VIEWS: 101 PAGES: 28 CATEGORY: Business POSTED ON: 1/20/2011 Public Domain
Chapter 4: NPV 1. Cash Flow: why focus on it? A. Cash: its our objective, it is what it is, no dispute (unlike financial statement). B. Useful: can buy car w/ net income: tells us how much availible for future. C. Final measurement: Cash outflow - cash inflow: but not be all end all measure. D. In any e.g. may want to say we assume cash flow after taxes. 2. NPV: difference b/w promised cash flow and investment value. A. Payment = time + risk. 1) These are 3 parts of cash flow. B. Risk: degree to which cash flow uncertain. C. PV = FV/ (1 + r) to N power where N is # of period. D. NPV = -(cost) + PV E. FV = PV * (1 + r) to N power. F. Simple r vs. compound r. 1) Compound r: note what compounding period is (Mo., year, etc.) G. Continuous compounding: FV = PV (e to the rN) 1) We use continuous compounding b/c in real world, financial markets are open 24/7 so can always get interest. H. PV = FV/ (e to the rN) I. Limits? Ignores options AKA what havn‟t yet decided to do. 3. Taxes: the later you pay, the less you pay, greater NPV. A. e.g. put 15Gs in pension at 10% after 30% tax rate. After 30yrs = 79.9 Gs. 1) Do 7% r, 30 N, 10,500 PV and hit FV. B. e.g. put 15Gs in pension at 10% before taxes. After 30 years = 261Gs but then pay 30% tax and get 182Gs which is still more than 79.9Gs. C. If putting $$ in pension every year, use PMT instead of PV in above equation. 4. Annuity: values a payment 1 period before its made. A. If annuity payment made at end of year leave calculator alone but if at beginning, must hit blue(g) and #7 to calculate from beginning of year. Blue(g) and #8 gets you back to using end of year. 1) Annuity in advance: annuity assumes payment in arrears, at end of 1st period, but what if its at beginning? E.g. 20 year lotto at 50Gs/ year at 8%. A) Then formula is: payment at date zero (50Gs) + N 19, r 8%, PMT 50G, hit PV and we get, 480G + 50G = 530Gs; OR B) Blue (g) #7, then 20 N, 8% r, 50G PMT and hit PV. B. Pension same as level payment loan except flipped over, it becomes how much you must pay per year to pay off, not how much per year you get under pension. 1) Also same as structured settlement. 2) e.g. 10 years, 10G per month assume 6% rate (so put 10G PMT, 120 N and .5 r and PV is only 900Gs not 1.2 million. 3) How much get in annual pension if have 991Gs (PV) in pension, 7% r, 20 year life expectancy, then hit PMT and get: 93.5Gs. C. e.g. Win 40 mil in lotto: get 1 mil per year and 20 mil at year 21. 1) 1st: PV of 20 mil in 21 years: use 7% rate and value only about 5 mil. 1 2) 2nd: PV of stream: 1 mil PMT, 20 N, 7% r and PV only about 10.5 mil. 3) Any stream can be broken up and still has same value. D. What need for comperable salary in future after inflation? 1) Assume inflation is 3% (r), salary is 90Gs (PV) and 30 years (N) from now need (hit FV) 218Gs to have comperable salary. 2) What is 90Gs today worth 30 years ago assuming same rate? A) Same as above but 90Gs is FV and hit PV: 37Gs. E. To find what annual rate of increase in tuition: 1250 PV (old tuition) 25Gs FV (today), 35 years (N), and hit r: get 8.94%. NOTE: either PV or FV must be entered in the negative. F. Delayed annuities: e.g. will get $500 annuity for 4 years starting in year 6. 1) 1st: get PV of annuity: PMT 500, N is 4, assume r is 10%. PV is 1585. 2) 2nd: discount back PV (NOTE: use N 5 not N 6 b/c we value annuity as of one period before 1st payment so we value from year 5 not 6.) A) FV is 1585, 10% r, 5 N, PV is $984. G. Infrequent annuity: get $450 every 2 years, over 20 years (N is 10) w/ r at 6%. 1) 1st: Find r per period or r over 2 years. (1.06 * 1.06 - 1) = 12.36%. 2) 2nd: $450 PMT, N is 10, r is %12.36 and hit PV and get $2505 H. Equating PV of 2 annuities: need to pay 30G per year at age 18 of son in college. So need to deposit enough so can w/draw 30G per year in years 18 - 22. We assume r is 14%. 1) 1st: PV of 4 years college. 4 N, 14% r, 30G PMT, hit PV and get 87Gs. A) This is PV at date 17. nd 2) 2 : PV of college at date zero: 14% r, N is 17, FV is 87G hit PV and get 9.4Gs. 3) 3rd: PV of 17 deposits must = 9.4Gs so 9400 is PV, 14% r, 17 N, and hit PMT and get $1475 per year. I. Growing annuity: can‟t do on calculator: 1) Formula = PV = Payment {1/r - g -- 1/r - g * (1+g/1+r) to the N} A) If PMT 50Gs, g is 9%, r is 20% and N is 40 you get 447,787. 5. Effective annual interest rate: when compounded more than per year, the stated r is less than the effective r. A. e.g. if get 24% r but r paid per month, then PV is 1, r is 2, N is 12 and hit FV. Get 1.2682 so effective r is 26.82%. 6. Perpetuity: constant steam of cash flows w/o end. A. British Consols: PV = payment/ r. 1) e.g. payment is 100$ per year where r is 8%, value of consol is 1250. 2) If r falls to 6% then value is $1667, so if interest rates in UK drop, then value of consols rises. 3) Consol assumes 1st payment is one year from purchases so if get yearly stream of 2420$ 3 years from now, its worth 20Gs if r is 10% b/c must discount back 2, not 3, periods to get PV of payment. B. Growing perpetuities: PV = payment/ r - growth rate: don‟t need to know. 7. Valuing a firm: add up the PV of the individual net cash flows. A. NPV of firm is PV - cost. 2 Chapter 5: Valuing stocks and bonds. 1. Bonds. A. Discount bond or zero coupon: enter face value of bond 1 mil (FV), (r) 10%, 20 years (N), and hit PV, that price of bond, 148.6Gs. If r drops, value of bond increases. 1) Why would C issue zero coupon bond? A) Cash flow: no payments until maturity date, good for C not expecting cash flow for several years. 2) Why would X lend on zero coupon basis? A) Taxes: don‟t pay taxes on interest until end of term. 3) Has term risk but that is compensated for in r. B. Level coupon bond: 2 factors: discounted PV of face + interest. 1) 10 year bond, semiannual payments, 8% r, $1000 face. A) 1st: PV of $1000: 1000 FV, 4% r, 20 N, hit PV and get $456. B) 2nd: PV of semiannual $40: $40 PMT, 4% r, 20 N and hit PV and get $543. C) The add the two and get PV of bond is its face price. OR D) Input all at once and calculator adds it for you. 2) If market r different from bond, use market r for r and bond r to get PMT. So if above bond issued in 10% r market its value drops to $875 and sells at discount. If market r is below bond r, then sells at premium. 3) Thus, risk free government bond has risk that market r increases and value of bond goes down. No change in PMT but its opportunity cost. A) Thus, risk free doesn‟t mean you get expected value of investment. B) Note: in inflation adjusted bonds, PMT changes. C. Consols: see above, chapter 4: Cash cow stock valued same as consol. D. Bonds are similar to loans. 1) If market r is low, banks lend for short term to decrease their risk that inflation pushes up r and value of loan (to them) decreases. 2) Loan may be floating rate that moves w/ market r or other criteria. 3) How much is monthly PMT for 120G loan, paid over 5 years at 17% r? A) 120G PV, 60 N, 1.42% r, and hit PMT and get $2985. Chapter 6: Alternate Investment Rules 1. NPV. A. Benefits: 1) NPV uses cash flows and not earnings. (see merits of cash flow above). 2) NPV uses all cash flows of project, doesn‟t set artificial cut off date. 3) NPV discounts cash flow properly, doesn‟t ignore time value of $$. B. Most commonly used by practitioners. C. Calculation: add up PV of each cash flow and subtract initial investment. If its positive, project is acceptable. 3 D. Incrimental NPV: Calculates value of incrimental cash flows, if NPV is positive, project is good. 1) e.g. Small budget: 25% r, outflow (10M), inflow 40M, NPV 22M. 2) e.g. Large budget: 25% r, outflow (25M), inflow 65M. IRR 27M. 3) Incrimental outflow Cfo (15M), inflow Cfj 25M, 25% r, hit NPV and get 5M so larger project is accepted. 4) We can also look to see which has higher PI. E. If you calculated IRR already and it is same as discount rate you are using for NPV calcualtion, don‟t bother, NPV = zero. F. If NPV is negative, we reject project. 