Need only Q4.

Anonymous
timer Asked: Nov 21st, 2016

Question description

The questions are in "hw3" and then you need the excel copy to answer q4 in the assignment.

UNIVERSITY OF TORONTO Joseph L. Rotman School of Management RSM332 PROBLEM SET #3 1. Consider three securities with the following payoffs for different states of the economy: Economic State Recession Normal Expansion Boom Probability R1 R2 R3 0.4 30% −30% 10% 0.4 10% 30% 15% 0.1 10% 50% 25% 0.1 0% 120% 45% (a) What is the expected return and standard deviation on each security? (b) What is Cov(R1 , R2 ), Cov(R1 , R3 ), and Cov(R2 , R3 )? What is Corr(R1 , R2 ), Corr(R1 , R3 ), and Corr(R2 , R3 )? (c) What is the expected return, µp , and standard deviation, σp , of a portfolio which has its funds invested equally in (i) securities #1 and #2, or (ii) securities #1 and #3, or (iii) securities #2 and #3? (d) What is µp and σp , of a portfolio which has its funds invested equally in securities #1 to #3? (e) What is the correlation of the return of the portfolio in part (d) with the return of an equally weighted portfolio of securities #1 and #2? 2. An investor has an opportunity to invest in two risky assets and a risk-free asset. The expected return of the two risky assets are µ1 = 0.12, µ2 = 0.15. Their standard deviations are σ1 = 0.05 and σ2 = 0.1, and the correlation coefficient between their return is 0.2. The risk-free rate is 0.05. Suppose the investor has $1000 and he wants to hold a portfolio with expected return of 0.1. If the investor is risk averse, how much should he invest in the two risky assets and the risk-free asset? 3. The Sharpe ratio of a portfolio p is defined as SR(p) = E[Rp ] − RF , σp where σp is the standard deviation of the portfolio. Suppose a portfolio T is the tangency portfolio (the tangency portfolio is the portfolio which has the maximum Sharpe ratio among all the portfolios) and it has a Sharpe ratio of 0.8. Also consider a portfolio p which may or may not be on the mean-variance efficient frontier. You find out that the correlation between the returns of portfolios p and T is −0.75. What is the Sharpe ratio of portfolio p? You need to show the work to support your answer. 1 4. hw3.xlsx contains the monthly return data for Microsoft (MSFT), IBM (IBM), Apple (AAPL) and Hewlett-Packard (HPQ) for the period 2006/1–2015/12. (a) Report the average return and sample covariance matrix of the four stocks based on the monthly data. (b) Using the estimates from part (a) as the expected returns and covariance matrix for the four stocks, find out the global minimum variance portfolio of the four stocks assuming (i) short-selling is allowed, and (ii) short-selling is not allowed. (c) Using the estimates from part (a) as the expected return and covariance matrix for the four stocks, find out the tangency portfolio of the four stocks assuming (i) shortselling is allowed, and (ii) short-selling is not allowed. Assume a monthly risk-free rate of 0.1%/month. Note: To do optimization in Excel, you may want to use “Tools, Solver.” 2
Month 20060131 20060228 20060331 20060428 20060531 20060630 20060731 20060831 20060929 20061031 20061130 20061229 20070131 20070228 20070330 20070430 20070531 20070629 20070731 20070831 20070928 20071031 20071130 20071231 20080131 20080229 20080331 20080430 20080530 20080630 20080731 20080829 20080930 20081031 20081128 20081231 20090130 20090227 20090331 20090430 20090529 20090630 20090731 20090831 20090930 20091030 20091130 20091231 20100129 20100226 20100331 20100430 MSFT 0,076482 -0,042273 0,012653 -0,112459 -0,058385 0,028698 0,032618 0,071904 0,064202 0,049726 0,026123 0,017030 0,033490 -0,083927 -0,010650 0,074273 0,028393 -0,039756 -0,016288 -0,005519 0,025409 0,249491 -0,084216 0,059524 -0,084270 -0,162273 0,043386 0,004933 -0,003156 -0,028602 -0,065067 0,065319 -0,021986 -0,163357 -0,088670 -0,038576 -0,120370 -0,047953 0,137461 0,102885 0,037512 0,137865 -0,010517 0,053571 0,043408 0,078149 0,065272 0,036382 -0,075459 0,022001 0,021538 0,042595 IBM -0,010949 -0,010578 0,027792 -0,001576 -0,025990 -0,038548 0,007680 0,049864 0,011980 0,126800 -0,001191 0,056897 0,020587 -0,059607 0,014203 0,084341 0,046864 -0,012664 0,051306 0,058202 0,009512 -0,014261 -0,090768 0,027762 -0,009158 0,066754 0,011242 0,048289 0,076471 -0,084215 0,079727 -0,044929 -0,039185 -0,205113 -0,116919 