Class 9 Financial Management, 15 - MIT OpenCourseWare
Risk and return (1)Class 9Financial Management, 15.414
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9TodayRisk and return Statistics review Introduction to stock price behaviorReading Brealey and Myers, Chapter 7, p. 153 – 165
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Road mapPart 1. ValuationPart 2. Risk and returnPart 3. Financing and payout decisions3
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Cost of capitalDCF analysisNPV CF0 CF1CF2CF3CF4CF5 .2345(1 r) (1 r) (1 r) (1 r) (1 r)r opportunity cost of capitalThe discount rate equals the rate of return that investors demandon investments with comparable risk.QuestionsHow can we measure risk?How can we estimate the rate of return investors require forprojects with this risk level?4
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9ExamplesIn November 1990, AT&T was considering an offer for NCR, the5th largest U.S. computer maker. How can AT&T measure therisks of investing in NCR? What discount rate should AT&T use toevaluate the investment?From 1946 – 2000, small firms returned 17.8% and large firmsreturned 12.8% annually. From 1963 – 2000, stocks with highM/B ratios returned 13.8% and those with low M/B ratios returned19.6%. What explains the differences? Are small firms with lowM/B ratios riskier, or do the patterns indicate exploitable mispricingopportunities? How should the evidence affect firms’ investmentand financing choices?5
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9BackgroundThe stock marketPrimary marketNew securities sold directly to investors (via underwriters)Initial public offerings (IPOs)Seasoned equity offerings (SEOs)Secondary marketExisting shares traded among investorsMarket makers ready to buy and sell (bid vs. ask price)Market vs. limit ordersNYSE and Amex: Floor trading w/ specialistsNASDAQ: Electronic marketCombined: 7,022 firms, 11.6 trillion market cap (Dec 2002)6
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9BackgroundTerminologyRealized returnrt Dt Pt Pt -1 D t Pt Pt -1 Pt -1Pt -1Pt - 1(DY cap gain)Expected return best forecast at beginning of periodE[rt] E[D t ] E[Pt Pt -1 ]Pt -1Risk premium, or expected excess returnRisk premium E[rt] – rf7
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Statistics reviewRandom variable (x)Population parametersmean µ E[x]variance σ2 E[(x – µ)2], standard deviation σskewness E[(x – µ)3] / σ3Sample of N observations1x i iN12sample variance s2 , standard deviation s(x x) iiN-1sample mean x sample skewness8
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Example0.45µ 0, σ 1, skew 00.360.270.18µ 0, σ 2, skew 00.090.00-6.0 -5.0 -4.0 -3.0 -2.0 -1.00.01.02.03.04.0[Probability density function: shows probability that x falls in an given range]95.06.0
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Example0.24µ 0, σ 2, skew 1.30.18µ 0, σ 2, skew 00.120.060.00-6.0 -5.0 -4.0 -3.0 -2.0 -1.00.0101.02.03.04.05.06.0
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Statistics reviewOther statisticsMedian50th percentile: prob (x median) 0.50Value-at-Risk (VaR)How bad can things get over the next day (or week)?1st or 5th percentile: prob (x VaR) 0.01 or 0.05‘We are 99% certain that we won’t lose more than Y in the next24 hours’11
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Example0.24µ 0, σ 2, skew -1.30.180.12meanmedian0.060.00-5.05th pctile-4.0-3.0-2.0-1.00.0121.02.03.04.05.0
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Statistics reviewNormal random variablesBell-shaped, symmetric distributionx N(µ, σ2)x is normally distributed with mean µ and variance σ2‘Standard normal’mean 0 and variance 1 [or N(0, 1)]Confidence intervals68% of observations fall within /–1 std. deviation from mean95% of observations fall within /–2 std. deviations from mean99% of observations fall within /–2.6 std. deviations from mean13
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Example0.50N(0, .04.0
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Statistics reviewEstimating the meanGiven a sample x1, x2, , xNDon’t know µ, σ2 estimate µ by sample average xestimate σ2 by sample variance s2How precise is x ?std dev (x ) s / N95% confidence interval for µx –2sNxx 215sN
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9ApplicationFrom 1946 – 2001, the average return on the U.S. stock market was0.63% monthly above the Tbill rate, and the standard deviation ofmonthly returns was 4.25%. Using these data, how precisely can weestimate the risk premium?Sample: x 0.63%, s 4.25%, N 672 monthsStd dev ( x ) 4.25 / 672 0.164%95% confidence intervalLower bound 0.63 – 2 0.164 0.30%Upper bound 0.63 2 0.164 0.96%Annual ( 12):3.6% µ 11.5%16
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Statistics reviewTwo random variablesHow do x and y covary? Do they typically move in the samedirection or opposite each other?Covariance σx,y E[(x – µx)(y – µy)]If σx,y 0, then x and y tend to move in the same directionIf σx,y 0, then x and y tend to move in opposite directionsσ x, ycovariance Correlation ρx,y stdev x stdev y σ x σ y-1 ρx,y 117
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Correlation34ρ 0ρ 340123400-3211-41-2-2ρ .80-14-40123-3-2-1-14-2-2ρ –.5-3-4-3-418