1) 2 exceptions: 1 good, bad. A) BAD: some managers in 70s (e.g. cigarette and oil Cs) invested in negative NPV projects b/c had lots of cash and didn‟t want to pay it out in dividends and lessen size of firm b/c of hubris. 1. 1 alternate explanation is that we simply calculated NPV wrong and managers were right. B) GOOD: Negative NPV may not be project you reject if it opens up a large amount of potentially lucritive options like walkman. 1. Also have option to abandon which should add cash flow in form of salvage value. G. Which DR should a manager use? 1) IRR. 2) WACC: but not good unless only want to invest in risky projects. 3) Risk adjusted DR. A) This is best b/c takes both risk and timing into account. 4) Rate that C could get from financial asset of comperable risk. 5) Marginal borrowing rate: what can borrow at: may ignore risk of project unless loan made knowing invest in that project. 6) DR of comperable project in market: A) If its not Cs normal project, then may add some basis points to account for extra risk that they never did simialr project before. H. Problem: Duration: 2 mutually exclusive projects may not last for same amount of time or project is same amount of time but cash flows front/back loaded. 1) This is where many errors occur: its hard to account for. 2) U.S. firms prefer quicker payback b/c think can get same growth rate later but this not necessarily best even if shorter one has higher NPV b/c longer one may have higher rate of return which can‟t be duplicated. A) Hard to predict more than 5 years out so US practice bad if talking about getting same rate after 5 years (also depends on type of project: consumer durable v. high tech). B) After 5 years, prof says just assume cash flow stays steady. 1. Time value of $$ keeps this assumption from bringing a big error into NPV. 2. Payback Period. (PB) 4 A. How long an investment takes to recoup its value. 1) e.g. cost is $500 and cash flows are 200, 300, 400. PB period is 2 years. B. Problems: 1) Timing of cash flows not discounted properly. A) e.g. A&B cost $50; A cash flows are $20 and $50 whereas B are reversed: B has higher NPV but same PB as A. 2) Payments after payback period are ignored. A) e.g. A&B costing $60 have $60 cash flows 1st year but B has $10,000 2nd year and A only $10 but have same PB. 3) Choice of period is arbitrary, nothing to compare to as w/ NPV and discount rate. C. Benefits: 1) Easy to use for low level managers deciding minor issues (e.g. fix truck). A) This is cost effective for C b/c saves higher management trouble. D. Discounted payback period. 1) Same as above except first discount the cash flows. 2) Benefit: address problem #1. 3) Problem: destroys above benefit so may as well chose NPV or PB. E. If NPV of 2 projects is equal, we may look to payback for solution. 1) Choose shorter PB: we do this b/c we are afraid of time risk and fluctuation of market r, maybe we can invest at higer r at end of shorter period. A) May depend on what type of project you have, high tech can‟t repeat but consumer durable, probably can repeat as same r. 2) Choose longer PB: we do this if we think market r will drop b/c value of project will go up so better to keep in solution longer. 3) May even do this if NPV not equal. F. In practice, most use this and NPV. 3. Average Return of Investment (ROI). A. Talks in terms of net income, not cash flow. 1) This is both a problem and benefit. A) Benefit: only analysis not based on cash flow. B) Problem: can manipulated like net income, cash flow is firmer. C) Problem: calculated number means nothing on its own. 1. Same problem as PB, # is arbitrary. 2. Usually try to measure vs. industry-wide ROI. D) Problem: takes no account of timing. B. Calcualtion: ROI = Avg. net income/ avg. investment. 1) Avg. investment is calculated by adding up each year (price paid - total depreciation). a) From year 1 to year 5 of a 500G project w/ 100G depreciation each year, we add up 6#s, 500G to 0G and divide by 6 to get 250G. 4. Internal Rate of Return (IRR). 5 A. IRR is the discount rate that causes NPV to be zero. B. IRR loses its probative value as it gets further away from expected rate. 1) Also if PB is very quick, # won‟t mean much. C. Calculation: Enter initial payment into Cfo (blue g) (Note: payment must be negative) and then subsequent cash flows into Cfj and then hit IRR. D. Problems for independant and mutually exclusive projects: 1) Every time get reversal in cash flow (turns negative then positive again) there is another possible IRR but if too many, IRR won‟t mean anything. 2) Investing vs. financing type projects. A) If cash flow is negative, then positive, it investing type and project is worth it if IRR is greater than market rate. 1. This type is the norm. B) If cash flow is positive, then negative, its financing type and project is worth it if IRR is less than market rate. 3) # is calculated in vaccuum b/c need to compare it to some DR to see if IRR is higher than approprite DR. E. Problems w/ IRR when projects are mutually exclusive: 1) Scale problem: IRR ignores issue of scale of projects. A) e.g. Outflow $1, in flow $1.50: IRR 50%. B) e.g. Outflow $10 in flow $11: IRR 10%. C) Problem: projects over same period of time. A has higher IRR but B makes more $$: should choose B. 2) Solution: incrimental IRR: measure incrimental cash flow from choosing large budget over small one. A) e.g. Small budget: outflow (10M), inflow 40M, IRR 300%. B) e.g. Large budget: outflow (25M), inflow 65M. IRR 160%. C) Incrimental outflow Cfo (15M), inflow Cfj 25M, hit IRR and we get 66.7%. D) Thus, choose large budget b/c DR is 25% and IRR is 66%. 1) IRR meaningless if didn‟t have DR to measure against. E) Can also measure NPV of projects or incrimental NPV. 3) Timing problem: IRR will be less in project whose NPV declines at quicker rate. But NPV of this project may be higher than other at lower discount rates. A) We don‟t know if its better to get $$ back sooner or later; if C is earning less than IRR on projects, then want $$ in solution for longer and return to be back loaded, if earning more, its reverse. 4) Solution: same as #2 and 2 E). F. Benefits: summerizes project up in one number. G. Need DR when applying IRR b/c w/o it IRR means nothing. 1) But don‟t need DR to compute IRR as you do in NPV. 5. Profitability Index. A. PI = NPV of cash flows after initial investment/ initial investment. 1) e.g. Investment is $20, cash flows are $70, then $10 & r is 12%. 6 a) PV of cash flows $70.5 / $20 = 3.53. 2) Book uses PV but prof uses NPV. B. Accept project if PI > 1 when dealing w/ independant projects (can do more than one.) C. If dealing w/ mutually exclusive projects, PI may fail b/c lower NPV project may have higher PI. 1) Problem: ignores scale as in IRR. 2) Solution, same as IRR, incrimental approach. 3) Problem: ignores duration of project. 4) Solution: may be a good thing: see NPV part G. D. PI is useful in capital rationing. 1) e.g. 3 projects. #1 has highest NPV but costs $20. #2&3 have lover NPVs but cost $10 each. Firm has $20 to spend. Add NPVs of 2&3 and they are greater than #1. Look at PI of 2&3 and greater than #1. So we can use PI when capital rationing: this is bang for buck. E. If NPV are different but timing also different, we may look to PI. 1) Longer lasting project w/ higher PI may be better if we don‟t think we can duplicate it after its over (see PB period at E.). 2) Most US companies choose shorter period b/c think they can reproduce PI but actually only interested in short term, not long term earnings. Chapter 7: NPV and Capital Budgeting 1. Incrimental Cash Flows A. In calculating NPV of project, we only use cash flows that are incrimental. 