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Q1. Calculating the GMVP involves three operations: Inverting the covariance matrix $\Sigma$ Multiplying the inverse by a column vector of 1's on the right: $x=\Sigma^{-1} \mathbf{1}$ Normalizing this vector so the elements sum to 1: $w= \frac{x}{1^T x}$ Note that the expected returns $\mu$ are nowhere used in this calculation. If you multiply the ...


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For Q1, it shouldn't. You're simply multiplying the covariance matrix by a constant. However, the optimal GMV portfolio is very sensitive to inputs. The difference could simply be due to rounding (I'm assuming the differences are quite small). Another way annualizing could change your outputs is if you're using transaction cost (of any other trade-off with ...


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Kelly DOES reflect the odds! The simple binary bet form of Kelly is: Kelly Fraction = (p(win) * (odds + 1) - 1) / odds So for a 60% chance of a 50% risk, ie 1:1 equals odds 1, that’s 20% of your capital at risk. More formally, Kelly seeks to maximise log-wealth (LW) LW = sum ( Pi * ln(1 + Stake * Payoffi) Maximise LW, then dLW/dStake = 0 For each ...


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If you're happy with equal stock weightings, then this can certainly be done iteratively. I don't know of any closed-form equation. It works for a universe of 100 stocks, but the calculations obviously grow exponentially if you want to increase your selection universe. Pick five stocks at random. Calculate the portfolio variance. There are then 4 * 95 =...


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An "equal[l]y-weighted basket of 5 stocks" will not have a zero volatility, so this is a meaningful problem. There is no "standard algorithm" to solve the problem. But it can be tackled via heuristics such as Local Search. A candidate solution can be coded as a vector of boolean variables ("included", "not included"). Such a solution maps, given ...


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Let y be the % invested in risky portfolio. \begin{eqnarray*} E(W) &=& p_1W_1 + p_2W_2\\ &=&0.5(y\cdot1.1\cdot100 + (1-y)\cdot1.03\cdot100) + 0.5(y\cdot0.98\cdot100 + (1-y)\cdot1.03\cdot100)\\ &=&103+y \end{eqnarray*} \begin{eqnarray*} E(W^2) &=& p_1W_1^2 + p_2W_2^2\\ &=&0.5(y\cdot1.1\cdot100 + (1-y)\cdot1.03\cdot100)^...


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There might be some differences in how we define things, but there should be only one set of assumptions (i.e., for each asset, there should be only one expected return and expected volatility). Your simulations, which generate potential realizations of returns, should conform to these expected returns and volatilities. It's also not necessary to run ...


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