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I just pushed Python implementations of some common portfolio optimizers to my GitHub. It uses the CVXOPT library to solve the resulting quadratic programs. It supports the construction of Markowitz portfolios, minimum variance portfolios and tangency portfolios (both long-only or long/short).


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I may not have fully understood your question, but I assume you are asking what will happen on a leverage portfolio over time if the underlying price stays the same. A leveraged portfolio would likely eventually go to zero (and below) simply because of the cost of leverage. At minimum, you are borrowing at the risk-free rate. An ETF would just go to zero.


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I would make a cumulative return chart, using a different color for each sector. Each line starts at 1, and each successive point is found by multiplying the previous point by (1+SectorReturn) for that sector. The horizontal axis shows dates. By looking at the lines on this chart you get a visual feel for what sectors performed best overall and also the ...


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First, for each of the 3 currencies taken separately, find out the leverage lambda_i (i=1,2,3) that would be required to produce an annual standard deviation of 12%. [In my experience the std dev of currencies is about 8 or 10%, so the three lambdas will be small, like 1.25 or 1.2]. Then find out what is the volatility that results when the three 12% vol ...


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With a dedicated portfolio all interest rate risk has been eliminated, since you hold ZCB's that deliver exactly the cash you need when you need it. So it is a perfect hedge against i.r. risk. With an immunized portfolio you have reduced i.r. risk (by matching duration and convexity) but you still have a probability distribution of outcomes. Yields at ...



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