1) Incrimental Cash flows are those cash flows that occur as a direct consequence of accepting the project. B. Examples: 1) Sunk costs: cost that has already occured. A) Not an incrimental cash flow. B) e.g. Test marketing analysis done in deciding whether to take on a project, even if take on, its a sunk cost. 2) Opportunity costs: cost that occurs when C forgoes opportunity by taking on project. A) Incrimental cash flow. B) e.g. C decides to use warehouse in project instead on leasing it out: must account for “rent” of warehouse. 3) Side effects: erosion. A) Incrimental cash flow. B) e.g. Sales of new sports car comes from, in part, some customers who would have bought C compact sedan. 1) Must account for a portion of the sales that are not incrimental (those cannabalized sales). 2. Net Working Capital: difference b/w current assets and current liabilities. A. Increases in working capital are out flows, decreases are inflows. 7 B. Net working capital = accounts receivable - payable + inventory + cash. C. Must be taken into account when expanding: many people ignore this. D. Mail order catalogs have less risk b/c less investment in net working capital b/c few capital/fixed costs. 3. Inflation and Capital Budgeting. A. Real interest rate = (1 + nominal interest rate/ 1 + inflation rate) - 1. B. Real vs. nominal cash flow. 1) May change cash flows to what their purchase power is as of date zero. 2) e.g. expect 6% inflation every year over four years: 4th year cash flow in real terms is: amount/ (1.06) to the 4th power. 3) Depreciation is always a nominal number. 4) Nominal cash flows are discounted at nominal rate, real at real rate. A) This avoids accounting for inflation 2Xs. 5) Most people factor inflation in. C. Most important point is to be consistant in either factoring in or taking it out. 4. Investments of Unequal Lives. A. Matching cycles: find NPV of each project/expense and then match cycles so have same timing. 1) e.g. Machine A has life of 3 years and NPV of $798; B lasts 4 years and has NPV of $917. A) Cycles match over 12 year period, 4 of A vs. 3 of B. B) Add each cycle: $798 + 798/1.10 to 3rd + 798/1.10 to 6th + 798/1.10 to 9th = $2188: same for B = $1971 so B is better. B. Equivilant annual cost (EAC): turn NPV of cost into annuity. 1) e.g. $798 annuity for 3 years (10% r) pays $321 per year and $917 annuity for 4 years pays $289 per year so B is better. C. If know that time horizon is set amount of years, them want to use NPV of machines during those years and not above method. 1) If horizon was only 5 years, B has higher NPV than A. Chapter 8: Stratagy and Analysis in Using NPV 1. Corporate stratagy and positive NPV. A. Ways to create positive NPV: 1) Introduce new product: Apple PC computer. 2) Develop core competnecy to produce goods or services at lower cost than competitors: Honda mastery of small motor. 3) Create barrier to entry: Poloroid patent on instatnt photos. 4) Introduce variation of existing product to take advantage on unsatisfied demand: Chysler minivan. 5) Create product differentiation via marketing/ads: Coke: “its real thing” 6) Use innovation in organizational process to achieve above: JIT management. 2. Decision trees: calculating NPV for project requireing multiple decisions. 8 A. Expected payoff = (probability of success * payoff) + (probability of failure * payoff.) B. Use to arrive at probability weighted PV of project. C. We assign NPV value and probability to each branch to arrive at expected payoff of that branch. D. We try to get 1 # to value project. E. When apply discount rate in NPV, we use risk free rate b/c risk is taken into account when assigning probabilities of success and failure. 1) Note: book doesn‟t do this. 2) By working risk into probability, we don‟t have best measure of risk. 3. Monte Carlo simulation: computer statistical programs that impose random distribution and computer runs a weighted average outcome of results which we discount back to see if its worth it. 4. Scenario analysis: run several senarios and their effects to see what would occur. A. Benefit: series of scenario may illuminate sensitivity analysis. 5. Breakeven analysis: see at what point in sales growth would NPV equal zero. A. If breakeven is at 5% growth but you project 5.2% growth and high NPV, project may be too risky. B. 3 parts: 1) (Sales price - Variable cost) * (1- Tax rate)= contribution margin. 2) (Fixed costs + depreciation) * (1- Tax rate)= fixed cost total. 3) #2 / #1 = Break even point. 4) Problem: doesn‟t consider PV. 5) Solution: see C. & D. C. EAC: take initial investment and figure out payment as if X year annuity. 1) r 15%, N 5 (# of projected years), 1500 initial investment, EAC=447.5. D. Using C allows us to take NPV into account in doing breakeven point. 1) fixed cost total = EAC + (Fixed costs + depreciation) * (1- Tax rate). 2) Then do #2 / #1 and get PV break even point which should be higher #. 6. Senstivity analysis: Toy w/ basic assumptions (risk free rate, premium rate, beta, sales growth, GDP growth, etc.) and see what effect it has on NPV of project. A. e.g. NPV may be highly sensitive to sales growth but not to discount rate. B. Allows you to assess risk b/c if highly sensitive to growth and there is a large margin of error there, it may be too risky. C. Benefits: 1) Lets us see if NPV should be trusted. A) e.g. high variability of mostly positive NPV projects makes us skeptical. 2) Knowing which factors NPV is sensitive to allows you to focus on them (where need more information) and be more careful in projections. D. Problems: 1) May increase false sense of security if all pessimistic forcasts have postive NPVs, may be that pessimistic forcats is very optimistic. 2) Treats variables in isolation when they are likely related. E. Prof suggest we use both decision tree and sensitivity analysis. 9 7. Options. A. Cs have options to expand or abandon when doing projects. B. Projects value may be understated if don‟t take options into account. 1) e.g. NPV of Sony walkman was X but incredibly higher if realize (as Sony did) that may allow C to expand into other areas (as it did e.g. discman, hand held computer etc.) 2) NOTE: Negative NPV may not be project you reject if it opens up a large amount of potentially lucritive options. A) We can try to use decision tree to measure this. C. Option to expand: 1) e.g. SAAB turbo charge. Started w/ one car, so successful it expanded to wholeline of cars. 2) Option can be very valuable if demand is high. D. Option to abandon: 1) e.g. if test marketing fails, loss if abandon is cost of test marketing whereas cost of going forward may be highly negative NPV. 2) If possibility that won‟t continue project for its lifetime, potential secondary market value of project is a consideration. 3) e.g. if buy plane and airline fails, can always sell plane, route Ks etc. E. Value of project = NPV + managerial options (puts and calls). 1) American business ignore mangerial options whereas japaneese recognize this. F. Oil field e.g: cost of land 10Gs, cost to drill 500Gs, NPV -110Gs: option b/c oil price may increase next year where NPV would = 1.4M. 1) Should buy land and wait till next year to decide if drill b/c it = option: if at 1 year NPV still negative b/c low oil price, don‟t drill and loss = PV 10Gs - salvage value of land. 2) If oil price increases, do drill and NPV is 1.4M + discounted value of 500Gs - loss from not drilling for 1 year. Chapter 9: Capital Market Theory: Overview 1. Returns. A. Total return = dividend return + capital gain (loss). B. % return = total return / initial investment. C. Statistics. 1) Order or return: inflation, t-bill, long bond, large cap, small cap. 2) Long bond chart: A) Shows that risk free bond not risk free b/c inflation rate may increase above % yield and you lose $$. B) Captures inflation rate b/c of longer maturity whereas not captured in t-bill chart b/c of short maturity. 3) If measured t-bill chart every 30 days, not every year, would see negative returns as in long bond. 10 4) Average risk premium for stocks is 8.5% based on 12.2% return and 3.7% inflation. 