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That's the way you apply. Usually you get the closest number of shares possible. However, if you use that strategy you are very likely to underperform the market. Check table 3 on this paper for the Out of sample performance of the Markowitz strategy. Over their sample the Sharpe Ratio is 0.07 whereas a simple naive strategy 1/N yielded 0.18.


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You will need the covariance matrix to calculate this. Say you have a collection of $n$ assets. The value of asset $i$ is represented by the random variable $X_i$ and the corresponding portfolio weight is are $w_i$, and $v_i$ for the two portfolios. The correlation between the two portfolios is: $$ \frac{\sigma(w^TX,v^TX)}{\sqrt{(w^T\Sigma w)(v^T\Sigma ...


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One standard approach is to shrink your forecasts towards zero (or to some reasonable value as in the Black-Littermann model). Shrinking towards zero is done by: $$w^*=\underset{w}{\text{argmax}} \ \ \lambda_{\alpha} r^Tw - \lambda_r w^{T} \Sigma w - tradingCost(|w-w_0|)\\$$ $$0\leq\lambda_{\alpha}\leq1$$ Shrinkage coefficient $\lambda_{\alpha}$ is best ...



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