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This 0 page Class Notes was uploaded by Heaven Gleichner I on Monday November 2, 2015. The Class Notes belongs to FIN4310 at California State University - East Bay taught by EricFricke in Fall. Since its upload, it has received 9 views. For similar materials see /class/234360/fin4310-california-state-university-east-bay in Finance at California State University - East Bay.
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Date Created: 11/02/15
Investments Risk and Returns Part Chapter 5 f Outline Measuring returns Historical returns 1 Measuring risk 7 Portfolio returns and risk Modern portfolio theory Investments Measuring Returns and Risk f Holding Period Returns Returns over a single time period P1P0D1 Po 1quot where r holding period return P1 beginning price time 0 P2 ending price time 1 D1 cash dividend during the period Investments Measuring Returns and Risk f Arithmetic Mean Return K Simple average over multiple periods Gives you expected return for a period Znggnmg Zn 7 n n where rt holding period return in period t n number of periods Investments Measuring Returns and Risk Geometric Mean Return 0 Compound average return assuming one initial investment and reinvestment of dividends o Calculates investment growth over time Investments Measuring Returns and Risk 5 Dollar Weighted Return Compound annual return assuming cash inflows and outflows Same as internal rate of return IRR 0CFO CE CF2 2 1IRR 1 IRR K Investments Measuring Returns and Risk 1IRRn Beardstown Ladies 7 x u r quotwrume W mams vm nun mm was w w wmza Investments Measuring Returns and Risk MultiPeriod Returns Example You invest 10 in a fund which returns 10 25 20 and 25 over the next three years At the end of the first year you plan on investing an extra 01 at the end of the second year you invest an extra 05 at the end of the third year you withdrawal 08 and at the end of the fourth year you withdrawal the entire account balance Calculate arithmetic geometric and dollar K weighted returns Investments Measuring Returns and Risk 8 MultiPeriod Return Example Beginning 10 Assets Holding 10 25 20 25 penod returns Assets after returns Investment 01 05 08 00 withdrawals Ending Assets Investments Measuring Returns and Risk Expected Returns To make estimates of future or expected returns Er two common methods are Arithmetic mean return Err1 r2 rnn Scenario returns Er p1r1 p2r2 p3r3 Where pt probability of scenario t occurring r1 returns in scenario t all p s must add up to 1 K Investments Measuring Returns and Risk 10 f K Scenario Returns Example 7 Develop a forecast of future stock returns assuming a 10 chance the economy goes into recession where returns will be 25 a 70 chance the economy will remain steady where returns will be 5 and a 20 chance the economy goes into a boom where returns will be 30 Investments Measuring Returns and Risk Annualized Returns Convert returns over any time period to annual returns r r periods year 1 period What is the annualized return for a 3 month treasury bill with a 12 return K Investments Measuring Returns and Risk 12 Measuring Risk Risk measured as sample variance 02 or sample standard deviation 0 of returns 2 2 r1 172 r2 172 rT 172 0 T l 0r1 172r 7392I39T 72 T l K Historical Returns Inflation Investments Measuring Returns and Risk Geom Arith Stan Series Mean Mean Dev World Stk 941 1117 1838 US Lg Stk 1023 1225 2050 US Sm Stk 1180 1843 3811 Wor Bonds 534 613 914 LT Treas 510 564 819 TBills 371 379 318 298 312 435 Distribution of Returns Small company stocks Geometric Mean 1180 Arithmetic Mean 1843 40 Standard Deviation 3811 90 60 30 0 30 60 90 Large company stocks Geometric Mean 1023 Arithmetic Mean 1225 quot quot quot 39 quot quot quot quot Standard Deviation 2050 H i H 0 90 450 30 0 30 60 90 Investments Measuring Returns and Risk Distribution of Returns Geometric Mean 510 Arithmetic Mean 564 Standard Deviation 819 Geometric Mean 2 371 Arithmetic Mean 379 Standard Deviation 318 Longterm gov t bonds 30 0 30 60 90 Treasury bills 90 60 3D 0 30 60 90 Investments Measuring Returns and Risk Time Series of Returns 