5) CPQ chart has lower beta but higher variability than MRK: need to rescale chart to cut out ideosyncratic risk that it shows. 2. Discount Rate A. DR for risky non financial project where risk is similar to market = 8.5% (historical risky premium) + risk free rate. B. DR if differs from market depends on measure of risk--discussed later. 1) e.g. if gold venture‟s cash flows are highly variable and utility not so much, which has higher DR? A) Assuming investors of C have diversified portfolio, utility b/c it moves w/ stock market whereas gold moves opposite way so risk will be diversified away. C. CAPM tells us that approprite DR for investment is based on inherant risk of investment relative to market based return that might otherwise be made. 3. Beta: measurement of assets risk. Chapter 10: Risk and Return: CAPM 1. Variance & SD A. Use to measure volatility of an individual security‟s return. B. Variation = sum of absolute variances after squaring each one / # of observations (some say # - 1 if observation sample is small) 1) We square the variation not to make it + but to magnify its effect. 2) Also, if added up absolute variance w/o it would always get zero. 3) Absolute variance = actual return - average return. C. SD = square root of variance. 1) This allows us to calculate ranges of returns w/in x number of SDs. 2) 1 SD=68%, 2=95.5%, 3=99.75%. 2. Covariance & correlation. A. Measures relationship b/w two securities. B. Covariance = sum of the product of absolute variances for 2 securities / # of observations (some say # - 1 if observation sample is small). 1) # has no meaning, +,-, or 0 has meaning. 2) Negative covariance says securities move in opposite directions. 3) 0 covariance says no relationship. 4) Measures if move in same or opposite directions. C. Correlation = covariance / product of both security‟s SDs. 1) Closer correlation is to 1 or -1 more highly correlated they are. 2) Sign of correlation is same as covariance. 3) If securities perfectly negatively correlated then can get return w/o risk. A) This of course is impossible. 4) Measures the magnitude of two securities movements (whether + or -). 11 5) Plotting 2 securities on graph w/ correlation coefficient of 1 is straight line that looks like CML. 6) As coeficient approaches -1, it curves backward more and more. A) At -1, its no longer a curve but 2 straight lines. 3. Portfolios (P) A. Goal is maximum return and minimum risk (SD). B. Need to know relationship b/w securities‟ SDs, correlations, and SD of P made of these securities. C. Expected return of P: weighted average of return of securities in it. D. Variance of P w/ 2 securities = squared weighted average of variance of A + 2XAXB (covariance) + squared weighted average of B. 1) S.D. is square root of variance. 2) SD of P is less than weighted average of SD of individual securities. A) Note: expected return of P is not less than weighted average. B) This is diversification effect. 1. Diversification is process of placing assets into a P in such a way as to minimize risk and maximize return. C) Diversification effect is less if two securities are highly correlated. 1. If correlation b/w securities is 1, SD of P = weighted average of SD of 2 securities. 2. Thus, no effect if perfect positive correlation, it must be less than 1. 3. As correlation decreases, effect increases. 3) By increasing investment in risky security, we may actually decrease risk of P. A) Risky security acts as a hedge. E. Minimum variance P: the P, of all possible Ps consisting of securities one invests in, that has lowest SD (variance). 1) Would not invest in a P where SD increase as return decreased (backwards part of curve). A) Feasible set vs. efficient set (only Ps above MV P) 2) In actuality, its about 80% U.S. stocks, 20% foreign. 3) This is not necessarily ideal P for all. A) Best P of efficient set of Ps depends on investors stratagy, tolerance for risk, etc. F. As we increase the number of securities in a P, variance of P approaches covariance. 1) We can thus eliminate all non-systematic risk (variance) but can never eliminate (diversify away) all systematic risk. 2) Total risk of stock X = P risk + unsystematic risk. 3) Risk averse investors choose well-diversified Ps. A) Risk averse investor avoids gamble w/ zero expected return. B) May look at more than expected return. 12 1. e.g. 60G, 80G 100G salary choice; exprected return is 80 but may not take chance b/c risk of loss is greater (60G may not be enough to pay bills). 2. May chose 80G b/c need certainty in cash flows. 3. Why risk 20G on some else when can invest it yourself. G. Ps w/ one risky asset and one risk-free asset. 1) Variance of P = weighted average of variance of risky asset. 2) One can leverage up return on P by borrowing $$ and investing more than 100% in risky asset. H. Capital market line: efficient set of all assets, risky and riskless. 1) See chart on pg 273 to see where risk averse, neutral and risk lover would stand. 2) All Ps comprised of ideal risky P + Rf asset lie on this line. I. Beta: B = Covariance of asset‟s return with market return / market return. 1) Beta of market = 1. 2) Negative beta asset is hedge or insurance policy. 3) Adding negative beta stock to P reduces risk. A) But few have negative betas. 4) Contribution of risk to market P depends on asset‟s contribution to P‟s variance. A) But since most P‟s are close enough to market P, beta of asset is a reasonable measure of contribution of risk to P. B) If one‟s P is not close to market, should look at variance of new asset, not its beta. C) Risky gold venture may be good for P b/c acts as hedge. 5) Beta measures a security‟s movement in relation to marketplace. 6) 2 most important factors effecting beta: A) Change in debt/equity ratio of C. B) Material change in P of Cs investment assets (e.g. merger). C) Main issue is beta depends on what changes cash flow. 7) Doesn‟t matter what period we use to measure beta but interval (month, year, week) does matter. A) Shorter interval shows higher volatility. J. Homogenous expectations: every investor has same belief re: return, variance and covariance of each security. 1) In this world, all would hold 100% risky asset P. K. CAPM: expected return of a security is linearly related to its beta. 1) Expected return = risk free rate + beta * (market return - risk free). A) (market return - risk free) = risk premium = (usually) 8.5%. B) If beta = 0, return is risk free rate. C) If beta = 1, return is market return. 2) What CAPM stands for: it tells us the appropriate DR for an investment has to do w/ inherent risk of the investment relative to market based return rate that might otherwise be made. 13 A) How it can be criticized: it states that only way to get higher returns is by taking on higher risk: see CML and SML. 3) Security market line (SML): represents relationship b/w expected return on security (including a whole P) and its beta. A) Any security (including a P) resting above line is underpriced, below is over priced. B) Can achive high return by investing in high beta stocks. 1. This does not increase ideosynchratic risk if diversified properly, but it does increase systemic risk. C) If borrow money to invest, you have then moved to CML. 1. Borrowing $$ gives you leverage which increase both risk and returns. 