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(solution) DNSC220 DNSC220 DNSC220 Q1. "Exam2_Q2.xlsx" includes


DNSC220DNSC220DNSC220

Q1. ?Exam2_Q2.xlsx? includes historical monthly stock returns on September 1994 - June 1999 for 6 stocks.

Find the minimum variance portfolio which will give you a return of at least 2.5%. You can assume that you have $1 to invest in total.

Obtain the efficient frontier for minimum returns ranging between 1.7% and 3% with increments of .1% as discussed in Lecture 7 (see page 20 for an example) and explain what it represents.

Date AXP EK CAT WMT XON KO
Sep-94 0.08000 0.04020 -0.061755309 -0.050758225 -0.033613445 0.061551817
Oct-94 0.02405 -0.07005 0.106909425 0.005342816 0.093478261 0.035989962
Nov-94 -0.04049 -0.04632 -0.094140339 -0.008886699 -0.039761431 0.018727186
Dec-94 0.00347 0.04945 0.018472428 -0.08601511 0.00621118 0.007334312
Jan-95 0.06780 0.02618 -0.063902187 0.076471045 0.028806584 0.01941712
Feb-95 0.06746 0.04904 0.004865314 0.038248802 0.022 0.047620188
Mar-95 0.03718 0.04412 0.075062175 0.081118662 0.043052838 0.029080447
Apr-95 0.00289 0.07981 0.058750471 -0.073167203 0.04315197 0.031039731
May-95 0.02158 0.05690 0.029911439 0.047364221 0.026978417 0.060217726
Jun-95 -0.00704 0.00414 0.066393258 0.07750147 -0.010507881 0.038273784
Jul-95 0.09924 -0.04948 0.100543599 -0.004672682 0.026548673 0.029410709
Aug-95 0.04870 0.00911 -0.046181371 -0.077970813 -0.051724138 -0.020953975
Sep-95 0.09907 0.02597 -0.152699623 0.010208354 0.050909091 0.07760044
Oct-95 -0.07968 0.05696 0.004630837 -0.126261077 0.057093426 0.041666166
Nov-95 0.04615 0.09615 0.081496729 0.112096774 0.01309329 0.056998405
Dec-95 -0.02647 -0.01832 -0.042769721 -0.072917289 0.048465267 -0.019801251
Jan-96 0.11784 0.09515 0.102859314 -0.08427504 -0.010785824 0.015151642
Feb-96 -0.00272 -0.02017 0.036894321 0.042950457 -0.009345794 0.071309484
Mar-96 0.07629 -0.00699 0.01872629 0.084733678 0.025157233 0.027930573
Apr-96 -0.01330 0.07746 -0.052090425 0.038044733 0.042944785 -0.01510726
May-96 -0.05670 -0.02255 0.023394255 0.083774741 -0.002941176 0.12883538
Jun-96 -0.02459 0.04538 0.032377999 -0.017362674 0.025073746 0.068058125
Jul-96 -0.01471 -0.04019 -0.021722015 -0.054189567 -0.05323741 -0.043367941
Aug-96 0.00000 -0.02319 0.045539902 0.101089136 -0.009118541 0.066667105
Sep-96 0.05714 0.08276 0.094374152 0 0.021472393 0.019934033
Oct-96 0.02106 0.01433 -0.084653888 0.004745114 0.064564565 -0.007370468
Nov-96 0.11170 0.02383 0.153004638 -0.037735559 0.064880113 0.01484633
Dec-96 0.08560 -0.01079 -0.048973583 -0.105954927 0.038410596 0.029338288
Jan-97 0.09956 0.08100 0.036914773 0.04395212 0.057397959 0.09976313
Feb-97 0.05634 0.03964 0.008049961 0.110529691 -0.032569361 0.053995795
Mar-97 -0.08762 -0.15320 0.025561703 0.059376973 0.074812968 -0.083997452
Apr-97 0.10220 0.09375 0.114300266 0.008968414 0.051044084 0.141255035
May-97 0.05704 0.00228 0.096909626 0.062220878 0.046357616 0.076621852
Jun-97 0.07194 -0.07391 0.099871128 0.13411227 0.033755274 -0.005262217
Jul-97 0.12757 -0.12704 0.047693906 0.109056881 0.048979592 0.016543961
Aug-97 -0.07164 -0.01785 0.036831245 -0.053336712 -0.04766537 -0.170886691
