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You have been not really precise in the explanation of your steps, however remember that "random number" is a rather generic expression since the method you describe can be applied to a restricted class of distribution ( among which normal and t ). Considering I am not sure about your methodology my advice is to follow a more classical approach, therefore ...


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Have you thought about opening an Interactive Brokers paper trading account? They keep track of the total return, though their reporting can be trickier to use than it should be. It's also a very good simulation of what investment professionals use, since it's what investment professionals use. If you want to teach investment, I believe Equities Lab might ...


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I'd question the assertion in your question, what proof do you have that leveraged ETFs must go to zero? A plausible price pattern can easily be constructed that leads to a leveraged ETF that climbs forever. That same leveraged portfolio would climb forever as well.


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That part of the paper is showing why the efficient frontier is the same regardless of whether you are maximizing utility, maximizing returns given variance, or minimizing variance given returns. Inequality constraints tend to be a bit more work to deal with analytically, so that might be a reason why they use the equality constraint on one of them. ...


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Take a step back and consider the purpose of immunization: your firm is planning future expenditures, and these are firm commitments. You need to make sure to have cash on hand when these expenditures occur. So you buy bonds, which you plan to sell right before your bills are due. Now you're exposed to interest rate risk. You have two basic options: You ...


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The simple answer is that when you calculate the value weighted return at time $t$ all you really need is the return during time $t$ and the market-capitalization weight as of $t-1$. You can filter the securities to remove the missing ones (and others that you may remove for other reasons, e.g. too small or price too low), calculate weights based on the ...



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