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Financial Portfolio Analysis

Choose five risky assets and give reasons for your choice. Download historical price information
from Yahoo Finance (use ‘adjusted close’ prices for the basis of the computation).
• Compute the sample mean, variance, and standard deviation of these shares (in annual
• Compute the variance-covariance matrix V .
• Plot the daily share prices and daily returns for each individual asset.
• Perform linear regression on your data using an appropriate index as proxy for the market
porfolio, and find the alpha, beta, and noise coefficients.
• Perform the two tests suggested in the lecture notes to assess whether returns are indeed
(at least approximately) market invariants. Discuss your findings.
Choose appropriate starting time points for the investment period and use previous data to
• compute the efficient frontier and plot it.
• use utility functions u(µ, σ) = µ−ασ2 and u(µ, σ) = µ/σ2
to select the ‘optimal’ portfolio.
Use subsequent data to
• compare the investment performance of your constructed portfolios against the index performance at some chosen future time points (say, every 20 trading days);
• study if asset protection would have been useful, e.g. using the following approach: if you
purchase an asset, buy the corresponding Black-Scholes priced put option for the intended
time period, if you short an asset, buy the corresponding Black-Scholes priced Call option
for the intended time period.
In all steps, discuss the asset allocations and other findings, and draw conclusions of your studies.
Where applicable try to include additional, more advanced concepts, for example
• short selling constraints,
• detection of outliers,

Sample Solution

ucational institutes beneficially affected the way students understood a concept. Marianne Stenger, a journalist from the online education provider OpenColleges, claims that it allows students to “learn from realistic scenarios without the risk of practicing an unfamiliar skill in an uncontrolled real-life situation”(Stenger 3). It also makes it possible to simulate environments. A common misconception is that VR is used only for video games, however, according to Stephen Babcock, the Market Editor for Baltimore, its “increased accessibility also presents an opportunity to use virtual reality in fields beyond” these game environments (Babcock 1). This simulation can range from environments as small as the inside of a biological cell to as big as space. This immersion creates educational settings where students are engaged and are able to experience situations personally. This personal experience also holds many opportunities for students “to construct their own knowledge from meaningful experiences”(Hu-Au and Lee 5). Similarly, VR helps students make connections that they could not have seen before because VR allows one to “construct visual and manipulable objects” making learning easier (Hu-Au and Lee 5). The explicit education that comes from VR education in a class environment provides a foundation to the implicit education that a student can form on his or her own through the connections he or she makes. A student can form connections faster through practice and improve academically when using VR as a learning tool. These connections and VR implementation are seen more in higher educational facilities and serve as a model to lower educational facilities. In medical schools, VR is being used as a training and informational guide on dealing with medical situations. The aspect of surgical training is one of the primary uses of VR in these facilities. According to Lan Li and his colleagues, collaborators of the National Center for Biotechnology Information, before VR was introduced into medical facilities, the only way junior doctors could receive medical training was by being in a real operating room under the supervision of experienced surgeons. However, this approach took too much time and was costly (Li et al 2). Additionally, as medical practices evolved and became more complicated, “sole observation was no longer enough for acquiring certain skills and special techniques”(Li et al 2). With the introduction of VR, surgical trainees are able to partake in such surgeries. These simulated surgeries are more interactive, with the abilities to zoom and label objects, and more hands on. VR allows the trainee to have prior experience with surgery so that when performed on a patient, they are experienced and not a hazard to the patient’s health. A possible counterargument to this is that VR programs to train surgical trainees aren’t precise enough to be considered as real training. However, the opposite is actually true. Li and his colleagues state that “VR simulations are more realistic due to very intuitive anatomic structures exhibited in the 3D graphics”(Li et al 2). Due to VR being more realistic, it can serve as a better tool than traditional methods of

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