x1 is the proportion of s tock 2. The beta of the portfolio is the weighted average beta of th e s ecurities in the portf olio B portfolio = B1 (x1) + B 2 ( 1 – x1) M arkowit z Portfolio theory: c ombining stocks into portfolios can reduce standard deviation, below the level obtained from a simple weighted average calculation. Cor relation coefficients make this possible . Pas t rates of returns on stoc ks confo rm fairly closely to a standard normal distributi on. Normal distribut ions can be completely defined by two numbers: expected return and standard deviation. W e assume standard deviation and expected returns are two measures investors c are about. Investors seek high returns and low volatility. o A port folio in inefficient whenever it is possible to find another port folio that is better in terms of both volatility and expected return . o If we remove the in efficient ones, what remain s is a set of efficient portfolios. Portfolios in an efficient set offer highe st rates of return given any level of risk. We cannot easi ly rank efficient portfolios since investors will choose among them according to their risk / return preferences . RISK FREE SAVING AND BORROWING Thu s far we have combined risky investments into portfolios . By includin g all risky investments in the efficient fro ntier, we can achieve ma ximum diversification. There is another way be sides diversification to reduce risk: we can keep some of our money safe, in a no risk investment. Of course, this will reduce our expected return. Conversely, if we are a n aggressive investor, we m ight decide to borrow money and invest it all in the stock maket. Len ding and borrowing extend the range of investment poss ibilities. • If you invest in a port fol io P and lend or borrow at a risk free in terest rate r f, you can achieve any point along the straight line from r f through P Borrowing money to invest in stocks is called using leve rage . You are buying a lever ed portfolio. TANGENT PORTFOLIO To earn the highe st possible ex pected return for any level of vola tility we must find the portfolio that generate s the steepest possible line when combined with the risk free investment. Start on the ver tical axis a t rf and draw the steepest line you can to the curved line of efficient portfolios . That line will be tan gent to the efficient frontier. The efficient portfolio at that tangenc y point will be be st a mong a ll the others. SHARPE RATIO The Sharpe ratio measure the ratio of reward to vola tility provided by the portfolio . It coincides with the slope of the line through a given portfolio . The best among efficient portfolio is the tangent portfolio , that being the portfolio th at provides for the highest Sharpe ratio Sharpe ratio = (rp – rf) / sd p Investors have homoge neous expectations regarding volatilities, correlations and expected return s of securit ies. Then each investor will identify the same portfolio as having the h ighest Sharpe ratio in the e conom y. Thus , all investors will demand th e same portfolio of risky securities . Therefore : the efficient , tangent portfolio o f risky securities must equal the market portfolio. Accor ding to the CAPM all inve stors should choose a portfolio on the tan gent line : every investor should invest in the tangent portfolio independently of their risk prefere nces. Prefer ences will determine only how much the investor is going to invest in the risk free vs tangent portfoli o invest ment. To sum up: it is a two stag ed job 1. The best portfolio of commo n s tocks m ust be selected ; 2. This portfolio must be blended with borrowing or lending to obtain an exposure to risk that suits the investor ’s preferences. THE RELATIONSHIP BETWEEN RISK AND RETURN • Treasury bills (risk free investments ) have a be ta = 0, since their return is fixed (unaffected by the market changes) • The market portfolio has a beta = 1 The difference between the return on the market and the return on the risk free investment is termed as the market risk premium. Since 1900 market risk premium has averaged 7. 7% . The market risk premium reflects investor s’ tolerance an d deter mines the market price of risk in th e economy: the reward forholding a portf olio with a beta of 1. CAPITAL ASSET PRICING MODEL W hat is the expected risk premium when b eta is not 0 or 1? The Capital Asset Pricing Model, or CAPM states that in a competitive market , the expected risk premium varies in direct proportion to beta. All investments must plot along the securities m arket line , that being the sloping line that connects rf to market portfolio on a graph of (beta ; retu rn) r = r f + B(r m – rf) in a compet itive market, the ris k premium varies in proportion to beta r – rf = B(r m – rf) Security M arket L ine Equilibrium : in equilibrium no stock can lie below the secu rity market line . ALTERNATIV E TO CAPM Return = a + b 1(rfactor 1) + b 2(rfactor 2 ) + … + noise Expected risk prem ium = r – rf = b 1(rfactor 1 – rf) +… Three factor model: 1. identify a relatively short list of factors that could affect stock return s 2. estimate th e expected risk premium on each of those factors (r factor1 – rf) ecc 3. measure t he sensitivity of each stoc k to t he factors (b 1, b 2, ecc) CHAPTER 9 RISK AND THE COST OF CAPITAL A firm ’s value can be stated as the sum of its va rious assets. The value additivity principle Firm value = PV (A+B) = PV (A) + P V (B) The firm ’s cost of capit al is the correct discount rate in re lation to th e beta . rassets = COC = r deb t (D / V ) + requity (E / V) E, D, V are market values of equity, debt and t otal firm value. rdebt = YTM on bonds requity = r f + B( rm - rf) After Tax Weighted Average Cost of Capital WACC is the traditional view of capital structure, risk and return WACC = (1 – Tc)rD (D/ V) + r E(E/V) The capital structure is the mix of debt and e quity financing of a co mpany. Exp and CAPM to include the capital structure of the company requity = r f + B( rm – rf) the SML , security market l ine, shows the relationship between return and risk. CAPM uses beta as a proxy of risk. Other method s can be employe d to determine the slope of the SML (and thus, beta). The company co st of capital COC , is based on the ave rage beta of the assets (based on the % of the funds in each asset): BASSETS = B DEBTS (D/V ) + B EQUITY (E/V) CHAPTER 13 EF FICIE NT MARKETS AND BEHAVI ORAL FINANCE The movement of stock prices every day does not reflect any pattern : statistically spea king, it is random. EFFICIENT MARKET THEORY • W eak for m efficiency : market prices reflect all historical inf ormation • Semi -strong efficiency : market prices reflect all pub licly available information • Strong efficiency: market prices reflect all information, both public and private Fundamental analyst Research the values of stocks using NPV and other measu rement s of cash flows Adjusted stock return = return on stock – retu rn on market index Expected stock return = a + B x return on mar ket index Expected stock return = ac tu al stock return – expected stock return = r – (a – B(rm)) BEHAVIORAL FINANCE • Attitu de towards risk • Belief about probabilities , sentiment • Limits to arbitrage • Incentive problem s and financial crisis of 2009 THE FIVE LESSONS OF MARKET EFFICIENCY 1. M arkets have no memory (markets have memory ) 2. Trust market prices (do not trust market prices) 3. Read th e entrails (?!?) 4. The do it yourself alternative (IS RISKY! ) 5. Seen one stock, seen them all (NO WAY! )