Return and Risk Notes
Return and Risk Notes FIN 302
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This 5 page Class Notes was uploaded by Quinn Shapiro on Monday October 19, 2015. The Class Notes belongs to FIN 302 at Arizona State University taught by Dr. Luke Stein in Summer 2015. Since its upload, it has received 28 views. For similar materials see Managerial Finance in Finance at Arizona State University.
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Date Created: 10/19/15
Return and Risk 0 Quantify return quantify risk and find difference 0 Returns 0 Returnsrisks of single assets vs returnrisk on portfolio I To get portfolio return you need returns on each individual investment I For risk you need to know individual and how they work 0 Returns in the past on a single investment 0 Can be expressed in 1 Dollars or 2 Rate S earnedamount invested 0 Ex 22020020 earned end pricebeginning price I Earn 20 in appreciation Capital Gain 0 Also get dividend add 10 to 22020030 I 30 is realized return in dollars dividend Capital gain I Remember opportunity cost 0 Percentage always percent of price paid at beginning I 3020015 I 102005 from dividendsdividend yield I 2020010 from capital gaincapita gain yield I Price endPrice beginningPrice beginning I Price endPrice beginning1 0 Historical Average Return 0 2 investment 4 years of data for each 0 Method 1 for Average Arithmetic method I Sum return over 4 years for each I Divide by 4 n periods Basis points1001 Arithmetic can skew returns 50 gain 1 year and 50 loss next year you lost 2500 but return using arithmetic is 0 0 Method 2 Geometric Ave Rate of Return I For the growth rate I Average Returns and Compounding I Tells you how much you have over 4 years I At t0 10000 1 Rate of Return 10 I T1 11000 1RoR of 7 I T2 10230 128 I T3 I T4 10000119312889 value at year 4 1165402 I Annual Rate of Return think of it as single pmt security where you invest 10k and 4 years later you have 1165402 0 PV10k FV1165402 n4 solve for 0 39 geometric average rate of return 0 Anything with a 0 arithmetic average is going to have a negative geometric average 0 Geometric rate ALWAYS lt Arithmetic 0 Not one is better good for answering different questions Use Arithmetic return for next year more useful for short term using historical Use Geometric mutiyear horizon more useful for longterm using historical because it takes compounding into account Historical Volatility 0 Sum returns gets 5 arithmetic RoR 0 Then for each period subtract the average from the return that we observed in order to get a deviation I Ex in year 1 10 return subtract 5 avg so deviation is 5 Add up all deviations and needs to be ZERO Average 1n sum of x Deviationssome will be neg some will be pos so the deviation total is zero Then square each of the deviations I 0025 25 basis point I 0144144 basis point 0 Calculate mean calculate deviations square deviations sum square deviations and divide by n1 gives you variance then take the square root of variance to get SD 0000 I Why n1 0 Looking at graph safe investments linear riskier investment are volatile upampdown on graph 0 Over 4 years but only 3 arrows on graph number of deviations we are are 1 fewer than the years of returns 0 Degrees of freedomnumber of red arrows I Why square SD Can read off graph which geometric rate of return was highest for each line Global financial market mean is 98 96 101 93 respectively Returns on many investments are approximately normally distributed 0 No maximum on investment return and typically not zero o If you draw distribution of Reutns the slopes each year some may have negative returns and some have positive and distribution gets pretty close to normal 0 Ex investment with lage stocks we get geometric ave return of 98 and SD of 20 I About 13 of time will be btw 1 SD and mean 13 will be btw mean and 1 SD in other direction SD of daily stock returns is about 1 on individual investment Expected return Divide things up into states 0 Good10 o Neutral2 o Bad8 Then find probability of each state States have to be mutually exclusive and probabilities have to add up to 100 o How confident we are how big the spread might be around the mean using SD or variance 0 Risks you can diversify away are IDIOSYNCRATIC o Tend to be risk that jus affect one particular investment 0 Positiverealy good or really bad for both 0 Negativereally good for one and really bad for other 0 Positive correlation going to come from positive covariance and neg correlation comes from neg cova ance 0 Pos correlation means no benefit from diversification o Neg correlation means good benefit from diversification 0 Risk on your portofilio is never equal to weighted average of risk of individual assets in portfolio o Is always less than or equal to weighted average due to diversification 0 Correlation is covariance divided by 0 Correlation coefficient always