Description Usage Arguments Value Author(s) References
Generate arithmetric returns and arithmetric covariance matrix given a distribution of log returns
1 |
mu |
a numeric containing the expected logarithmic returns for each security |
sigma |
a covariance matrix of log returns |
a list containing two elements:
arithmeticMean a numeric containing the mean arithmetic returns
arithmeticCovariance a variance-covariance matrix in simple arithmetic return terms
M_{ τ }^{i} = e^{ μ ^{τ} _{i} + \frac{1}{2} Σ^{ii} _{τ} }, \\ S^{ij} = e^{ μ ^{τ} _{i} + μ ^{τ} _{j} + \frac{1}{2} \big(Σ^{ii} _{τ} + Σ^{jj} _{τ}\big) } \big(e^{Σ^{ij} _{τ}} - 1\big)
Ram Ahluwalia ram@wingedfootcapital.com
# formula (7) and (8) on page 5 of Appendix to "Meucci - A Common Pitfall in Mean-Variance Estimation" http://www.wilmott.com/pdfs/011119_meucci.pdf
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