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Under the assumption of normality of returns, an active risk of x per cent would mean that approximately 2/3 of the portfolio's active returns (one standard deviation from the mean) can be expected to fall between +x and -x per cent of the mean excess return and about 95% of the portfolio's active returns (two standard deviations from the mean) can be expected to fall between +2x and -2x per ...
where , is the correlation of the two returns, and , are the respective volatilities. This equation shows that the idiosyncratic risk is related to but often very different to market beta. If the idiosyncratic risk is 0 (i.e., the stock returns do not move), so is the market-beta.
Basket options are usually priced using an appropriate industry-standard model (such as Black–Scholes) for each individual basket component, and a matrix of correlation coefficients applied to the underlying stochastic drivers for the various models.
The binomial correlation approach of equation (5) is a limiting case of the Pearson correlation approach discussed in section 1. As a consequence, the significant shortcomings of the Pearson correlation approach for financial modeling apply also to the binomial correlation model.
An optimal approach to capturing trends, which differs from Markowitz optimization by utilizing invariance properties, is also derived from physics. Instead of transforming the normalized expectations using the inverse of the correlation matrix, the invariant portfolio employs the inverse of the square root of the correlation matrix. [17]
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An exchange-traded fund (ETF) is a type of investment fund that is also an exchange-traded product, i.e., it is traded on stock exchanges. [1] [2] [3] ETFs own financial assets such as stocks, bonds, currencies, debts, futures contracts, and/or commodities such as gold bars.
Like conventional indexes, the VIX Index calculation employs rules for selecting component options and a formula to calculate index values. [6] [7] Unlike other market products, VIX cannot be bought or sold directly. [8] Instead, VIX is traded and exchanged via derivative contract, derived ETFs, and ETNs which most commonly track VIX futures ...
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