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# Introduction to Finance UGBA 103

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This 7 page Class Notes was uploaded by Melba Champlin on Thursday October 22, 2015. The Class Notes belongs to UGBA 103 at University of California - Berkeley taught by J. Berk in Fall. Since its upload, it has received 25 views. For similar materials see /class/226751/ugba-103-university-of-california-berkeley in Business Administration at University of California - Berkeley.

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Date Created: 10/22/15

CA PM RonMW You cannot change sections Wharwouldxhappm fwa addedwrmam I Assume the riskless return is 5 We could take combinations of any portfolio on the frontier with the riskless asset mm W Expected Return E 54 8 U1 a M aowvVMLOvnw Ef cient 77on p E 75 5 2quot Tangency Portfolio Q 39 5 3 15 39 0 3 i 5 ShwpaRafw I The Sharpe Ratio is Excess Return E R Ff Volatility 61 I Fact The tangency portfolio has the maximum Sharp Ratio of any portfolio or stock in the economy Towng PatWW WMowwmabShwpaRafm Eff F m TangencyPortfolio r quot5 x f i 5 to is 20 30 W Ma a 0 6 5 Recoilb owvlaxfleotwa I The expected return of a portfolio is just the weighted average return I The standard deviation of a portfolio is NOT the weighted average standard deviation it is SD RP039P ExiGiCorrRPR Now how doI know ofpr I If I cannot raise the Sharpe ratio that is by adding any stock to the portfolio the Sharpe ratio cannot go up so that means I Portfolio P is the tangency portfolio if for every stock in the economy ERirf ltERPrf 6C0rrRRP 0391 Whataboutaytodo already powt of tatW portfolio I If ERirf ltERPrf sparrow up You can raise the Sharpe ratio by selling some ofi I But if ERirf gtERPrf GiCorrRRP 039 You can raise the Sharpe ratio by buying some ofi I SO ERirf ERPrf G 39C0 RiaRp 6 P For EVERY stock in the portfolio and if you allow short sales for every stock in the world 8 RWV aW Termy Uri09075720510 I For ANY stock or marketed investment 139 and rf w ERP rf tangency portfolio P P P zoiopcoltampaRPgtERP1 rf EtRiJ rf B ERP rf P Where C0VR12399RP ERPrf C0VRiRP 6P 1 612 Q Do you recognize this definition of 3 1quot C0 OfCathwLofPrqy eot with CoatofCap tal beta3P I Recall that the cost of capital of a project is the expected return of a marketed P investment opportunity an opportunity r rf Bi Ia trading in a NORMAL market of the same risk that is that has the same BETA I To calculate beta we need to identify the tangency portfolio I Why not just calculate means and standard deviations draw the frontier and locate the tangency portfolio I So you can calculate the cost of capital of any project by just calculating the expected return of a portfolio of the same beta as project SW14me I Markets are Competitive I People only hold Efficient Portfolios I People have the same expectations regarding volatilities correlations and expected returns I Is this last assumption realistic Sharpe wa I Two facts I Everybody s portfolio is a combination of the tangency portfolio and the riskless asset I The sum of everybody s portfolio of risky assets is the portfolio of all risky assets the market portfolio I This implies that everybody must be holding the market portfolio because I Everybody holds the same portfolio I Sum of everybody s portfolio is the marlllt4et CAPM BEE F bl 520 MarketPortfolio 15 g i f 39 CAPM 1011301ng Relatwa ERir BiERm1r 6 where Bi 3 6 m SeemEly Market LawW CapotaLMMketh A4 A few quasi Lam I What is the expected return of a stock with lt0 I What is the expected return of a stock with i0 I So you are telling me that you could have a choice between a risky stock that earns less than the riskless rate and the riskless asset itself and you would choose the risky stock 18 I Mainow I What does a risky stock give you that the I39iskless asset does not give you I Insurance I What would you rather have I stock that pays o in good times and not in bad times I Stock that pays offin bad times but not in good times I This is the fundamental insight of the CAPM Intuitoow Comfab I You only get rewarded for holding systematic risk because you can always get rid of unsysternatic risk for free by just diversifying I This is like fire insurance I Think of the dice example Genet0w I People only pay for risk that is economy wide I The reason why is risk that is not economy wide or idiosyncratic can be gotten rid of in a fair trade I In equilibrium everybody trades all this risk things like fire insurance and what is left over is risk that cannot be traded away systematic risk 21 ArtExample I Your father39s retirement savings are invested as follows 30000 in 1 month T Bills yielding 5 and 70000 in IBM stock He was wondering if your degree had any use so he asked you for your advice You decide you have no choice but comply and you are going to base your analysis on the CAPM AriWig comfob I What is IBM s beta and standard deviation I What is the expected return on your father s portfolio I What is the standard deviation of the portfolio I Can you do better I I At the time the model was derived it had a huge impact because it appeared to have the following implications I TestableHH I To price assets you did not have to know anything about fundamentals chtLeotwa I Topic I Finish Risk and Return I Chapter 13

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