ARE 171a Winter 2016

Homework 4

Due Thursday, March 10th, in class

1 . a. Lawrence used $20,000 to purchase $5000 each of four stocks:

Stock A has b_{A =} 1.2; stock B has b_{B =} 1.4; stock C has b_{c =} 1.6; and stock D has b_{D =} 1.8.

What is Lawrence's portfolio beta? If the risk-free rate is 2%, and the market risk premium (Rmbar ? Rf) is 8%, what is Lawrence's expected rate of return on this portfolio?

b. Claire has $10,000. She is very competitive with her brother Lawrence, and wants a portfolio that has the same expected rate of return as his. However, she plans to invest in a stock mutual fund (like an S&P 500 index fund, for instance), while possibly borrowing at the risk-free rate from her broker, to achieve her goal. What are her portfolio weights, and what is the standard deviation of her portfolio's return? Assume the market standard deviation is sm = 9%.

c. Can we assume that Lawrence's portfolio has the same standard deviation of return as Claire's? Why or why not? Which strategy is generally considered more prudent, Lawrence's or Claire's, and why?

2. a. Lindsell Products recently paid a dividend of $0.80/share. Its beta estimate is 0.8, and its expected dividend growth rate is 5%. Find investors? required rate of return for this stock, and the stock?s current stock price, if the risk free rate of return is 2%, and the market risk premium is 7%.

b. Now suppose that the management of Lindsell is considering expanding into foreign markets. This planned acquisition is expected to increase the future growth rate of the dividend from its original 5% level, to a new level of 8%. However, because revenues from foreign markets are subject to currency-related swings and more uncertain demand conditions, this change of strategy is expected to raise the firm's beta value to 1.1. Should investors buy more of this stock, or sell their current shares, when they learn about this planned expansion? Explain your answer.

3. Estimating beta from stock price and dividend data.

We will estimate beta for Twitter (TWTR), whose beta value is not yet being published by financial web pages because the firm's price history has not yet reached 5 years.

On Yahoo finance, search for TWTR, then choose "historical prices"

Downloand the daily closing price, (not adjusted) for the dates Nov 7, 2013 through March 2, 2016. Typically we would also look up dividends if there were any, but Twitter has none.

Also look up the asset SPY (Standard and Poor's 500 ETF), and download its daily closing price (not adjusted) and dividends for the same dates. This is a tradable index fund that mimics the S&P500 index; it will be our proxy for "the market". By definition, its beta is 1.

Now we are ready to examine how TWTR returns respond to changes in market returns. Hint: before calculating your daily returns, notice the price data from Yahoo finance is "upside down", newest to oldest date, but we want oldest to newest. So first use the Sort command by date, to reverse the order.

a. Step 1: calculate daily returns R_twtr, and R_m using Excel.

Ex. Our first observation for each asset return will be R1= (P2 ? P1)/P1.

For Spy, there are a few days where we will also need to include the dividend.

Recall our general equation for the characteristic line for any stock j is

(Rj ? Rf) = aj + Bj (Rm- Rf) + errorj

However, on a daily basis, Rf, the risk free rate, is essentially zero at this time, due to super low interest rate environment*. Also, alpha is expected to be zero. Thus, our simplified equation is Rj = Bj* Rm + errorj , where Rj = daily return on stock j, in this case TWTR; and Rm = daily return on the market or SPY

*during most of the time period above, the 1 year treasury rate was about 0.1% annually, though lately it has risen to about 0.6%. Given there are about 250 business days per year, this would give a daily rate of from .000004 to .000024. So that is why we are ignoring it for convenience.

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

TWTR

(Rtwtr? Rf) = Btwtr *(Rm ? Rf) + e

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

Method: make an X-Y scatter chart, with the market return Rm on the X axis and Rtwtr return on the Y-axis. (Excel command is Insert Chart). Then add a trendline with equation, setting intercept = 0 (this means we are setting alpha to zero, so the line goes through the origin rather than elsewhere on the Y-axis). The slope is your beta estimate.

Does TWTR appear to be more, or less, risky than an average stock, when added to a diversified portfolio?

