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Why not just use Geometric Mean Returns? Each time you buy/sell an ETF calculate the holding period return as a percentage and plug into the formula. The answer is a percentage that you can use to calculate the approximate money appreciation (or loss) against your "fixed notional"


3

You are right, the rules to time-scale a T-years transition matrix $M_T$ are: $M_{k·T} = M_T^k$ $M_{T/k} = \sqrt[k]{M_T}$ The root of a matrix M can be obtained using the spectral decomposition: $M = P·D·P^{-1} \Longrightarrow M^k = P·D^k·P^{-1}$ where $P$ and $D$ are the eigenvectors and eigenvalue matrices of $M_T$. Note: The Perron-Frobenius tells ...


2

In the dot.com era the Internet was considered a-winner-takes-it-all market, new tech start-ups (like Netscape, Amazon.com and the famous Pets.com) was measured by how much the capital they where able to chew through, the logic being that the more they spend the more aggressive they were (at least in the investors' eyes), conquering this new market known as ...


1

Despite the initial reaction, this is actually an interesting question. A related question arises naturally in the context of filling in missing financial time series data or perhaps in back-testing path dependent strategies again with data limitations. An approach based on a Brownian bridge appears here.


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"Burn rate" is a measure of "spend rate" relative to cash on hand. So if you have $10 million dollars, and you spend $1 million dollars a month, you will "burn through" your cash in ten months, at which time your company will either "take off," get new financing, or go under. Strategies that rely on "burn rate" are risky ones. Nevertheless, they are ...


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