Textbook Exercise Solutions Part 2

# Textbook Exercise Solutions Part 2 - TOPIC 5 3-9(i...

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TOPIC 5 3-9 (i) Risk/return graph Risk / Return A B D C E F 0% 5% 10% 15% 20% 25% 0% 5% 10% 15% 20% 25% Risk Return (ii) An investor willing to take risks would invest in the two shares of F and C, as F offers the highest return with the highest standard deviation. C offers a lower return and a lower level of risk. E would not be selected as it offers the same return as C but at a higher level of risk. (iii) A cautious investor would select A and C, as A offers the lowest return at the lowest level of risk. C offers a return of 15% with a standard deviation of 15%. Investment B would not be selected as it offers a lower return than C but at a higher level of risk. (iv) No. It means that investors will require higher returns for taking on higher risk investments. (v) Government bonds are considered to be low risk, as the government will always pay the redemption value of such bonds, either by printing money or increasing tax rates. The risk of government not being able to meet its commitments is very small. However, the values of long term bonds will be highly variable, due to the sensitivity of such bond values to changes in interest rates. 1

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3-11 1., 2., & 3. 1 2 1 x 2 Return - ER Deviation 2 x Prob. Expected return Deviation Weighted Sq. Deviation Probability Return X 0.20 10% 2.00% -5.00% 0.05% 0.60 15% 9.00% 0.00% 0.00% 0.20 20% 4.00% 5.00% 0.05% Expected Return (sum) 15.00% Variance = sum of sq. deviations 0.10% Std Dev = Var 0.5 3.16% Coefficient of Variation (Stdev/ER) 21% Workings Expected return 0.2 x 10% = 2% Deviation 10% - 15% = -5% Squared deviation x Prob. (-.05) 2 x 0.20 = 0.0005 1 2 1 x 2 Return - ER Deviation 2 x Prob. Expected return Deviation Weighted Sq. Deviation Probability Return X 0.20 0% 0.00% -15.00% 0.45% 0.30 10% 3.00% -5.00% 0.08% 0.30 20% 6.00% 5.00% 0.08% 0.20 30% 6.00% 15.00% 0.45% Expected Return (sum) 15.00% Variance = sum of sq. deviations 1.05% Std Dev = Var 0.5 10.25% Coefficient of Variation (Stdev/ER) 68% Workings Expected return 0.3 x 10% = 3% Deviation 10% - 15% = -5% Squared deviation x Prob. (-.05) 2 x 0.30 = 0.0008 Share X Share Y 4. Share X and Share Y offer the same expected return of 15%. However, the risk associated with investing in Share Y is significantly greater than investing in Share X. The higher risk in absolute terms is measured in terms of a standard deviation of 10.25% for Share Y as compared to a much lower standard deviation of 3.16% for Share X. As the expected returns are equal in this case, the additional calculation of the coefficient of variation is not required but has been calculated in this case. The CV of Share Y is significantly higher than the CV of Share X. 2
5. 1 2 1 x 2 Return - ER Deviation 2 x Prob. Expected return Deviation Weighted Sq. Deviation Probability Return X 0.20 0% 0.00% -17.00% 0.58% 0.30 10% 3.00% -7.00% 0.15% 0.30 20% 6.00% 3.00% 0.03% 0.20 40% 8.00% 23.00% 1.06% Expected Return (sum) 17.00% Variance = sum of sq. deviations 1.81% Std Dev = Var 0.5 13.45% Coefficient of Variation (Stdev/ER) 79% Share Y The expected return increases to 17%, but the risk also increases. The standard deviation is now 13.45%, and the CV is 79%. The investment decision would probably not change due to the fact that the additional 2% return will result in a significantly higher risk. A comparison of the Coefficient of Variation ratios for both companies indicates that the level of risk relative to

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