500A 30 32 E e 3 10 E 5 39 139 53 10 4 m a 30 Stocks Tabonds T bills 50 1 1926 1936 1946 1956 1966 1976 1986 1996 2006 Investments Measuring Returns and Risk 17 Portfolio Return Two Assets Portfolio return is the weighted average of the rates of return of each asset comprising the portfolio with the portfolio proportions for each asset as weights Portfoliv Return rp H t K w1 Proportion of funds in Security 1 w2 Proportion of funds in Security 2 1 w1 r1 Return on Security 1 r2 Return on Security 2 Investments Measuring Returns and Risk 18 Portfolio Variance Two Assets Where 03912 Variance of Security 1 03922 Variance of Security 2 Covr1r2 Covariance of returns between Securities 1 and 2 Investments Measuring Returns and Risk Covariance and the Correlation Coefficient where p12 Correlation coefficient between 1 and 2 10 S p S 10 If p 10 securities perfectly positively correlated If p 10 securities perfectly negatively correlated 55Xlr i N 6 i I i l L Investments Measuring Returns and Risk 20 Portfolio Example Assume Microsoft has a Er20 and 039 30 and GE has a Er10 and 039 20 The correlation coefficient between the two returns What is the expected return and standard deviation of a portfolio investing 80 in Microsoft and 20 in GE is 30 Weights Mean Std Dev MSFT 8000 2000 3000 GE 20 10 20 Portfolio 100 Investments Measuring Returns and Risk Portfolio Risk and Asset Correlations Returns 20 MSFT 39 39 39 39 39 39 39 39 39 39 39 39 39 I 20 GE amp I 80 MSFT I I 10 r GEI 5 I l Std Dev K 20 30 Investments Measuring Returns and Risk 22 f Portfolio Example Now recalculate the portfolio return standard deviations assuming the correlation equals 00 and 10 Weights Std Dev Std Dev p 10 p 10 MSiT 80 30 30 GE 20 20 20 Portfolio 100 Investments Measuring Returns and Risk Portfolio Risk and Asset Correlations Returns The smaller the correlation p the greater the risk reduction potential 20 I I 10 I I 39 Std Dev K 20 30 Investments Measuring Returns and Risk 24 Country Correlations TAB LE 2539quot Sample Period monthly excess return in US Correlation of US 2001 2005 19962000 19911995quot 19701989 equity returns with country equity World 95 92 64 86 returns Sweden 89 60 42 38 Germany 85 66 33 33 France 83 63 43 42 United Kingdom 82 77 56 49 Netherlands 82 63 50 56 Australia 81 64 36 47 Canada 80 79 49 72 Spain 78 59 51 25 Hong Kong 75 63 33 29 Italy 75 44 12 22 Switzerland 73 56 43 49 Denmark 74 56 36 33 Norway 70 58 50 44 Belgium 56 49 54 41 Japan 43 54 23 27 Austria 40 53 19 12 Source Datastream MSource Campbell R Harvey quotThe World Price of Covariance Riskquot Journal of Finance March 1991 Investments Measuring Returns and Risk f Portfolios with Many Assets Portfolio return N rp Zwiri i1 Portfolio return variance N of Z WiZO39i2 i1 iJ1i J Investments Measuring Returns and Risk i w w COVi 26 Three Asset Portfolio Variance oi wfof wjof W320quot W wz Cov 12 w1w3C0v13 w w1C0v21 w W C0v23 w2w1C0v31 w W C0v32 039 w1203912w 3922w3203932 2w1w2 C0v12 2w1w3C0v13 2w2 W3 C0v23 K Note Covij Covji for example Cov12 Cov2 1 Investments Measuring Returns and Risk 27 Portfolio Risk and Number of Assets 2i 9 c E 9 E E 50 1003 5 i5 3 40 45 g g 30 g g 5CI o I 20 uh 40 m 9 2 Hg 10 8 0 I I I I I I I I I I I I l l I I I l I l I I I I l I I I IV 0 5 Number of stocks In portfolio Investments Measuring Returns and Risk I 00 K Portfolio Risk and Diversification 7 Unique risk Market risk B Market and unique risk Investments Measuring Returns and Risk Unigue risk Firmspecific diversifiable or nonsystematic Market risk Beta Systematic or Non diversifiable 29 Efficient Frontier Generate all possible portfolios using different security weights Some portfolios dominated by others higher return for the same risk lower risk for the same return The efficient frontier is made up of only dominant portfolios Efficient mean variance efficient Optimize both mean returns and variance of returns K Investments Measuring Returns and Risk 30 Efficient Frontier Er Efficient frontier Global Individual minimum Assets and portfolios vanance portfono Minimum vanance 7 frontier St Dev Investments Measuring Returns and Risk 31 Introducing