Quantitative Portfolio Management - Homework 1 Case Study

Quantitative Portfolio Management - Homework 1 - Case Study Example From the graph, Roy (1952) argued that investors should pick portfolios in order to maximize the likelihood of getting above some threshold minimum return.. Drawing a straight line from this minimum return tangent to the efficient frontier. Lower thresholds result in optimal portfolios with less return / risk, once you have identified the efficient frontier Using the idea that risks come from different sources, a â€Å"single index model† assumes that actual returns can be separated into systematic (i.e. market-related) and firm-specific parts †¦ here, the â€Å"market† (e.g. S&P500 index) is the source of market-related movements in security i: Since there is no perfect match for this assets, that various portfolio combinations of most two-asset portfolios will lie on a curve to the left as you reduce correlation between pairs of assets, you will have to risk for a given level of portfolio return. Result: One portfolio (P) dominates all of the other efficient portfolio on the efficient set Investors who choose combinations of P and the risk-free asset get the highest return for a given level of risk, compared to all other risky

Leonardo da Vinci - the Phenomenon of the Universal Self-Taught Genius Essay

Leonardo da Vinci - the Phenomenon of the Universal Self-Taught Genius - Essay Example One of the quintessential aspects of Leonardo da Vinci’s artistic and scientific acumen was his aspiration to learn from nature, to imitate it and then to move ahead to conquer it. Indeed, Leonardo da Vinci was an exceptional personality who left his indelible mark on the ages to come.Leonardo da Vinci could indeed be called a Renaissance man in the true sense of the word. Right from an early age, Leonardo had access to the scholarly texts owned by his family and friends (Clark 3). He was indeed mesmerized by the natural beauty of his homeland Tuscany that motivated and inspired him (Clark 3). He was also influenced by the painting traditions prevalent in his times. At the young age of 15, Leonardo was apprenticed to the renowned artist of Florence, Andrea del Verrocchio (Clark 5). Leonardo started exhibiting his natural aptitude for art at a very early stage of his apprenticeship at Verrocchio’s workshop (Clark 5). In the quest for better climes, Leonardo entered the s ervice of the Duke of Milan in 1482. It was during his 17-year stay in Milan that Leonardo achieved the heights of artistic and scientific achievement (Clark 37). At Milan Leonardo not only spent his time painting and sculpting but also designed machines, buildings, and weapons for the Duke (Clark 38). Sometime in 1490, Leonardo developed the habit of noting his observations in meticulously illustrated notebooks filled with varied themes like painting, architecture, mechanics and human anatomy (Clark 56). Once he left Milan, Leonardo spent the next 16 years traveling throughout Italy and working for varied masters (Clark 28). In the period 1513 to 1516, he served the Pope at Rome (Clark 163).