1. Download monthly data on prices and dividends from finance.yahoo.com from January 1 2011 to January 1 2013 for McDonalds Corporation (NYSE:MCD) and Yum! Brands, Inc. (NYSE:YUM), for the period. Assume that you trade at the close price and that all dividends are only available to you on the first trading day of the month after they are paid. For instance, the dividend paid on July 11, 2012 is not available to you until the first trading day in August 2012.

(a) Calculate the monthly return on each stock for each month in 2011 and 2012.

(b) Using these returns, calculate the following:

i. The expected monthly return on each stock

ii. The variance of the monthly return on each stock

iii. The standard deviation of the monthly return on each stock iv. The covariance between the two stocks

v. The correlation between the two stocks

(c) Given your calculations of expected return, variance, and covariance above, cal- culate the expected return and the standard deviation of return for the following portfolios of MCD and YUM. Please do this question without first calculating each portfolio return in each month. Rather, use the formulas for expected return and variance of return of a portfolio given the statistics of the individual assets.

Weight in MCD Weight in YUM

-1 2

0 1

0.25 0.75 0.5 0.5 0.75 0.25

1 0

2 -1

(d) Plot the expected return of these portfolios as a function of their standard de- viation. In Excel, use an X-Y or Scatter plot, and put Expected Return (the 7 values calculated above) on the Y axis and Standard Deviation on the X-axis.

(e) Using the return data for IBM I calculated in class, find the expected return and the variance of return on IBM. Also find the correlation and the covariance of return between IBM and MCD and, separately, IBM and YUM. Are these correlations lower or higher than the correlation of YUM and MCD? Does this agree with your intuition? (Data for IBM below)

(f) Consider the portfolio which has equal weights in MCD and YUM. Think of this portfolio as just another asset, and call it MY (for MCD and YUM). Find the covariance and correlation of this portfolio with IBM. To do this, first find the return on this portfolio in each of the 24 months.

(g) Given your calculations of expected return, variance, and covariance above, calcu- late the expected return and the standard deviation of return for portfolios of the following two assets: (1) IBM stock (2) Asset MY. Please do this question without first calculating each portfolio return in each month. Rather, use the formulas for expected return and variance of return of a portfolio given the statistics for IBM and MY.

Weight in IBM Weight in MY

-1 2

0 1

0.25 0.75 0.5 0.5 0.75 0.25

1 0

2 -1

(h) Plot the expected return of these portfolios as a function of their standard de- viation. In Excel, use an X-Y or Scatter plot, and put Expected Return (the 7 values calculated above) on the Y axis and Standard Deviation on the X-axis.

(i) You are a financial advisor with a client who wants to invest in one of two assets (a) A portfolio of MCD and YUM or (b) a portfolio of IBM and asset MY. What advice would you give this client? Remember that option (a) has many possible portfolios, as does option (b). In your analysis, you do not have to give a definite recommendation: you dont need to say: I pick this portfolio as being best for you, but you could, for example, talk about which portfolios the client should avoid.

IBM Data

Date	Close	HPR			(r-Er)^2
Dec-10	147.21		Date	Dividends
Jan-11	162	0.100468718			0.007607884
Feb-11	161.880005	0.003271636	2/8/11	0.65	9.94786E-05
Mar-11	163.070007	0.007351136			3.47439E-05
Apr-11	170.580002	0.046053809			0.001076383
May-11	168.929993	-0.005276169	5/6/11	0.75	0.000343053
Jun-11	171.550003	0.015509442			5.12529E-06
Jul-11	181.850006	0.060040821			0.002189799
Aug-11	171.910004	-0.050536166	8/8/11	0.75	0.004068105
Sep-11	174.869995	0.017218259			1.57826E-05
Oct-11	184.630005	0.055812948			0.001811985
Nov-11	188	0.022314872	11/8/11	0.75	8.22529E-05
Dec-11	183.880005	-0.021914867			0.001236254
Jan-12	192.600006	0.047422236			0.001168047
Feb-12	196.729996	0.025337434	2/8/12	0.75	0.000146214
Mar-12	208.649994	0.060590648			0.00224156
Apr-12	207.080002	-0.007524525			0.000431395
May-12	192.899994	-0.064371295	5/8/12	0.85	0.006024372
Jun-12	195.580002	0.013893251			4.19539E-07
Jul-12	195.979996	0.002045168			0.000125448
Aug-12	194.850006	-0.001428666	8/8/12	0.85	0.000215332
Sep-12	207.449997	0.064665079			0.00264397
Oct-12	194.529999	-0.062280059			0.005704115
Nov-12	190.070007	-0.018557508	11/7/12	0.85	0.001011433
Dec-12	191.550003	0.007786584			2.98001E-05

	Average	0.013245533		My Est var	0.001665781
				SD	0.040813975
Excels	variance	0.001665781
	std dev	0.040813975