4) Differences b/w SML and CML: A) SML compares return to beta not SD. B) SML holds for all individual securities and possible Ps whereas CML only holds for efficient Ps formed from risky and riskless assets. C) SML is a derivation of CML; we created CML when talk about combination of risky assets and risk free to create a P; SML is core of CAPM b/c since we can get a security to act as if in a P under the CML, the market will price the security so it looks like a P. 1. Thus, if you buy one security, it return relative to risk will be less than if security was in well-balanced P. D) If we want e.g. a return higher than 100% of risky asset, we can invest in proper mix of risky P and risk free asset under the CML (borrow money to buy more stock) or invest in high beta stocks under SML. 4. Fama and French: Beta is dead! A. 2 points: 1) Relationship b/w average return and beta is weak from „41-‟90 and nonexistant from „63-‟90. A) Counter: Beta is not said to be related to average returns but to projected average returns. B) Counter: there is positive relationship b/w „27-‟90. C) Counter: average returns are positively related to beta over shorter period when annual, rather than monthly data is used. 1. And there is no reason to favor monthly over yearly data. D) Counter: 50 year period may not be long enough to test CAPM properly. 2) Average return on security is related to both PE and market/book value. A) Counter: PE and M/B are two or many factors so results may be nothing more than data mining. B) Counter: Book value is subject to manipulation via accounting so M/B variable is meaningless. 14 C) More promising and hence better Cs will have high M/B and PE and thus higher return, and vice versa: tautological. D) Counter: B is fixed so only variation is M which almost by definition will increase as return increses: tautological 1) Market cap = shares outstanding * price. 2) Market cap may increase while return doesn‟t if firm keeps issuing shares and stock price doesn‟t move. B. Commentators agree: beta is rightly criticized but F&F give us nothing to replace it. 5. Critiques of CAPM: A. F&F: see above # 4. B. Chaos and noise theories: argue that can get higher returns w/o higher risk. 1) Based on math models finding market doesn‟t have movement that is calculatably random or rational. 2) There are movements short/long run that don‟t fit any rules 3) Over long run, noise cancels out but some can trade on this noise (Soros claims he can). 4) We have machines that can separate out digital noise so if can do it for market, can make cash. 5) Fat tails which say that one event likely to be followed by similar one. A) More leptokutoric curve is, more misleading SD is b/c its calculations are skewed by largest price changes. C. Neural systems: short term technical analysis that allows you capture over bought/sold positions. 1) Thus can get higher returns w/o higher risk. D. ABT: claims that movement isn‟t based on single factor but on multiple factors we use to get a better picture. E. Stock value as a call option: risk may actually decrease required return/increase price of stock: binomial pricing theory. F. Certain anomolies: small caps, temporal, PE, M/B: but these (except temporal) may simply be better ways to measure risk. Chapter 11: Risk and Return: APT 1. APT. A. Its a more powerful predictor (ex ante and ex post) than CAPM b/c takes more variables into account. 1) Its now possible to do the APT b/c of increase in technology allowing us to solve multiple regressions. B. Actual return = Average return (expected) + U (unexpected). 1) We don‟t add risk free rate b/c its not risk premium based formulation, its absolute return. 2) Its mostly included if use CPI, change in long/short rates, and change in risky/ risk free rates, factors. 3) If no factors include risk free rate, then we need to add it. 15 4) We need to take some %s out of 1st factor for each added factors in U that overlaps w/ it. 5) Anouncement = expected part + surprise. C. We plug into U the product of different factors and their betas. 1) We keep plugging in factors until we exhaust what we can know and are only left w/ ideosynchratic risk. 2) Hard to determine which are appropriate factors to add. 3) APT looks to industry and market wide factors. 4) Correlation occurs b/w securities in the APT when they are effected by the same factors. 5) Determining which factors is based not on P but on multiple regression. D. Possible factors: GDP, interest rate, CPI, etc. 1) Note: determination of factors not based on P but on multiple regressions. 2) Market model is APT w/ 1 factor being market risk premium. A) When market P is only factor CAPM = APT. 3) Note: if stocks should be priced like options, then APT may be better than CAPM b/c takes difference of long/short rates ect into account. E. Beta of factor is how responsive stock is to systematic risk. 1) e.g. utility stocks have high interest rate betas b/c if rates go up or down, there is a high effect on stock. 2) Each beta has its own scale, not scale of market return (as in CAPM). 3) If CPI beta is 2 and we expecting CPI to be 3%, we add 6% to expected return; if CPI turns out to be 4%, we have 2% unexpected return. 4) e.g. R = average R(usually ~.3%) + BF1 + BF2 … + unexpected risk. A) Note: we must remove expected returns of F1 and F2 from average R so we don‟t count it 2Xs unless F1 and F2 only measure up or downside surprise of factor (e.g. increase in interest rate). F. APT for P. 1) Return consists of 3 parameters: A) Expected return of each security. B) Beta of each security multiplied by factor. C) Unsystematic risk. 2) But in large P, C) disappears so its only A and B. 3) #2 is why APT better predictor b/c expected return can be adjusted as each factor changes so formula is more dynamic than CAPM which doesn‟t have as many factors. 2. Alternatives to APT and CAPM: parametric or empirical models. A. CAPM and APT are risk based models. B. Empirical models look at regularities and relations in past history of market. 1) e.g. small cap v. large cap, growth v. style, M/B. 2) Possible explanation of merits of empirical data is that those successful e.g.s like #1 are simply better measures of risk than trying to estimate beta from data. 16 C. Critics of empirical model say its mostly data mining. 1) e.g. we could find relation b/w size of moon and market return. D. See options section: perhaps a binomial option pricing theory. 3. Style Ps. A. P of stocks that share a particular stock attribute. B. Growth Ps: P of stocks who have above average PE. C. Value Ps: P of stocks who have below average PE. D. Benchmark: index used to measure market returns of particlar stocks. 1) e.g. S&P 500, Philadelphia bank index etc. 2) Only measure P vs. a benchmark whose stocks are part of the P. 3) I say may use S&P 500 anyway b/c if invested in index options, could have gotten that return. 4) We also measure managers versus other managers in their group. Chapter 12: Risk, Return, and Capital Budgeting 1. Cost of Equity Capital A. Value of firm = value is discounted cash flows of firm, Value of project = discounted cash flow of project. 1) DR of project should be pegged to expected return rate on asset of comperable risk. 2) Use DR to value projects financed w/ either debt or equity. 3) Project should be undertaken only if provides greater expected return than that of financial asset of comperable risk. A) Or else SH rather have $$ in divdend and invest it themselves. B. SML analysis: graph chart of projects IRR vs. firm beta (see pg 317). 1) Should accept project if IRR is greater than cost of equity. C. Cost of capital: all equity firm. 1) Use CAPM w/ firm beta as B. 2) Note: only applies if risk (B) of new project is similar to old projects b/c of A. 1). D. Measuring company beta: covariance of stock and market / variance of market. 1) Problems: A) Beta may vary over time. 1. Solution: can be moderated by more sophisticated statistical techniques. B) Sample size may be inadaquate. 1. Solution: can be moderated by more sophisticated statistical techniques. C) Beta influenced by changing financial leverage and business risk. 1. Solution: look at average beta estimates for comperable firms in the industry. 17 2) Determinents of beta. A) Cyclicality of revenues: 1. High tech, retail and auto fluctuate w/ business cycle. 2. Food, RR, utilities and airlines less dependant on cycle. 3. Highly cyclical stocks have high betas. 