CHAPTER 6 Risk, return and CAPM.docx - CHAPTER 6 RISK RETURN and CAPITAL ASSET PRICING MODEL I Expected Rate of Return Based on Historical Data 1

CHAPTER 6 Risk, return and CAPM.docx - CHAPTER 6 RISK...

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CHAPTER 6: RISK, RETURN and CAPITAL ASSET PRICING MODEL I. Expected Rate of Return Based on Historical Data 1/ Historical data Year/risk 2013 2014 2015 2016 Stock A 15% 5% -5% 9% Stock b 13% 4% -2% 5% 2/ The expected return of stock A & Stock B in 2017: Since we don’t have a probability distribution, the expected return for 2017 is simply the mean of all the returns. E(R A2017 ) = R A = T = 1 n RAT / n E(R A2017 ) = (0.15+0.05-0.05+0.09)/4 = 6% E(R B2017 )= R B = T = 1 n RAT / n E(R B2017 )= (0.13+0.04-0.02+0.05)/4 = 5% 3/ The variance of stock A and stock B retunes (This measures how the return differs from the expected return) : E(R A ) = T = 1 n ( RAt RA ) 2 ( n 1 ) E(R A ) = ( 0.15 0.06 ) 2 +( 0.05 0.06 ) 2 +(− 0.05 0.06 ) 2 +( 0.09 0.06 ) 2 4 1 = 0.00707 E(R B ) = ( 0.13 0.05 ) 2 +( 0.04 0.05 ) 2 +(− 0.02 0.05 ) 2 +( 0.05 0.05 ) 2 4 1 = 0.00380 4/ The standard deviation (Measures the Risk/Divarication level): σ (R A ) = ( R A ) = 0.0071 =8.4% σ (R B ) = ( RB ) = 0.0038 =0.06164 = 6.16% 5/Coefficient of variation (Standard Deviation on the expected return/Risk per unit of return) 1
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CV = σ ( R A ) E ( R A ) CV A = 0.084 0.06 = 1.4 For each 1% of return is stock A the risk is equal to 1.4%. Meaning this stock is relatively risky. CV = σ ( RB ) E ( RB ) CV B = 0.0616 0.05 = 1.23 For each 1% of return in stock B the risk is equal to 1.23%. 6/ The covariance between stock A and stock B (It measures the quantity of association between A & B, either associated positively or negatively, if the calculated number is positive then we have a positive association and if it’s negative vice versa) : Cov(R A ,R B )= t = 1 n ( R At R A ) ( R Bt R B ) ( n 1 ) Cov (R A ,R B ) = ( 0.15 0.06 )( 0.13 0.05 )+( 0.05 0.06 )( 0.04 0.05 )+(− 0.05 0.06 )(− 0.02 0.05 )+( 0.09 0.06 )( 0.05 0 4 1 = -0.05/0.025 0.01500 7/ Correlation Coefficient (Measures the intensity (not quantity) of correlation between two variables): r AB = Cor ( R A ,R B ) σ ( R A ) σ ( R B ) -1 ≤r AB≤ + 1 It should be between -1 and +1, Meaning if: r AB =+1, if both R A & R B are positive they are positively and perfectly correlated r AB = -1, if both R A & R B are negative they’re negatively correlated r AB = 0, No correlation between R A & R B 8/ Calculating the Stock return (Not the expected): Q: Assume you bought a stock for 12 and sold it for 16 and you received 1 riyal as dividends. R t = ( Pt Pt 1 )+ Dt ( Pt 1 ) 2
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II.Data based on probability Distribution:We predict the future by hypothesizing the following: State of the worldProbability of OccurrenceRAKRBKExpansion0. 3%30%16%Stagnation0. 4%20%2%Rescission0.3%-5%-18%What changes here is that formula here is based in k. 1.1 2% 3
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