the Riskless Asset Consider what happens once we add a risk free asset Combining the riskfree asset with one particular portfolio of risky securities generates a new efficient frontier which is linear This will be the Capital Allocation Line CAL with the highest slope attainable K Investments Measuring Returns and Risk 32 f Portfolio Risk with RiskFree Asset When a risky asset is combined with a riskfree asset the portfolio standard deviation equals the risky asset s standard deviation multiplied by the portfolio proportion invested in the risky asset r K Investments Measuring Returns and Risk 33 Example Assume the risk free return is 7 and the return on a risky asset is 15 The standard deviations of the risk free asset and risk asset are 0 and 22 What is the return and std dev of a portfolio investing 75 in the risky asset and 25 in the risk free asset Weights Mean Std Dev Risk Free 25 7 O Risky 75 15 22 Portfolio 100 K Investments Measuring Returns and Risk 34 K Alternative Capital Allocation Lines CAL Er CAL F tCAL E x 5 f xquot fc quot9quotquot eff arti xquot LIA K 39iltw quotf 039 t r CAL D if fir rst I 391 fr quotdf 7 xx M aquot f 39 a Iquot 5 f r f Std Dev Investments Measuring Returns and Risk 35 Sharpe Ratio 7 Performance to variability ratio that takes both returns and risk into account where S Sharpe ratio r stock or portfolio return rf risk free rate K o stock or portfolio std deviation Investments Measuring Returns and Risk 36 f Modern Portfolio Theory E r Optimal Emilem Risky ron Ier Port Individual Assets Risk IBM Stock Free 39 SONY Bond Asset Portfolios etc Investments Measuring Returns and Risk f Creating Portfolios with Leverage K Assuming the example from the previous page what is the portfolio return and standard deviation if you borrow 50 at the RiskFree Rate and invest 150 in stock Weights Mean Std Dev Risk Free 7 O Risky 15 22 Portfolio 100 Investments Measuring Returns and Risk 38 Investor Risk Aversion and Utility Theory EI Utility Eur 12qu Investments Measuring Returns and Risk f Portfolio Selection Using Utility Theory and CAL Er CAL 7 Optimal Portfolio r Different levels of Utility f where Utility Er 12Ao2 Std Dev Investments Measuring Returns and Risk 40 Build an Optimal Portfolio MPT Calculate arithmetic mean returns standard deviations and correlations Each security Various portfolio combinations Calculate Sharpe ratio for each portfolio given the risk free rate Find the Capital Allocation line by choosing the highest Sharpe ratio Pick the investor s portfolio mix based on hisher risk tolerance K Investments Measuring Returns and Risk 41 f Practice Problems A The expected return of portfolio is 115 and the risk free rate is 40 If the portfolio standard deviation is 180 what is the reward to variability Sharpe ratio of the portfolio A 00 B 042 C 064 D 135 Investments Measuring Returns and Risk 42 Practice Problems Asset A has an expected return of 15 and a rewardtovariability Sharpe ratio of 4 Asset B has an expected return of 20 and a rewardto variability Sharpe ratio of 3 A riskaverse investor using MPTwouId prefer a portfolio using the risk free asset and A asset A B asset B C no risky asset D can39t tell from the data given K Investments Measuring Returns and Risk 43 Practice Problems Suppose the optimal risky portfolio has r10 and Sthev30 and the risk free return is 5 A What are the portfolio weights and Sthev if an investors requires an 8 return B What are the portfolio weights and Sthev if an investors requires a 25 return C What are the portfolio weights and return if the investor wants no more than a 20 Sthev K Investments Measuring Returns and Risk 44 Practice Problem Er CAL optimal Iiiisky Portfolio rp Wm X rm Wmgtlt rrf rp rrf O fOp m St Dev Investments M gjring Returns and Risk 45 Practice Problem You have 500000 available to invest The riskfree rate as well as your borrowing rate is 8 The return on the risky portfolio is 16 If you wish to earn a 22 return you should A invest 125000 in the riskfree asset B invest 375000 in the riskfree asset C borrow 125000 D borrow 375000 K Investments Measuring Returns and Risk 46