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Not acutally a paper, but there is even a book on Multifractal Models. It is, to my knowledge, the standard reference on this topic by Calvet and Fisher: Multifractal Volatility: Theory, Forecasting, and Pricing (Academic Press Advanced Finance)


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The paper "A Multifractal Model of Asset Returns" by B. Mandelbrot, A. Fisher and L. Calvet (1997) discusses the creation of multifractal processes in Section 3.4.


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The initial investment is the capital in the account used to support the portfolio, not the cost of the assets in the portfolio. For example, when you sell a stock or bond short, your account doesn't actually accrue any cash. Instead you start receiving a regular cash flow. There isn't necessarily a difference between these quantities in a long-only ...


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Following Daniel, Grinblatt, Titman, and Wermers (1997) "D.G.T.W.!", DGTW subtracts from each stock return the return on a portfolio of firms matched on market equity, market-book, and prior one-year return quintiles. Daniel, K., Grinblatt, M., Titman, S., Wermers, R., 1997. Measuring mutual fund performance with characteristic-based benchmarks, Journal of ...


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I would absolutely use a mark-to-market value in your daily pnl for the purposes of evaluating performance (e.g. Sharpe). So, yes, that would include the value of open positions in addition to your cash balance. If you hold something for a year, that performance was earned one day at a time, not all at once. If you only look at cash, you will have a large ...


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This is not a perfect solution but perhaps the following approach could also serve you well as an indicator. Assuming you are only using a finite number (e.g. $n$) of bonds with fixed yields $r_i$ you can write $r_f(w_1, \dots,w_n)=\frac{\sum_0^n w_ir_i}{\sum_0^n w_i}$ with most of the weights being zero. Using the quotient rule you can now calculate ...


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For a single day as long as $K(t+1)$ includes the intraday cash flows it is the same, however if you do not simulate your cash balance interest rate you forget that your cash get compounded over time, which is slightly incorrect. This is why someone suggested you simulate your cash balance. This is more correct as well if you are not always 100% invested or ...


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You are not doing anything wrong. You just need to multiply the absolute return by the currency conversion factor. Example: You trade 200,000,000 yen notional and generate a return of 16% on that notional, then simply multiply 32,000,000 jpy gain by your conversion factor 0.0126 to yield a return of 403,200 USD. The return of 16% was generated on the ...


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I would suggest writing the joint density as the product of the conditional densities then estimate parameters using an optimization package. The joint density is given by $$f(r_0, \ldots, r_T) = f(r_0) \prod_{t=1}^T f(r_t|r_0, \ldots, r_{t-1})$$ then the log likelihood function is $$L = \log(f(r_0)) + \sum_{t=1}^T \log(f(r_t | r_0, \ldots, r_{t-1}) ...


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This is the equity line i got after i repeated your code. how is this good ? may be you have run with only one set of numbers. any ways here are a few things you can do to come closer to reality : take the close prices as lognormal distribution instead of a normal distribution. you are adding up the returns later on. this is only right if you have ...


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It seems to me that you want to use the series of option prices to estimate the Sharpe ratio given the option prices in your sample. If so, the idea is to realise that for each option price you have at different times $t_1, t_2, ...$ you could actually close the position and realise the profit or loss. So, basically if you have the option prices you just ...


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We actually managed to come up with the answer to this question ourselves but wanted to share the answer since it might be relevant to others as well. The calculation depends on what method is used to calculate the cost. There is the FIFO, LIFO and the average cost method, see: http://www.accounting-basics-for-students.com/fifo-method.html If FIFO or LIFO ...


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Compounding the monthly excess returns won't provide the annual excess return. You need to compute the difference between the annual return of the portfolio and the annual return of the benchmark. To illustrate this let's look at an example. Consider the following two situations: The benchmark performs well with a $2\%$ return each month; The benchmark ...


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2) you only take trading days for your analysis because taking in account days on which no price changes took place would shift results in a wrong direction. For exmple, you mostly take 250 trading days p.a. 3) Your time interval up to 2007 is okay and excludes the financial crisis, which is a non-normal circumstance. Therefore, your time interval can be ...


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It obviously depends on what you're trying to do but since we're speaking about returns zero centering is what's usually done because of the null hypothesis claiming that expected excess returns are zero. You zero center the distribution because you want to obtain a distribution satisfying the null hypothesis. In this distribution you then plug your sample ...


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You should definitely check out the Virtual Stock Exchange Games* by Marketwatch it provides simple interface, and many options for the rules of the game. Its instantly online, free, and uses real-time prices, but it only allows trading NASDAQ stocks, as far as I know. These games are meant to be played by students, and thought, so I hope it fits your ...



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