Capital markets and the pricing of risk

4. You bought a stock one year ago for $50 per share and sold it today for $55 per share. It paid a $1 per share dividend today. a. What was your realized return? b. How much of the return came from dividend yield and how much came from capital gain? 7. The last four years of returns for a stock are as follows: Year 1 2 3 4 Return -4% 28% 12% 4% 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? 11. Consider an investment with the following returns over four years: Year 1 2 3 4 Return 10% 20% -5% 15% a. What is the compound annual growth rate (CAGR) for this investment over the four years? b. What is the average annual return of the investment over the four years? c. Which is a better measure of the investment’s past performance? d. If the investment’s returns are independent and identically distributed, which is a better measure of the investment’s expected return next year? 20. Consider two local banks. Bank A has 100 loans outstanding, each for $1 million, that it expects will be repaid today. Each loan has a 5% 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 $100 million outstanding, which it also expects will be repaid today. It also has a 5% probability of not being repaid. Explain the difference between the type of risk each bank faces. Which bank faces less risk? Why? 21. Using the data in Problem 20, calculate: a. The expected overall payoff of each bank. b. The standard deviation of the overall payoff of each bank. 23. Consider an economy with two types of firms, S and I. S firms all move together. I firms move independently. For both types of firms, there is a 60% probability that the firms will have a 15% return and a 40% probability that the firms will have a −10% return. What is the volatility (standard deviation) of a portfolio that consists of an equal investment in 20 firms of (a) type S, and (b) type I? 33. Suppose the market portfolio is equally likely to increase by 30% or decrease by 10%. a. Calculate the beta of a firm that goes up on average by 43% when the market goes up and goes down by 17% when the market goes down. b. Calculate the beta of a firm that goes up on average by 18% when the market goes down and goes down by 22% when the market goes up. c. Calculate the beta of a firm that is expected to go up by 4% independently of the market. 4. Suppose all possible investment opportunities in the world are limited to the five stocks listed in the table below. What does the market portfolio consist of (what are the portfolio weights)? Stock Price/Share ($) Shares Outstanding (millions) A 10 10 B 20 12 C 8 3 D 50 1 E 45 20 6. Suppose Best Buy stock is trading for $30 per share for a total market cap of $9 billion, and Walt Disney has 1.65 billion shares outstanding. If you hold the market portfolio, and as part of it hold 100 shares of Best Buy, how many shares of Walt Disney do you hold? NOTE: Answers must be submitted in an Excel spreadsheet. One tab per problem and please label your tabs. Show all inputs and calculations. when appropriate you can use Excel functions directly to solve the problems (For example, you don't have to work out the standard deviation of a set of returns - you can use STDEV.S to calculate the value.) Highlight your answer cell