The Sharpe Ratio allows us to quantify the relationship the average return earned in excess of the risk-free rate per unit of volatility or total risk. Sharpe, the Sharpe Ratio is a measure for calculating risk-adjusted return and has been the industry standard for such calculations. Sharpe Ratioĭeveloped by Nobel Laureate William F. You can learn more about the MLQ app here or sign up for a free account here.
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If you're interested in learning more about machine learning for trading and investing, check out our AI investment research platform: the MLQ app. In our previous articles on Python for Finance, we've focused on analyzing individual stocks, but we will now shift our focus to the more realistic scenario of managing a portfolio of assets. The following guide is based on notes from this course on Python for Finance and Algorithmic Trading and is organized as follows: Finally I should note that we do not even need convexity but often merely quasi-convexity (which might be the case for constrained optimizations).In this guide, we're going to discuss how to use Python for portfolio optimization. However, as Arshdeep's existing answer notes, a concave function can be made convex by multiplying by -1. Note that coherent risk measures (like CVaR/ES/TCE/ETL) are convex as discussed in Föllmer and Schied (2008).īoth of these objectives are concave. That is very different from a portfolio where weights of $1/N$ diversify our exposure to multiple sources of risk and thus tend to reduce the total variance.įor a mean-variance portfolio optimization, we have the following problem: So your initial presumption of concavity is not correct.įor a Bernoulli random variable, the uncertainty of outcomes is most uncertain for outcomes that are equally likely. However, the variance of a portfolio, $w^T\Sigma w$, is not concave in $w$. First, a correction is in order: the math question you cite is the variance for a Bernoulli random variable as a function of the parameter $p$.
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