Risk and Return. Gestão Financeira II Undergraduate Courses Gestão Financeira II Licenciatura Clara Raposo

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1 Risk and Retun Gestão Financeia II Undegaduate Couses Claa Raposo

2 Outline Common Measues of Risk and Retun Histoical Retuns of Stocks and Bonds Histoical Tadeoff between Risk and Retun Claa Raposo

3 Retuns How do me measue the etun fom investment in one asset? We compae initial value of the investment in the asset with the final value, at the end of the investment peiod. Fo Stocks we have: Dolla etun: Pt Dt Pt Pecentage etun: Pt Dt t whee Pt Pt P t : pice at beginning of peiod P t+ : pice at end of peiod : dividend (cash flow paid duing peiod D t+ Claa Raposo

4 Retuns: Example Suppose you bought 00 shaes of Wal-Mat one yea ago at $25. You eceived $20 in dividends (20 cents pe shae 00 shaes. At the end of the yea, stock sells fo $30. How well did you do? Investment $25 00 = $2,500; At the end of the yea, stock is woth $3,000 and dividends of $20 Dolla etun: 520 = 20 + (3,000 2,500 Pecentage etun: t 3, ,500 2, % 20% 0.8% Claa Raposo

5 Holding Peiod Retuns The holding peiod etun is the etun that an investo would get when holding an investment ove a peiod of n yeas (assumes immediate einvestment of dividends: Holding peiod etun ( ( ( 2 n whee i is the etun duing yea i Claa Raposo

6 Holding Peiod Retuns: Example Suppose you investment povides the following etuns ove a fou-yea peiod: Yea : 0% Yea 2: -5% Yea 3: 20% Yea 4: 5% Holding peiodetun (. ( ( 2 n % Claa Raposo

7 Aveage Retun Aithmetic aveage: etun eaned in an aveage yea ove a paticula peiod Geometic aveage: aveage compound etun pe yea ove a paticula peiod Geometic aveage will be less than the aithmetic aveage unless all the etuns ae equal Which is bette? Geometic aveage is an excellent measue of past ealized pefomance and good estimate of annual etun to be obtained ove extended peiods of time in the futue Aithmetic aveage is best estimate of the expected etun in a single peiod in the futue Claa Raposo

8 Aveage Retun: Example What is the geometic aveage etun? ( 4 ( ( 2 ( 3 ( % So, ou investo made an aveage of 9.58% pe yea, ealizing a holding peiod etun of 44.2% Aithmetic aveage etun is highe: 0% ( 5% 4 20% 5% 0% Claa Raposo

9 Retun Statistics Histoy of capital maket etuns can be summaized by descibing the: aveage aithmetic etun 2 T standad deviation of those etuns T Va ( 2 ( 2 2 T ( T 2 the fequency distibution of the etuns Claa Raposo

10 Retun Statistics Histoical ates of etuns on common stocks, bonds, and Teasuy bills (Ibbotson and Sinquefeld. Yea-by-yea histoical ates of etun stating in 926 in the United States: Lage-company Stocks Small-company Stocks Long-tem Copoate Bonds Long-tem U.S. Govenment Bonds U.S. Teasuy Bills Claa Raposo

11 Histoical Retuns U.S Aveage Standad Seies Annual Retun Deviation Distibution Lage Company Stocks 2.3% 20.2% Small Company Stocks Long-Tem Copoate Bonds Long-Tem Govenment Bonds U.S. Teasuy Bills Inflation % 0% + 90% Souce: Stocks, Bonds, Bills, and Inflation 2006 Yeabook, Ibbotson Associates, Inc., Chicago (annually updates wok by Roge G. Ibbotson and Rex A. Sinquefield. All ights eseved. Claa Raposo

12 Cumulative Retuns U.S Claa Raposo

13 Risk Pemium Risk Pemium is the added etun (ove and above the isk-fee ate esulting fom beaing isk Stock makets offe long-un excess of stock etun ove the isk-fee etun: Aveage excess etun fom lage company common stocks: 8.5% = 2.3% 3.8% Aveage excess etun fom small company common stocks: 3.6% = 7.4% 3.8% Aveage excess etun fom long-tem copoate bonds: 2.4% = 6.2% 3.8% Given the supeio pefomance of stocks ove such long peiod, why does anyone hold bonds? Claa Raposo

14 Annual Retun Aveage Risk-Retun Tade-off 8% 6% Small-Company Stocks 4% 2% Lage-Company Stocks 0% 8% 6% 4% 2% T-Bonds T-Bills 0% 5% 0% 5% 20% 25% 30% 35% Annual Retun Standad Deviation Claa Raposo

15 Risk Risk is uncetainty about the futue Stocks do bette on aveage, but investos know that in any yea, stocks may do much wose Summaize isk though standad deviation, σ, a measue of dispesion Standad Deviation Stocks 20.2% T-bills 3.% Long-tem Govenment Bonds 9.2% Copoate Bonds 8.5% Inflation 4.3% Souce: Ibbotson, CRSP 5 Claa Raposo

16 Nomal Distibution Suppose stock etuns ae nomally distibuted Pobability Pobability that a yealy etun will fall within 20.2% of the mean of 2.3% will be appoximately 68% [-7.9%, 32.4%] % 2 28.% 7.9% 0 2.3% 68.26% % % % Retun on lage company stocks 95.44% 99.74% 6 Claa Raposo

17 What about the Futue Retuns and Risk? No one knows the futue, but we fom expectations about it. We will want a measue of Expected Retun, based on pobability distibutions: Expected Retun E R PR R R We will want a measue of Expected Risk, such as the Vaiance o the Standad Deviation of Expected Retuns: 2 2 Va( R E R E R P R R R E R SD( R Va( R In the end, we typically use past (histoical etuns to pedict the futue. We ll see moe when pesenting potfolios. Claa Raposo