4. Note: cyclical doesn‟t = variable so movie house has variable cash flow but may not be cyclical. a) This is so b/c variability includes non-systematic risk and cyclicality doesn‟t. 5. Banks have low inflation beta but high GNP beta. B) Operating leveage: change in EBIT/EBIT * change in sales/sales 1. Higher fixed cost, lower variable cost = higher contribution margin. a) Fixed costs act like fulcrum. 2. Higher contribution margin = higher operating leverage. 3. Reasoning: if make no sales, lose more if have higher fixed cost but if make lots of sales, make more b/c lower variable cost so there‟s higher risk. 4. Operating leverage magnifies cyclicality of C‟s revenues. 5. Mail order company has very low fixed costs and high variable costs so not so risky. a) Why would sellers supply mail order? No marketing or ads necessary. b) Also mall shop that pays, in part, variable rent based on % of sales. 6. 2 trucking Cs have in substance same beta but if one rents and one buys trucks, renter has lower beta. a) Limits to reducing fixed costs: BMW has no cars on lot but poeople won‟t buy as many then. C) Financial leverage: a levered firm has some debt in its capital. 1. Refers to firms fixed cost of finance (interest payments). 2. If firm too highly levered (like utilities in 30s) small variation in return may send to b-ruptcy. 3. Debt is also fixed charge so higher debt, higher leverage, higher beta. a) Issue here is that inflow is variable, not fixed. b) If infow were fixed, increase leverage would be good and not risky. 4. Higher debt also increases ROE. E. Asset beta: Beta asset = (equity/ debt + equity) * Beta equity 1) Note: debt above is not nominal face value but market value of debt. A) Further note: thus every change in interest rate effects stock beta b/c market value of debt changes. 18 2) Equity beta always greater than asset beta if there is financial leverage. 3) Asset beta = beta of common stock if firm is all equity. 4) Equity beta we pull out of market place. 5) Real leverage is what is fixed cost of debt. F. Firm vs. project. 1) If project beta is different from firm, should discount it w/ own beta. A) e.g. if publishing firm does software venture, may want to use DR of software company. B) If not, firm will underestimate cost of capital and will accept too many high risk projects. 1. Problem: beta of new project probably higher than that for similar project by existing firm. 2. Solution: today‟s practice: ad hoc slight increase in beta. 3. Problem: new project may not have any peers: e.g. home shopping network in early 80s. 2) Other names: corporate discount rate, hurdle rate, cutoff, cost of capital. 3) If firm is not public, can use beta of comperable public firms. G. Weighted Average Cost of Capital: cost of capital with debt. 1) WACC = weighted average cost of debt + weighted average cost of equity (using CAPM). 2) e.g. debt of 40, equity of 60, firm pays 15% on new debt, beta is 1.41, corporate tax rate is 34% risk premium 8.5%, t-bill 11%. A) Pretax cost of debt = 15% * .66 = 9.9%. B) Cost of equity = 11% + 1.41*8.5% = 23%. C) WACC = .4 * 9.9% + .6 * 23% = 17.8%. 3) If new project beta is above/below 1.41, WACC will adjust accordingly. A) Note: this is relevant b/c investors (especially savvy institutions) invest in C b/c of its risk so any unwanted increase or decrease in risk of firm may adversely affect stock price. B) Note: effect will depend on how large the project is in proportion to whole firm b/c if project only 1 million and firm is IBM, effect is negligible. 4) Note: debt/equity ratio of .6 does not mean 60% debt but 6 parts debt for every 10 parts equity or 6/ 6+10 = .375 or 37.5%. 5) This is same as return on asset base of firm. 6) Capital structure tells us nothing in valuing firm. 7) If given WACC we can calculate beta from the CAPM. A) WACC is 15%, Rf is 4%, Rm is 11.5%: using CAPM we solve for beta and get 1.47. B) NOTE: this assumes all equity firm: if know there is debt, then subtract out debt portion of WACC and then plug rest into CAPM. 1. Thus, we must be calculating equity and not firm beta!!! 2. To calculate firm beta, we would need beta of debt and need to know debt/equity ratio. 19 3. However, since beta of debt is very low, some people ignore it but then we don‟t have true measure of beta. 8) Can then calculate what beta moves to after project by making assumption on size of firm: A) Firm is $1 Million and project cost 750,000; $$ for project comes from sale of stock; NPV of project is 29,750; Beta of project is 1.2 and firm is 1.47. 1. Firm value becomes 1,778,750; 56.19% of this is from old firm beta of 1.47 and 43.81% from new project at 1.2; weighted average of new firm beta is 1.35. 2. If old WACC was 15% and Rf is 4% and Rm is 11.5% then new WACC is 14.13% B) If $$ for project comes from debt, Chapter 13: Corporate Financing Decisions and Efficient Capital Markets 1. Efficient Market Hypothesis: EMH: current market prices reflect availible information. A. Does say: 1) Prices reflect underlying value. 2) Financial managers cannot time stock and bond sales. A) But see Ritter & SEO/IPO analysis. 3) A firms sales of stocks and bonds will not depress prices. A) Some very minor evidence of price pressure but not much (and usually recovers) and more research is needed. 4) You can‟t cook the books. B. Does not say: 1) Prices are uncaused. 2) Investors are foolish and too stupid to be in market. 3) All shares of stock have same expected return. 4) Investors should throw darts. A) All it says is that managers can‟t achieve abnormal return, must still decide how risky a portfolio you want. 5) There is no upward trend in stock prices. C. Why doesn‟t everybody believe it? 1) There are apparent patterns, illusions etc. in stock market returns. 2) Truth is less interesting. 3) There is evidence against efficiency: A) Seasonality. B) Insider trading. C) Excess stock price volitility. 4) Tests of market efficiency are weak. D. 3 forms: 1) Weak: Prior history is no guide to future performance: today‟s price = last period price + expected return + random error: random walk. 20 A) Theoretical justification: price of share will trade at discounted PV of future cash flows and stock price is based on what is known. 1. Problem: empirical studies prove 15 minute window. a) Smaller the time frame, better predictive value there is. 2. Problem: neural networks, computer models etc. that “frontiers of finance” insist can outperform market. 3. Problem: serial corelations: a) Counter: given t-action costs and error, coefficients not big enough to disprove weak form. B) On other side are technical analysts, say can predict future prices from previous prices: 3 tops, support levels, bounces etc. C) Window may be about 15 minutes. 1. Like car slowing down e.g. 2. Market needs some time to react to info. D) Head & shoulders, 3 tops after 15 minute window is illusion. E) Serial correlation: 1. Positive coefficient: higher than average returns today mean likely similar tomorrow. 2. Negative coefficient: opposite of #1. F) Verdict: good theory but only after 15 minute window. 1. Must be somewhat right b/c its so cheap to do anyone could beat market and that‟s not happening. 2. Trading w/in window is what makes market efficient. G) Information set: past prices. 2) Semi-strong: Prices reflect all public information rapidly, reagrdless of medium of dissemination, financial analysis is useless. A) Empiricle data supports this. B) Thus, don‟t need GAAP b/c market will see through any accounting manipulation and price stock accordingly. 1. Fundamental analysis: data about C, industry etc.: SS says this is bogus b/c already included. 2. Location of info: financial statement, notes etc. is irrelevant. 3. Timing is only relevant as to when public finds out, not when info actually released. a) If stock has surprise info, we usually see a rise in stock before b/c analysts asking for info, WSJ rumors etc. C) We can test this via empirical tests by watching Cs that switch LIFO/FIFO or depreciation methods: event study. 