1. (5) A broad diversified bundle of stocks is expected to return R_Mbar = 9%, with a variance of

s_M² = 36%². The risk-free rate of return R_F = 1%.

a. Gabrielle is somewhat cautious, so she invests 30% of her $10,000 portfolio in stocks, and 70% in risk-free Treasury bills. What is the expected return, standard deviation and coefficient of variation for her portfolio?

b. Gabrielle's friend Thomas is more adventuresome. He also has $10,000 in funds, but he invests twice that much in the stock market by using his stockbroker's margin account. (That is, he borrows another $10,000 to buy stocks). What is the expected return, standard deviation and coefficient of variation for his portfolio? How much interest (in $) must he pay back to the broker per year?

c. Their friend Sarah wants to earn a return of 12%. What should her portfolio weights be for stocks and for Treasury bills? What is the standard deviation and CV for this portfolio?

d. Sketch a graph showing how these friends' portfolios are positioned along the capital market line.

2. (11) Suppose stock A has a beta value of b_A= .6. Stock B has a beta of b_B = 1.0. Stock C has a beta of b_C= 2.5.

a. Find the required rate of return for each stock, if the risk-free rate of return is 2% and the market risk premium is 6%.

b. Suppose each stock recently paid a dividend of $1.00. Stock A's dividend is expected to grow forever at 2%; stock B's dividend is expected to grow forever at 4%, and Stock C's dividend is expected to grow for 2 years at 25%, then at 4% thereafter. Using your answer from part a, find the current market price of each stock.

c. Consider the following 4 changes to the security market line in part a:

1. The risk free rate of return increases to 3% (market risk premium still 6%)

2. The risk free rate of return declines to 0% (market risk premium still 6%)

3. The market risk premium rises to 8% (risk free rate still 2%)

4. The market risk premium declines to 4% (risk free rate still 2%)

For each scenario above, sketch a graph that shows the original and the new SML. Now, find out the new price of A, B and C in each case.

3. (20) Look up the following 9 stocks (recommended site: http://finance.yahoo.com/ .)

Exxon Mobil XOM a. For each stock, find:

Google (Alphabet) GOOGL *location of its headquarters

Newmont Mining NEM *sector and industry

Macys M *price (will vary by day you look it up)

General Electric GE * trailing EPS (past 12 months) and P/E ratio

Apple AAPL *trailing dividend per share (past 12 months)

Merck MRK *beta estimate

Ford Motor F *market cap

Wells Fargo WFC *long term debt (from financials, balance sheet)

*calculate debt ratio = long term debt/market cap

Note: firms with negative EPS will not have a P/E ratio, and some firms pay 0 dividends

3. cont'd

b. Looking at your results, which 3 stocks had the lowest P/E ratios? Which 3 had the highest P/E ratios? (for the moment, ignore firms with negative earnings)

What are some possible reasons why P/E ratios differ so much between firms? Do you see any relationship or pattern between the level of the P/E ratio and the type of industry?

c. Looking again at your results, which 3 stocks had the lowest beta estimates? Which 3 had the highest beta estimates? Does there appear to be any relationship between beta, the type of industry, and/or the debt ratio?

4. Estimating beta from stock price and dividend data.

From the same website as in problem 3, go to Historical Prices and download the following data:

Daily closing price (not adjusted) and dividends, for the dates 11-27-2015 through 11-25-2016 for these two assets: RACE (Ferrari N.V ) and SPY (Standard and Poor's 500 ETF). The latter is a tradeable asset that mimics the S&P500 market index; it will be our proxy for "the market" Ferrari went public only a little over a year ago, thus its beta estimate has not yet been published by Yahoo. We will estimate it ourselves.

a. Step 1: calculate daily returns Rr and Rm. (We will call Ferrari stock r since in the CAPM model, Rf is the risk free asset). There are 254 price observations in our data set; use them to calculate 253 observations of Rr and Rm.

Ex. Day 1's return will be (P2 P1)/P1; day 253will be (P254 P253)/253

On 1 of the days for Ferrari, and on 4 dates for SPY, you will have to add in the dividend: (Pnew + Div Pold)/Pold

If you type in the formula above into the first cell, you can copy it down the column, so it should only take a few minutes to prepare the returns data.

Hint: the order of the data from Yahoo finance is "upside down", newest to oldest date. We want oldest to newest. You can use the Data Sort command and sort by date., to easily reverse the order

b. Step 2, we will chart the characteristic line and estimate the following regression for RACE

(Rr Rf) = Br *(Rm Rf) + e

where e is a random error. Since we are using daily data, and Rf is near zero even on an annual basis, we can simplify this to Rr= Bn * Rm + e

Method: make an X-Y scatter chart, with the market return on the X axis and RACE return on the Y-axis. (Excel command is Insert chart). Then add a trendline with equation, setting intercept = 0. The slope is your beta estimate.

