I require assistance with this assignment. Any help would be appreciated. It mostly involves calculating probabilities, variances, etc. in regards to stocks

UNIVERSITY OF TORONTO Joseph L. Rotman School of Management RSM332 PROBLEM SET #3 1. Suppose there are two risky assets, A and B. You collect the following data on probabilities of different states happening and the returns of the two risky assets in different states: State State 1 State 2 State 3 Probability RA RB 0.3 7% 14% 0.4 6% 4% 0.3 8% 8% The risk-free rate of return is 2%. (a) Calculate expected returns, variances, standard deviations, covariance, and correlation of returns of the two risky assets. (b) Calculate expected return and standard deviation of the tangency portfolio. (c) Suppose now that the lending rate differs from the borrowing rate: you can borrow at RF,b = 2% but can deposit money in a risk-free asset only at RF,l = 0.5%. There are three investors. The first one wants a portfolio with standard deviation of 3%, the second one wants a portfolio with standard deviation of 5%, and the third one wants a portfolio with standard deviation of 7%. Each investor has only $1,000 to invest. Describe how much each investor should allocate to different assets to create the desired portfolios. What is the expected return of the portfolio of each investor? 2. (a) Given three securities: Stock 1 Stock 2 Stock 3 Expected Return 0.15 0.20 0.08 Standard Correlations of Returns Deviation Stock 1 Stock 2 Stock 3 0.20 1.00 0.20 0.30 0.30 1.00 0.80 0.10 1.00 (a) Find the expected return and standard deviation of a portfolio with 25% in stock 1, 50% in stock 2, and 25% in stock 3. (b) For the portfolio in part (a), find the covariance of its return with the return of an equally weighted portfolio of stocks 1 and 2. (c) Suppose the risk-free rate is 5%. Someone claims you that an equally weighted portfolio of Stocks 1 to 3 is the tangency portfolio of these three stocks. Do you believe his claim? Justify your answer. 1 3. Can Financial Engineering Cure Cancer? Before you do this question, you may want to watch the following video first: https://www.youtube.com/watch?feature=player_embedded&v=xu86bYKVmRE Consider a hypothetical drug-development program requiring $200 million in out-ofpocket costs over a 10-year period during which no revenues are generated, and with only a 5% probability of success. However, if the drug development is successful, it is plausible to assume that it could generate a net income of $2 billion per year over a 10-year period of exclusivity from years 11-20. The present value of this income stream in year 10 is $12.3 billion (using a 10% cost of capital). (a) Compute the expected return and standard deviation (over a 10-year period) of this investment. (b) Suppose we setup a megafund to fund 150 drug-development programs, with the same amounts of investment and payoff as the one in part (a). Assuming that the success or failure of each program is independent of each other, what is the probability for the megafund to score three or more successes in the 150 drug-development programs. (c) Compute the expected return and standard deviation (over a 10-year period) of the megafund. 4. hw3.xlsx contains the monthly return data for Microsoft (MSFT), IBM (IBM), Apple (AAPL) and Hewlett-Packard (HPQ) for the period 2007/1-2016/12. (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 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 20100528 20100630 20100730 20100831 MSFT 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 -0.150811 -0.108140 0.121686 -0.085819 IBM 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 -0.023953 -0.014210 0.039844 -0.035981 AAPL 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 -0.016125 -0.020827 0.022741 -0.055005 HPQ 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 -0.114682 -0.057596 0.063771 -0.164857 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 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 0.089418 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 0.167215 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 0.096229 -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 20140630 20140731 20140829 20140930 20141031 20141128 20141231 20150130 20150227 20150331 20150430 20150529 20150630 20150731 20150831 20150930 20151030 20151130 20151231 20160129 20160229 20160331 20160429 20160531 20160630 20160729 20160831 20160930 20161031 20161130 20161230 0.018564 0.035012 0.059082 0.020471 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 -0.007030 -0.069886 0.085495 -0.097049 0.069982 -0.034528 0.107680 0.020113 0.002436 0.040278 0.012183 0.031198 -0.016761 0.057373 0.009026 -0.012845 -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 -0.093228 0.060421 0.155842 -0.036382 0.063040 -0.012749 0.058242 -0.002117 -0.000189 -0.032483 0.064611 0.023240 0.027662 0.028731 0.077092 -0.017073 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 -0.075242 -0.001335 0.127211 -0.139921 0.071368 -0.042660 0.090063 0.023606 0.065504 0.004334 -0.021578 0.047955 0.010149 0.057304 0.067116 -0.062368 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 -0.179899 0.100927 0.164079 -0.004058 0.090465 -0.052765 0.116335 0.025696 0.089353 -0.066967 0.062802 -0.027747