1) Problems: a) Other reasons stock may be moving. b) Don‟t want to mine data. 21 2) Solution: we look before and after event and see if return is abnormal. 3) This done by looking at portfolio of stocks that do and don‟t change methods and see if there is statistically significant abnormal return. 4) Problem: time of change may not be at announcement but when public finds out about it. D) Change to LIFO makes price rise then level off b/c redues tax in short run so increase near term cash flows. 1) Thus, increase has to do w/ tax not actual change. E) Purchase v. pooling of interest has no effect b/c no tax benefit. F) Conclusion of commentators: market sees through change so semi-strong EMH proven. G) Conclusion matters to those who say we should eleminate financial regulations. 1) This view dependent on fact of high institutional ownership b/c they will make market react. 2) EMH moves us away from producing financial statement that everyone can understand. 3) Even strongest supports (E&F, Posner) agree need anti- fraud and auditing provision b/c info may be fraudulant. a) But may not need ‟33 or ‟34 Act. b) Need audit to ensure efficiency of timing b/c financial statments allow us to predict timing and amount of future cash flows. c) Need anti-fraud to ensure integrity of #s. 4) Prof says GAAP only SS for certain data: see E. below. H) Semi-strong applies to 3 types of Cs: 1) Heavily traded: SS holds firmly. 2) Lightly traded: SS holds but market reaction is slower. 3) Not traded: SS does not hold. I) Verdict: best of 3 theories; much evidence supports it but there is some evidence that shows inefficiency on fringes (e.g. small cap) and that it doesn‟t hold for all Cs. J) Information set: all public information. 3) Strong: Prices reflect all that is knowable, no one consistantly makes superior profits. A) Contradicted by fact that insiders trade and make superior profits and market may not react. B) Verdict: strong empirical evidence shows its just not true. C) Information set: all information (at least one investor knows) relevant to stock. 1) Even more strict view says that this 1 investor can‟t beat market b/c once they try to trade, people will know what‟s going on and price will adjust before they do it. 22 E. Arguments against propostion that we can eliminate financial reporting: 1) Degree of transparency: A) All empirical studies deal w/ completely transparent data. 1. e.g. depreciation, LIFO/FIFO, purchase/pooling, foreign exchange etc. B) W/o regulations, we would not get executive compensation #s, inflation data, ESOPs, pension and health care exposure etc. 1. We know we wouldn‟t get it b/c before required, it wasn‟t volunteered. 2. This type of data can only be analyzed if its disclosed, can‟t “figure it out” like other data. 3. Seligman‟s book shows strong historical and cross- sectional data to support this. C) Market is not SS for all information, only those in studies. 1. e.g. we don‟t have one re: inflation and probably would prove that market not efficient on this point. 2. Not efficient re: court records as Prof‟s e.g. shows. D) There is no evidence that we do not need regulations. 1. We shouldn‟t assume away differences in expertise, we don‟t know everything. 2. There is new info that effects market price that we can get via due diligence. E) Main problem w/ studies: don‟t examine effect that requirement of disclosure ex ante has on efficiency ex post. 1. Need to distinguish b/w what form data takes and disclosure itself. F) In evalutaing empirical studies we must look at what data it focuses on. 2) Not everything is on market: close corporations. A) Most Cs that file w/SEC aren‟t on exchanges. B) If no market for C, then no way to value C w/o SEC disclosure. B) Every study done on NYSE or AMEX, not even NASDAQ. F. Some people (Posner) try to extend EMH to areas like family, abortion etc. but if actually did sudy, data wouldn‟t pan out. 2. 3 ways to create valuable financing opportunities. A. Fool investors. 1) Under strict EMH, this can‟t happen b/c market prices things properly at all times. 2) If it does happen, its rare and may be close to fraud. B. Reduce costs or increase subsidies. 1) e.g. threaten to leave citiy unless they issue tax exempt bond for you: this save on DR (b/c use lower bond rate rather than your normal cost of capital. C. Create new security. 23 1) Previously unsatisfied clientel pays premium for security b/c offers them something that no other can. 2) Problem: value created is small b/c others in market learn and do it and premium drops. 3) Real beneficiaries are IBs that invent new security. 3. See chart on 337 showing 4 possible market reactions to an announcement: efficient market, early response, delayed response, and overreation and reversion. 4. Making markets efficient. A. Arbs, guys on floor, insider traders AKA people trading w/in 15 minute window make market efficient. 1) The faster they get info and can trade on it, the smaller the window and hence the more efficient the market gets. 2) Some markets get to point where window is seconds and highly rtained arbs pick off profits from this window. 5. How can person get abnormal returns? A. Possibility that there are those out there who have greater skill/insight that us or can acquire/use information in a way that is actually cost effective. 1) Lawyers analyzing court records. 2) People who can trade on noise. 3) Soros or College retirement equity fund. 4) This isn‟t failure of market, they make it more efficient. 5) Whether forcaster and soybean futures. B. People that are closer to trading floor and get information faster (w/in 15 minute window) 1) May be form of insider trading but its good kind. C. Improper insider trading 1) We try to stop it but it occurs and proves strong form is wrong. 2) Signalling function: still makes markets efficient b/c people know its going on and react to insiders buying. 3) Some argue it should be legal b/c makes markets more efficient. D. Boarderline insider trading: when managers buy/sell on “non- material” inside information: empirically proven: also serves signalling function. E. Evidence that EMH doesn‟t play out on boarders. 1) Size: small caps return more even when adjust for risk. 2) Temporal anomolies: January has higher return. 3) Value versus glamour: value stocks (low PE or PB) outperform glamour stocks (high PE, PB) 4) IPOs and SEOs have lower returns for 5 years after offering. (Ritter) A) Shows managers may be able to time market. F. Luck: statistical anomolies: if 50 million people flip coin X times, a few will get all heads. 1) Like mutual funds survivorship bias: some funds get lucky every year. G. Finding some system no one has yet. H. Other illegal means of trading: “pump and dump.” I. Computer modelling/nueral networks/non-linear stats: see Frontiers of Finance. 24 1) Works to extent they can actually predict returns and benefits > costs. J. Trading in inefficient market such as new, small, foreign, and muni markets. Chapter 21: Options 1. Payoff charts: see 576, 578, and notes 11/20. A. Note: Payoff does not equal profit. 2. European option: can only excercise on expiration date. 3. American option: can excercise at any time up to expiration date. 4. Derivative: financial instrument that derives its value from another. A. Stock is technically a dervitive of assets but we don‟t think of it this way b/c its direct ownership of assets. B. Leap: is a future and option: its futre at first and then becomes option. 5. Value of option not same as price of option. A. Minimum/maximum call value: 1) Minimum: bargain purchase value + loan value. A) Loan value may get incredibly small but its still there. 2) Maximum: stock price: would be no point buying option if could by stock cheaper. 6. Option can be uncovered but hard to do for real estate b/c property is unique. A. ESOP is covered option. 1) C not heavily exposed here b/c can just print more stock. 