ARE 171a Winter 2016 Homework 4 Due Thursday, March 10th, in class 1 . a. Lawrence used $20,000 to purchase $5000 each of four stocks: Stock A has stock B has stock C has cand stock D has D What is Lawrence's portfolio beta? If the risk-free rate is 2%, and the market risk premium (Rmbar - Rf) is 8%, what is Lawrence's expected rate of return on this portfolio? b. Claire has $10,000. She is very competitive with her brother Lawrence, and wants a portfolio that has the same expected rate of return as his. However, she plans to invest in a stock mutual fund (like an S&P 500 index fund, for instance), while possibly borrowing at the risk-free rate from her broker, to achieve her goal. What are her portfolio weights, and what is the standard deviation of her portfolio's return? Assume the market standard deviation is m = 9%. c. Can we assume that Lawrence's portfolio has the same standard deviation of return as Claire's? Why or why not? Which strategy is generally considered more prudent, Lawrence's or Claire's, and why? 2. a. Lindsell Products recently paid a dividend of $0.80/share. Its beta estimate is 0.8, and its expected dividend growth rate is 5%. Find investors' required rate of return for this stock, and the stock's current stock price, if the risk free rate of return is 2%, and the market risk premium is 7%. b. Now suppose that the management of Lindsell is considering expanding into foreign markets. This planned acquisition is expected to increase the future growth rate of the dividend from its original 5% level, to a new level of 8%. However, because revenues from foreign markets are subject to currency-related swings and more uncertain demand conditions, this change of strategy is expected to raise the firm's beta value to 1.1. Should investors buy more of this stock, or sell their current shares, when they learn about this planned expansion? Explain your answer. 3. Estimating beta from stock price and dividend data. We will estimate beta for Twitter (TWTR), whose beta value is not yet being published by financial web pages because the firm's price history has not yet reached 5 years. On Yahoo finance, search for TWTR, then choose "historical prices" Downloand the daily closing price, (not adjusted) for the dates Nov 7, 2013 through March 2, 2016. Typically we would also look up dividends if there were any, but Twitter has none. Also look up the asset SPY (Standard and Poor's 500 ETF), and download its daily closing price (not adjusted) and dividends for the same dates. This is a tradable index fund that mimics the S&P500 index; it will be our proxy for "the market". By definition, its beta is 1. Now we are ready to examine how TWTR returns respond to changes in market returns. Hint: before calculating your daily returns, notice the price data from Yahoo finance is "upside down", newest to oldest date, but we want oldest to newest. So first use the Sort command by date, to reverse the order. a. Step 1: calculate daily returns Rtwtr, and Rm using Excel. Ex. Our first observation for each asset return will be R1= (P2 - P1)/P1. For Spy, there are a few days where we will also need to include the dividend. Recall our general equation for the characteristic line for any stock j is (Rj - Rf) = aj + Bj (Rm- Rf) + errorj However, on a daily basis, Rf, the risk free rate, is essentially zero at this time, due to super low interest rate environment*. Also, alpha is expected to be zero. Thus, our simplified equation is Rj = Bj* Rm + errorj , where Rj = daily return on stock j, in this case TWTR; and Rm = daily return on the market or SPY *during most of the time period above, the 1 year treasury rate was about 0.1% annually, though lately it has risen to about 0.6%. Given there are about 250 business days per year, this would give a daily rate of from .000004 to .000024. So that is why we are ignoring it for convenience. b. Step 2, we will chart the characteristic line and estimate the following regression for TWTR (Rtwtr- Rf) = Btwtr *(Rm - Rf) + e where e is a random error. Again, since we are using daily data, and Rf is near zero even on an annual basis, we can simplify this to Rtwtr = Btwtr * Rm + e Method: make an X-Y scatter chart, with the market return Rm on the X axis and Rtwtr return on the Y-axis. (Excel command is Insert Chart). Then add a trendline with equation, setting intercept = 0 (this means we are setting alpha to zero, so the line goes through the origin rather than elsewhere on the Y-axis). The slope is your beta estimate. Does TWTR appear to be more, or less, risky than an average stock, when added to a diversified portfolio