4 Solved Problems on Foreign Stock Markets - Assignment 1 | ECON 136, Assignments of Economics

Download 4 Solved Problems on Foreign Stock Markets - Assignment 1 | ECON 136 and more Assignments Economics in PDF only on Docsity! Problem Set 1 Solutions Econ 136, Fall 2009 Grading. This problem set is graded by Xing Huang and Sung Bin Sohn. Xing grades Q1 and Q2, and Sung Bin grades Q3 and Q4 for all students. For both halves of your solution, your get a grade on a 0 to 5 scale. The grade for the problem set is the avarage of these grades. 5= no major or minor errors 4= no more than a few minor errors 3= a major or many minor errors 2= multiple major errors 1= multiple major errors and portions left blank 0= blank or never turned in 1. Internet Exercise: US and Foreign Stock Markets in the Past Five Years (a) To clearly see the di¤erence between the linear and log scales, examine the “max”histor- ical range of the chart of the Dow Jones Industrial Average. Even though the linear scale is easier for most people to construct and interpret, when looking at the max historical range of the Dow, the linear scale obscures the ‡uctuations of the Dow in the …rst half of the range. Even though the log scale is harder for most people to construct and interpret, when looking at the max historical range of the Dow, the log scale clearly shows the ‡uctuations of the Dow for the entire historical range. Plus, since a log scale shows a variable that grows at a constant rate as a straight line, the growth rate of the Dow is more easily interpreted when using a log scale. In my opinion, the log scale gives a better picture of the past performance of the Dow because it clearly shows the ‡uctuations in the value of the Dow for any time period in the full range of available data. (b) The symbols for each index are ^GSPC for the S&P500 and ^IXIC for the Nasdaq. The one-year chart shows that the Nasdaq has performed the best and the S&P500 has performed the worst over the past year. Using prices on September 9th, 2008 and September 8th, 2009, the Nasdaq has changed by (2,037.77 - 2,209.81) / 2209.81 = -7.79% and the S&P500 has changed by (1,025.39 - 1,224.51) / 1,224.51 = -16.26%. The …ve-year chart shows that the Nasdaq has done the best and the S&P500 has done the worst. [Since the percentage changes of the S&P500 and the Dow are very close to each other, using di¤erent dates may give the answer that the Dow has done the worst. We accept both answers.] 2. How much is your return? (a) Net simple return Rt;t+2 = Pt+2+Dt+2 Pt 1 = 12:77+0:5380 1 = 83:38% Geometric average return RGt;t+2 = p 1 +Rt;t+2 1 = p 1 83:38% 1 = 59:23% (b) Nominal net simple return = 107:2+0:891 1 = 18:68% 1 Real net simple return = 1+18:68%1+14% 1 = 4:11% If you were comparing the 1980 performance of Rolling S Co. to that of other companies in 1980 in the same country (where the same in‡ation rate applies), then comparing nominal returns would give you an accurate comparison of the companies’performances. You could also compare their real returns. If you were comparing the 1980 performance to performance in some other year (when in‡ation would likely be di¤erent), you can only accurately compare the company’s performance using real returns. Notice that in the example above the nominal return for the company is 18.68%, which looks pretty good until you consider that in‡ation was 14% so the stock in the company went up only 4.11% in terms of its purchasing power. Note that if in 1990 in‡ation was 0% and the stock’s nominal return was 5%, then by comparing nominal returns, you would inaccurately think that the company performed better in 1980 than 1990. 3. Create your portfolio (a) The following table summarizes how to compute the various returns. Equally weighted Price weighted Market-value weighted Asset return Ri = Pi;t+1Pi;t Pi;t RH = 6360 60 = 5% RP = 25% RO = 12:5% Weight !i = 1N !i = PiP i Pi !i = PiMiP i PiMi !H = !P = !O = 1 3 !H = 60 60+28+32 = 0:5 !H = 6050 6050+2850+32100 = 0:3947 !P = 0:2333; !O = 0:2667 !P = 0:1842; !O = 0:4211 Portfolio return RP = P i !iRi R EW P = 2:5% RPWP = 0% RVWP = 2:63% The following is an alternative way of computing the price-weighted return RPWP and the value- weighted return RVWP : RPWP = 63+21+36 60+28+32 1 = 0% (since the number of shares of each stock is equal in price-weighted portfolio) RVWP = 6350+2150+36100 6050+2850+321001 = 2:63% (since the number of shares of each stock is propotional to total shares of that stock in market-value portfolio) (b) For the equal-weighted portfolio at the end of 2009, the share of wealth held in asset 1 is ( 1=360  63) = 0:975 = 0:3590, for asset 2 is 0:2564, and for asset 3 is 0:3846. Thus, you have to sell some Historic and some Optimistic and buy some Present to return the weights to 1/3 each. 2