Tutorial Solutions- Tutorial 8 Note to Tutors and Students: The solutions provided to the theory questions are a guide only and would not represent a sufficient answer for exam purposes. Chapter 10 10-6. Using the data in the following table, calculate the return for investing in Boeing stock (BA) from January 2, 2008, to January 2, 2009, and also from January 3, 2011, to January 3, 2012, assuming all dividends are reinvested in the stock immediately. Historical Stock and Dividend Data for Boeing Date 1/2/2008 2/6/2008 79.91 5/7/2008 8/6/2008 11/5/2008 49.55 1/2/2009 Price 86.62 84.55 65.40 45.25 Date 1/2/2008 2/6/2008 79.91 5/7/2008 84.55 0.4 8/6/2008 65.4 0.4 -22.18% 11/5/2008 1/2/2009 Price 86.62 49.55 45.25 Date 1/3/2011 66.4 2/9/2011 72.63 5/11/2011 79.08 8/10/2011 57.41 11/8/2011 66.65 1/3/2012 74.22 Price Dividend R Dividend 0.40 0.40 0.40 0.40 Dividend 0.4 0.4 -23.62% 0.42 10.02% 1.1001506 0.42 9.46% 1.09458901 0.42 -26.87% 0.73128477 0.42 Dividend Date 1/3/2011 2/9/2011 72.63 0.42 5/11/2011 8/10/2011 57.41 0.42 11/8/2011 1/3/2012 Price 66.40 79.08 0.42 66.65 74.22 0.42 R 1+R -7.28% 6.31% -8.68% 0.92715308 1.06307095 0.77823773 0.76376147 0.91321897 -46.50% 0.535006 1+R 16.83% 1.16826337 11.36% 1.11357839 14.56% 1.14564829 ... .. . ...
10-7. The last four years of returns for a stock are as follows: Year Return 1 -4.3% 2 +27.7% 3 +12.1% 4 +4.3% a. What is the average annual return? b. What is the variance of the stock's returns? c. What is the standard deviation of the stock's returns? Given the data presented, make the calculations requested in the question. a. Average annual return = -4.3%+27.8%+12.1%+4.3% 4 = 9.975% b. Variance of returns = (-4.3% - 9.975%)2 + (27.8% - 9.975%)2 + (12.1% - 9.975%)2 + (4.3% - 9.975%)2 3 = 0.018608 C. Standard deviation of returns = Vvariance = v0.018608 = 13.64% The average annual return is 10%. The variance of return is 0.018608. The standard deviation of returns is 13.64%. 10-20. Consider two local banks. Bank A has 76 loans outstanding, each for $1 million, that it expects will be repaid today. Each loan has a 6% probability of default, in which case the bank is not repaid anything. The chance of default is independent across all the loans. Bank B has only one loan of $76 million outstanding, which it also expects will be repaid today. It also has a 6% probability of not being repaid. Explain the difference between the type of risk each bank faces. Which bank faces less risk? Why? The expected payoffs are the same, but bank A is less risky. 10-21. Using the data in Problem 20, calculate a. The expected overall payoff of each bank. b. The standard deviation of the overall payoff of each bank. a. Expected payoff is the same for both banks Bank B = $76 million x 0.94 = $71.44 million Bank A= ($1million x 0.94) x 76 =$71.44million b. Bank B Variance = (76-71.44 )2 0.94 + (0 - 71.44 )2 0.06 = 326 Standard Deviation = v326 = 18.05 Bank A Variance of each