7. Factors effecting value of call option. A. Strike price: as it increases: call decreases but put increases. 1) Bargain purchase value: + Difference b/w strike price and stock price. B. Expiration date: as date becomes more distant: both options increase. 1) Not necessarily true for European b/c if one can excercise b/4 a large dividend is paid and other after, option expiring before is more valuable. C. Stock price: as price increases: call increases but put decreases. 1) Note change in option price is greater as it moves further into $$: see chart on 583. D. Risk free interest rate: as it increases: call value increases b/c loan value increases but put decreases b/c PV of strike price decreases. 1) Loan value: value of not having to buy stock now: A) e.g. strike price is $100 in 1 year, risk free rate = 4%, the loan value = X - PV of X or $100 - $96.15 = $3.85. 2) PV of strike price: as r increases, PV of X (sell price) decreases so value of put decreases as well. 3) As interest rate increases, stock price decreases. E. Volatility: variance of underlying security: as increases: both options increase. 1) Rationale: if finish out of money, doesn‟t matter how far b/c price can‟t be negative but if finish higher on up side, its better. 2) Decrease in stock price caused by increase risk is less than proportion of increase to option holder. 3) See chart on 583 which sets price limit on option: limit boundaries: 25 A) Max: can‟t be worth more than stock price b/c then cheaper to buy stock than option. B) Min: can‟t be less than Bargain purchase value + loan value. 4) You are only buying on side of probability (either side of strike price) curve w/ option so extremes become more valuable. 5) Don‟t talk about risk of option in portfolio b/c we want to take advantage of ideosynchratic risk, not eliminate it. 6) This is most difficult to determine. 7) Calculated by cumulative probability that option finish in $$ and degree to which it will. 8. Why you wouldn‟t excericese American option before maturity: A. Option has loan value which is lost if excercise before expiration date so its worth more just to sell option to someone else than to excercise it. 1) Value upon excercise = stock price - X is always less than value of holding = stock price - PV of X. B. Saves you trouble of buying stock and spending $$ now and if stock paying no dividend, no point in buying it now. C. 2 exceptions: 1) Dividnd paying stock: same as reason for valuing a shoter term European call more than longer term, will pay out large dividend and drop value of stock. 2) Options and underlying stock are not freely t-ferrable: e.g. ESOPs where can‟t sell option or underlying security. 9. Preferred stock = mix of stock and bond. 10. Convertible Bond: A. CV Bond= Bond + call + put. 1) 3 values: PV of face bond value + interest, option value, and conversion value. B. Call value: if stock increases to price above strike price of bond, then value of bond increases as well b/c call is in the $$. 1) e.g. 1000 bond, r = 7%, CV into 10 shares: if stock is worth 50$, no one converts but if stock is worth 200$, call value is 100$/sh; strike price is 100$ b/c 1000 / 10. 2) If stock worth 200$ bond worth more than 2000$ b/c also add in 7% interest and still have option value (either to hold bond or put/call value). C. Put value: if interest rate increases, market value of bond drops to say 850$ but if conversion into stock is worth 900$, then convert and you are “putting” bond by selling it at conversion price. 1) Problem: if interest rate increases, value of stock probably drops as well but put may be in money. 2) This put value is more valuable when interest rates are low b/c it acts as a big hedge against future rate hikes. D. Term of these options is measured by term of bond (or term in which bond can be converted). 26 1) Thus, if can only convert 5 year bond w/in 3 years of maturity, option value becomes a leap. 11. Hedging: A. If C is selling planes in UK for fixed amount of pounds sterling in 1 year, they don‟t want to take currency risk and can eliminate risk for a fixed price b/c they are on both sides of the t-action: How? 1) Buy a put to sell pounds sterling in one year at a strike price = to conversion price they anticipate when make K (probably conversion rate). A) Thus, if value of pounds to $$ decreases, they excercise put and get the conversion rate anticipated in K. 1. Actually they realize a gain in put and convert rest at market price to make it + to original conversion rate. a) This may lead to capital gains tax but usually done w/ futures K which wouldn‟t and is also cheaper than put/call. B) If value of pounds to $$ increases, they throw put away and convert pounds to $$ in market and get more $$ than they thought they would. 2) Buy a call to buy $$ at anticipated conversion rate. A) Thus, if value of pounds to $$ decreases, they excercise call. B) If value of $$ to pounds decreases, they throw away call and convert in market and get more $$ than thought they would. 3) Note: writer of puts/calls is taking on risk. 12. Pricing options: A. Puts are priced by first pricing call and using put-call parity equation. 1) Call price - put = stock price - PV (at risk free rate) of strike price. 2) If above equation wasn‟t right there would be huge arb opportunities which we know don‟t exist: option models better than stock models. B. Black-Scholes: can look at option valuation as series of future events buying stock w/ debt. 1) Many assumptions needed but can adjust for some and still works well. 2) Only factor not observable in market is volatility. 3) Doesn‟t depend on expected return of stock. 4) #2 and more liely #3 may explain why option pricing better than stock. 13. Firm expressed as an option: a limited liability firm w/ debt has actually has a payoff structure that resembles either a put or call. A. Thus, SH value may increase as risk increases. 1) This cuts directly against CAPM. 2) One would assume then that SHs would vote for inordinate amount of risk and kill bondholders but empirical studies show otherwise. A) I say if did so, would never get loans in future. 3) Further, bond value must decrease as stocks increase. 4) We look to LBO t-actions and how stock price goes up even though take on large amounts of risk. 27 A) Counter: stock value increases b/c LBO make people think cash flow would increase. B. This is cuting edge, wherther it says firms are undervalued or that EMH has taken this factor into account is unclear. C. Inflection point is at net assets = 0 not at strike price. D. If assets increase, SH excercise call and keep stock. E. If assets decrease below 0, SHs walk away from calls. 1) Can also see this as having covered put. F. Debt holders value of risky bond = value of default free bond (liabilities) - put value (written to SHs which allow them to put assets when net assets < or = 0. 1) Thus real world bond payoff graph looks like a seller of put (see notes). 2) Can also be written: value of firm - value of call (written to SH) = value of risk bond. A) This payoff graph looks like a covered call. 3) Given put-call parity, 2 above equations are =. G. CAPM vs. APT: APT may actually measure negative part of stock curve whereas we know CAPM doesn‟t. 1) APT may pick some up in measuring stock sensitivity to changes in interest rates, differences in long/short term rates etc. H. Firm as a call: bondholder (BH) own firm; liabilties of firm are 800$ and BH write a call to SH w/ X price of 800$. 1) If cash flow greater than 800$, SH excercise call and BH get $800. 2) If cash flow 800$ or less, SH walk away from call and BH get any cash flow 800$ and under. I. Firm as a put: SH own firm; liabilities 800$ and BH write put to SH w/ X price at 800$. 1) If cash flow greater that 800$, SH walk away from put and pay off 800$ seperately to extinguish debt. 2) If cash flow 800$ or less, SH excercise put and sell firm to BH for 800$ but since they owe BH 800$, no money changes hands. 28