0,031373 0,088997 0,009602 0,052809 0,065229 0,035074 -0,017501 0,129381 0,005681 0,013215 0,008361 0,052152 0,036011 -0,065011 0,043468 0,008572 0,005848 AAPL 0,050355 -0,092968 -0,084246 0,122290 -0,150874 -0,041827 0,186660 -0,001619 0,134562 0,053261 0,130488 -0,074405 0,010490 -0,013064 0,098097 0,074158 0,214339 0,007005 0,079646 0,051002 0,108247 0,237701 -0,040695 0,087038 -0,316640 -0,076389 0,147816 0,212195 0,085082 -0,112901 -0,050705 0,066562 -0,329558 -0,053405 -0,138675 -0,078990 0,056005 -0,009098 0,177024 0,197013 0,079313 0,048745 0,147160 0,029500 0,101896 0,016995 0,060531 0,054134 -0,088591 0,065380 0,148470 0,111021 HPQ 0,089067 0,052277 0,005181 -0,013070 -0,002772 -0,019148 0,007260 0,145722 0,005744 0,055874 0,018585 0,045869 0,050740 -0,090804 0,022109 0,049826 0,084718 -0,022096 0,031600 0,072127 0,010537 0,037959 -0,010062 -0,011728 -0,133914 0,092635 -0,042495 0,015112 0,015318 -0,058861 0,013345 0,047321 -0,012788 -0,172145 -0,078370 0,030896 -0,042436 -0,164604 0,107131 0,122271 -0,045303 0,127511 0,120310 0,036721 0,053464 0,005295 0,033713 0,051569 -0,086197 0,079031 0,048041 -0,022201 20100528 20100630 20100730 20100831 20100930 20101029 20101130 20101231 20110131 20110228 20110331 20110429 20110531 20110630 20110729 20110831 20110930 20111031 20111130 20111230 20120131 20120229 20120330 20120430 20120531 20120629 20120731 20120831 20120928 20121031 20121130 20121231 20130131 20130228 20130328 20130430 20130531 20130628 20130731 20130830 20130930 20131031 20131129 20131231 20140131 20140228 20140331 20140430 20140530 20140630 20140731 20140829 20140930 -0,150811 -0,108140 0,121686 -0,085819 0,043682 0,088812 -0,046784 0,105018 -0,006628 -0,035528 -0,044771 0,020874 -0,028935 0,039584 0,053846 -0,023358 -0,064286 0,069908 -0,031919 0,014855 0,137519 0,081612 0,016226 -0,007441 -0,081993 0,047962 -0,036613 0,052596 -0,034393 -0,040995 -0,059390 0,003558 0,027717 0,021129 0,028957 0,157140 0,061329 -0,010172 -0,078304 0,056219 -0,003593 0,063852 0,084875 -0,018883 0,011494 0,019820 0,069956 -0,014394 0,020297 0,018564 0,035012 0,059082 0,020471 -0,023953 -0,014210 0,039844 -0,035981 0,089418 0,070523 -0,010376 0,037466 0,103843 0,003272 0,007351 0,046054 -0,005276 0,015509 0,060041 -0,050536 0,017218 0,055813 0,022315 -0,021915 0,047422 0,025337 0,060591 -0,007525 -0,064371 0,013893 0,002045 -0,001429 0,064665 -0,062280 -0,018558 0,007787 0,060141 -0,006845 0,062092 -0,050445 0,031747 -0,081290 0,020564 -0,060603 0,015965 -0,032239 0,007924 0,043911 -0,058058 0,053430 0,039531 0,020676 -0,056039 -0,016761 0,057373 0,009026 -0,012845 -0,016125 -0,020827 0,022741 -0,055005 0,167215 0,060723 0,033790 0,036670 0,051959 0,040935 -0,013314 0,004656 -0,006569 -0,034960 0,163285 -0,014469 -0,009121 0,061523 -0,055783 0,059655 0,127111 0,188311 0,105284 -0,025969 -0,010702 0,010853 0,045822 0,093539 0,002803 -0,107607 -0,012413 -0,090738 -0,144094 -0,025116 0,002855 0,000271 0,022596 -0,118303 0,141225 0,083389 -0,021481 0,096386 0,069673 0,008902 -0,107697 0,057311 0,019953 0,099396 0,078293 0,027662 0,028731 0,077092 -0,017073 -0,114682 -0,057596 0,063771 -0,164857 0,096229 -0,000713 -0,002617 0,005962 0,085273 -0,045086 -0,059134 -0,014645 -0,074065 -0,023007 -0,033791 -0,259881 -0,132924 0,185301 0,050357 -0,074061 0,086180 -0,095425 -0,053734 0,039026 -0,084006 -0,107496 -0,092989 -0,074561 0,018483 -0,188159 -0,062094 0,107159 0,158597 0,219867 0,190268 -0,135906 0,185437 0,021507 0,035484 -0,130062 -0,053930 0,161029 0,122281 0,028344 0,036455 0,030345 0,087858 0,021632 0,013309 0,010149 0,057304 0,067116 -0,062368 20141031 20141128 20141231 20150130 20150227 20150331 20150430 20150529 20150630 20150731 20150831 20150930 20151030 20151130 20151231 0,012726 0,024920 -0,028446 -0,130248 0,093069 -0,072862 0,196409 -0,030222 -0,057832 0,057758 -0,061456 0,017004 0,189336 0,039324 0,020791 -0,133962 -0,006873 -0,010668 -0,044440 0,063466 -0,008892 0,067227 -0,001985 -0,041202 -0,004119 -0,079017 -0,019744 -0,033731 0,004569 -0,012911 0,071960 0,105556 -0,071891 0,061424 0,100461 -0,031372 0,005786 0,045146 -0,037266 -0,032888 -0,066117 -0,021816 0,083409 -0,005690 -0,110228 0,011559 0,088629 0,031490 -0,099676 -0,035704 -0,101033 0,058087 0,013042 -0,096228 0,016994 -0,080603 -0,081041 0,052714 -0,047536 -0,045933

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