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Properties of stock pricesTime-series behaviorHow risky are stocks?How risky is the overall stock market?Can we predict stock returns?How does volatility change over time?19
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Stocks, bonds, bills, and inflationBasic statistics, 1946 – 2001Monthly, %SeriesAvgStdevSkewMinMaxInflationTbill (1 yr)Tnote (10 yr)VW stock indexEW stock 73-22.49-27.09-33.491.851.3413.3116.5629.9241.6720
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Stocks, bonds, bills, and inflation, 1 in 194610000cpitbill10 -77Dec-85Dec-93Dec-01
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Tbill rates and inflation20%InflationTbill ar-96
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 910-year Treasury Jan7123Jan76Jan81Jan86Jan91Jan96Jan01
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9U.S. stock market returns, 1946 – an66Jan7124Jan76Jan81Jan86Jan91Jan96Jan01
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Motorola monthly returns, 1946 – 200125%20%15%10%5%0%-5%-10%-15%-20%-25%25
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9U.S. monthly stock eturn269%15%21%27%
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Motorola monthly eturn279%15%21%27%
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Scatter plot, GM vs. S&P 500 monthly returns25%correlation %
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Scatter plot, S&Pt vs. S&Pt-1 daily2.0%correlation 5%
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Scatter plot, S&Pt vs. S&Pt-1 monthly20%correlation %
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Volatility of U.S. stock market30%Monthly standard deviation25%20%15%10%5%0%Jan 26Jan 36Jan 46Jan 56Jan 66Jan 76[Monthly std dev std dev of daily returns during the month 21 ]31Jan 86Jan 96
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Properties of stock pricesCross-sectional behaviorWhat types of stocks have the highest returns?What types of stocks are riskiest?Can we predict which stocks will do well and which won’t?32
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Size portfolios, monthly returnsAvg returns (% monthly)1.401.201.000.800.600.40Small2345678Firms sorted by market value (deciles)339Big
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Size portfolios in January9%Avg returns (% monthly)8%7%6%5%4%3%2%1%0%Small2345678Firms sorted by market value (deciles)349Big
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9M/B portfolios, monthly returnsAvg returns (% s sorted by Mkt / Bk equity (deciles)359High
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Momentum portfolios, monthly returnsAvg returns (% ms sorted by past 12-month return (deciles)36High
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Time-series propertiesObservationsThe average annual return on U.S. stocks from 1926 – 2001was 11.6%. The average risk premium was 7.9%.Stocks are quite risky. The standard deviation of monthlyreturns for the overall market is 4.5% (15.6% annually).Individual stocks are much riskier. The average monthlystandard deviation of an individual stock is around 17% (or 50%annually).Stocks tend to move together over time: when one stockgoes up, other stocks are likely to go up as well. The correlationis far from perfect.37
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Time-series propertiesObservationsStock returns are nearly unpredictable. For example,knowing how a stock does this month tells you very little aboutwhat will happen next month.Market volatility changes over time. Prices are sometimesquite volatile. The standard deviation of monthly returns variesfrom roughly 2% to 20%.Financial ratios like DY and P/E ratios vary widely over time.DY hit a maximum of 13.8% in 1932 and a minimum of 1.17% in1999. The P/E ratio hit a maximum of 33.4 in 1999 and a minimum of 5.3 in 1917.38
MIT SLOAN SCHOOL OF MANAGEMENT15.414Class 9Cross-sectional propertiesObservationsSize effect: Smaller stocks typically outperform larger stocks,especially in January.January effect: Average returns in January are higher than inother months.M/B, or value, effect: Low M/B (value) stocks typically outperform high M/B (growth) stocks.Momentum effect: Stocks with high returns over the past 3- to12-months typically continue to outperform stocks with low pastreturns.39
15.414 Class 9 Application From 1946 – 2001, the average return on the U.S. stock market was 0.63% monthly above the Tbill rate, and the standard deviation of monthly returns was 4.25%. Using th
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SECTION - B : FINANCIAL MANAGEMENT Study Note 3 : Overview of Financial Management 3.1 Objective of Financial Management 3.1 3.2 Key Decisions of Financial Management 3.5 3.3 Planing Environment 3.6 3.4 Functions of Financial Management 3.7 3.5 Sources of Finance 3.9 3.6 International Sources 3.13 3.7 Emerging Role of Finance Manager 3.23
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Chapter 14. 14-2 14,500' MSL Nontowered airport with instrument approach Nontowered airport with no instrument approach 700' AGL 700' 18,000' MSL FL 600 1,200' AGL 700' AGL 1,200' 1,200' Class A Class B Class C Class D Class E Class G Class G Class G Class G Figure 14-1. Airspace profile. Controlled Airspace