. 1. (5) A broad diversified bundle of stocks is expected to return RMbar = 9%, with a variance of M2 = 36%2. The risk-free rate of return RF = 1%. a. Gabrielle is somewhat cautious, so she invests 30% of her $10,000 portfolio in stocks, and 70% in risk-free Treasury bills. What is the expected return, standard deviation and coefficient of variation for her portfolio? b. Gabrielle's friend Thomas is more adventuresome. He also has $10,000 in funds, but he invests twice that much in the stock market by using his stockbroker's margin account. (That is, he borrows another $10,000 to buy stocks). What is the expected return, standard deviation and coefficient of variation for his portfolio? How much interest (in $) must he pay back to the broker per year? c. Their friend Sarah wants to earn a return of 12%. What should her portfolio weights be for stocks and for Treasury bills? What is the standard deviation and CV for this portfolio? d. Sketch a graph showing how these friends' portfolios are positioned along the capital market line. 2. (11) Suppose stock A has a beta value of AStock B has a beta of B Stock C has a beta of C. a. Find the required rate of return for each stock, if the risk-free rate of return is 2% and the market risk premium is 6%. b. Suppose each stock recently paid a dividend of $1.00. Stock A's dividend is expected to grow forever at 2%; stock B's dividend is expected to grow forever at 4%, and Stock C's dividend is expected to grow for 2 years at 25%, then at 4% thereafter. Using your answer from part a, find the current market price of each stock. c. Consider the following 4 changes to the security market line in part a: 1. The risk free rate of return increases to 3% (market risk premium still 6%) 2. The risk free rate of return declines to 0% (market risk premium still 6%) 3. The market risk premium rises to 8% (risk free rate still 2%) 4. The market risk premium declines to 4% (risk free rate still 2%) For each scenario above, sketch a graph that shows the original and the new SML. Now, find out the new price of A, B and C in each case. 3. (20) Look up the following 9 stocks (recommended site: http://finance.yahoo.com/ .) Exxon Mobil XOM a. For each stock, find: Google (Alphabet) Newmont Mining Macy's GOOGL NEM M *location of its headquarters *sector and industry *price (will vary by day you look it up) General Electric Apple Merck Ford Motor Wells Fargo GE AAPL MRK F WFC * trailing EPS (past 12 months) and P/E ratio *trailing dividend per share (past 12 months) *beta estimate *market cap *long term debt (from financials, balance sheet) *calculate debt ratio = long term debt/market cap Note: firms with negative EPS will not have a P/E ratio, and some firms pay 0 dividends 3. cont'd b. Looking at your results, which 3 stocks had the lowest P/E ratios? Which 3 had the highest P/E ratios? (for the moment, ignore firms with negative earnings) What are some possible reasons why P/E ratios differ so much between firms? Do you see any relationship or pattern between the level of the P/E ratio and the type of industry? c. Looking again at your results, which 3 stocks had the lowest beta estimates? Which 3 had the highest beta estimates? Does there appear to be any relationship between beta, the type of industry, and/or the debt ratio? 4. Estimating beta from stock price and dividend data. From the same website as in problem 3, go to Historical Prices and download the following data: Daily closing price (not adjusted) and dividends, for the dates 11-27-2015 through 11-25-2016 for these two assets: RACE (Ferrari N.V ) and SPY (Standard and Poor's 500 ETF). The latter is a tradeable asset that mimics the S&P500 market index; it will be our proxy for "the market" Ferrari went public only a little over a year ago, thus its beta estimate has not yet been published by Yahoo. We will estimate it ourselves. a. Step 1: calculate daily returns Rr and Rm. (We will call Ferrari \"stock r\" since in the CAPM model, Rf is the risk free asset). There are 254 price observations in our data set; use them to calculate 253 observations of Rr and Rm. Ex. Day 1's return will be (P2 - P1)/P1; day 253will be (P254- P253)/253 On 1 of the days for Ferrari, and on 4 dates for SPY, you will have to add in the dividend: (Pnew + Div - Pold)/Pold If you type in the formula above into the first cell, you can copy it down the column, so it should only take a few minutes to prepare the returns data. Hint: the order of the data from Yahoo finance is "upside down", newest to oldest date. We want oldest to newest. You can use the Data Sort command and sort by date., to easily reverse the order b. Step 2, we will chart the characteristic line and estimate the following regression for RACE (Rr- Rf) = Br *(Rm - Rf) + e where e is a random error. Since we are using daily data, and Rf is near zero even on an annual basis, we can simplify this to Rr= Bn * Rm + e Method: make an X-Y scatter chart, with the market return on the X axis and RACE return on the Y-axis. (Excel command is Insert chart). Then add a trendline with equation, setting intercept = 0. The slope is your beta estimate