Sep-97 0.05305 -0.00669 -0.071043988 0.033527157 0.046986721 0.066933149
Oct-97 -0.04470 -0.07796 -0.045850734 -0.044363993 -0.04097561 -0.071722342
Nov-97 0.01122 0.01989 -0.06463455 0.144638893 -0.007121058 0.10616834
Dec-97 0.13448 -0.00103 0.011735089 -0.013954027 0.00307377 0.067000713
Jan-98 -0.06232 0.07740 -0.004946495 0.009507559 -0.030643514 -0.02905328
Feb-98 0.07618 0.01254 0.136719903 0.16326417 0.074815595 0.059845261
Mar-98 0.01943 -0.01143 0.009163221 0.098833643 0.060784314 0.130750316
Apr-98 0.11540 0.11272 0.038638898 -0.004917273 0.080406654 -0.02017768
May-98 0.00428 -0.00503 -0.035126189 0.090233432 -0.035072712 0.032948591
Jun-98 0.11064 0.02364 -0.036974516 0.103541399 0.012411348 0.092927372
Jul-98 -0.02967 0.14799 -0.077965258 0.03909216 -0.015761821 -0.058479587
Aug-98 -0.29332 -0.06367 -0.134020205 -0.065345041 -0.068505338 -0.190993228
Sep-98 -0.00481 -0.01600 0.059524535 -0.072995161 0.079274117 -0.112977483
Oct-98 0.13847 0.00813 0.016198726 0.264299882 0.014159292 0.172451155
Nov-98 0.13586 -0.05738 0.100139627 0.090498645 0.047120419 0.039128037
Dec-98 0.02436 -0.00861 -0.069532896 0.082439482 -0.025 -0.04371076
Jan-99 0.00593 -0.09201 -0.052343254 0.056024712 -0.039316239 -0.025186072
Feb-99 0.05468 0.01893 0.051949779 0.001452055 -0.052491103 -0.02200998
Mar-99 0.08724 -0.03494 0.008229604 0.071508367 0.060093897 -0.036687577
Apr-99 0.10988 0.17025 0.4082095 -0.002033037 0.177147919 0.108960989
May-99 -0.07365 -0.08961 -0.147572606 -0.073368897 -0.038374718 0.00642878
Jun-99 0.07677 0.00185 0.093393898 0.133296849 -0.034428795

-0.092695762



Q2. A company is in the process of deciding whether to introduce a new product to the market or not. As in many new product scenarios, there is uncertainty about the success of the new launch. The company estimates that the market response will be great with probability 0.45, OK with 0.35 and will be bad with 0.20.

The company also considers developing some form of R&D to improve the product which could potentially improve their chances of success in the market. It costs $100,000 to conduct the R&D project. If they were to go with the R&D option there are 3 potential outcomes: they can improve the market response, they do not affect the market or they make the market response worse with probabilities 0.70, 0.20 and 0.10, respectively. When the market response improves, the probability of a great response will be 0.70, OK response 0.20 and the bad response will be 0.10. When the market response worsens, the probability of a great response will be 0.20, OK response 0.50 and the bad response will be 0.30.

In addition, the profit margin per item sold for the new product is $1.8 and it is expected that if the market response is great they will sell 600,000 units, if it is OK they will sell 300,000 units and if it is bad they will only sell 90,000 units.

  1. a)  Develop a decision tree to solve this problem and use the EMV criterion.
  2. b)  Obtain the risk profile of the optimal decision (probability distribution) and comment on what it represents.
  3. c)  Calculate the expected value of perfect information (EVPI) for the R&D results and explain what it represents.


 


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