Finance Chapter 7 handout

Chapter 7 Risk and Return
Recap - Expected Return and Standard Deviation for single asset and 2-asset Portfolio
Probability

Return(A)

Return(B)

Good

0.3

- 0.05

-0.10

OK

0.4

0.10

0.15

Poor

0.3

0.20

Portfolio

0.30

E(R)

8.5%

Covariance

0.014177

15.68%

11.91%

0.0153

Corr.

0.0246

9.76%

S.D.

10.25%

0.009525

Variance

12%

0.99

EQ 7.2 Expected Return:

E(RA) = (0.3) (‐0.05) + (0.4) (0.10) + (0.3) (0.20) = 0.085 = 8.5%
E(RB) = (0.3) (‐0.10) + (0.4) (0.15) + (0.3) (0.30) = 0.12 = 12%

EQ 7.3 Variance of Return:

Var(RA) = (0.3) (‐0.05 – 0.085)2 + (0.4) (0.10 – 0.085)2 + (0.3)(0.20 – 0.085)2 = 0.009525
SD(RA) = Var(RA) ½ = (0.009525) ½ = 0.097596 = 9.76%
Var(RB) = (0.3) (‐0.10 – 0.12)2 + (0.4) (0.15 – 0.12)2 + (0.3)(0.30 – 0.12)2 = 0.0246
SD(RB) = Var(RB) ½ = (0.0246) ½ = 0.156844 = 15.68%

EQ 7.6 Expected Return for a portfolio:

Assuming equal weight for each stock; i.e., 50% of the fund invested in Stock A and 50% in Stock B:
E(RPort) = (0.5) (0.085) + (0.5) (0.12) = 0.1025 = 10.25%

EQ 7.7 Variance for a 2‐asset Portfolio:

EQ 7.8 Covariance of the return between 2 assets: Cov (RA&B) = (0.3) (‐0.05 – 0.085) (‐0.10 – 0.12) + (0.4) (0.10 – 0.085) ( 0.15 – 0.12)
+ (0.3) (0.20 – 0.085) (0.30 – 0.012) = 0.0153
Var(RProt) = (0.5)2(0.0976)2 + (0.5)2(0.1586)2 + 2(0.5)(0.5)(0.0153) = 0.014177
SD(RPort) = Var(RPort) ½ = (0.014177) ½ = 0.1191 = 11.91%
EQ7 Correlation between the returns of the 2 assets in the Portfolio:

Corr(RA&B) = Cov (RA&B) / SD(RA) x SD(RB) = 0.0153 / (0.0976) (0.1586) = 0.9884  0.99  The returns of A and B are almost Perfectly Positively Correlated

Chapter 7 Risk and Return
Recap - Expected Return and Standard Deviation for single asset and 2-asset Portfolio
Probability

Return(M)

Return(W)

Portfolio

Good

0.3

- 0.10

0.30

OK

0.4