in range of 1 to 1 1 is perfectly correlated o The more positively correlated they are the less diversification you get o If perfectly correlated 1you would have no benfit from diversifciatoin o If you have investments perfectly negatively correlated umbrella and parasol the more benficial diversification is 0 Square wight of asset 1 square SD of asset 1 square weight of asset 1 Square SD of asset 2 o If rho 1 all assets move in same direction no benefit from diversification 0 Portfolio insurance invest in airline and oil comp as oil prices go up stock of airline decrease but stock of oil comp increases Evens out o nt equity tends to have higher returns and associated higher risk as well 0 Example 0 Challenge isn t maximizing returns it is minimizing risk while still giving you good returns 0 One main shortcoming of this tool is that is only works with two investments Beyond two investments requires technology 0 What happens with more than two investments 0 No formula just point towards intuitive aspects 0 Going from 2 investments to a lot of investments 0 When you invest in lots of things you are able to avoid lots of risks 0 Not just by things that are negatively correlated but by not putting a lot of money in any one of those assets Smaller amounts in lots of assets 0 The more things you invest in the smaller your returns may be but your probability of a return is higher 0 New slide 0 Portfolio with many assets 0 With appropriate diversification you can lower portfolio risk I Assets less than perfectly correlated I Many risks don t affect all firms 0 Risks can be eliminated by diversification idosyratic risks are not necessarily rewarded in the financial market place I Bc some things only affect some firms With more than two assets you can put smaller amount of money in each asset With two you have to have half your money in each but with multiple you can minimize your exposure to risks 0 Example Car Companies 0 Only one company can succeed if you put money in comp that succeeds you double your money If you invest in loser 0 S return 0 As you spread your investment across more firms you raise the probability that one will succeed but you decrease the amount by which you succeed o The more you diversify the more stocks you buy the greater to chance of you winning but the smaller the return 0 Idiosyncratic only ones that apply to onlyi that given firm or industry I Is mngt good or bad labor strikes etc o Betaway of measuring how much systematic risk a firm is exposed to 0 Home Depot Example Time series data on market and individual investment When the market does well home depot generally does well When market does poorly HD generally does poorly Had correlation coefficient here we use market data for 1 of 2 assets and use linear regression or OLS ordinary least squares regression and then check slope 0 Negative beta commodity like gold people buy when they are nervous I But almost every investment has a positive beta 0 Beta is slope coefficient on market returns and firm 0 EX ON SLIDES I Apple beta is 29 so when market goes up apple increase by about 3 but when market goes down apple decreases by almost 30 I Engery companies lower beta People tend to demand more energy when market is up 0 Risk Free Asset putting your money in bank or buyind bonds from really safe govt that is def gunna pay you back 0 Market goes up get return Market goes down nothing happens 0 Beta of 0 o No systematic risk 0 Market portfolio put your money in the market little bits of money in every possible 0000 investment o If SampP goes up 10 your portfolio goes up 10 0 Beta of 1 0 Beta is measure of risk anything with beta of less than 1 is safer than market 0 An investor who holds everything in one portfolio 0 CAPM tells us the relationship btw betas and expected returns Description of the risk return tradeoff Should earn higher returns if willing to tolerate higher risk 0 CAPM says if two investments have the same beta they are going to have the same expected return 0 Everyone wants low beta stocks so there is a lot of competition I If everyone wants to buy then the price goes up I And if the price today goes up the expected return goes down 0 Price tomorrow price today dividends price today price tomorrow price today dividends 1 o If price today goes up bc everyone wants it that means the return bc its in the denominator is going to go down 0 High beta will make portfolio riskier bc contributes less to diversification less ppl want them so price is low so they earn high expected returns 0 Not every asset with beta of 0 is risk free bc it may have idiosyncratic risk 0 CAPM says same data same expected return 0 Anything with beta 0 Errisk free rate 0 Aren t compensated for idiosyncratic 0 Can invest in whole market broad diversified basket 0 Beta is ogoing to be 1 o CAPM says if you tell me beta I can tell you expected return