EAA main formula
EAA controls the optimal portfolio asset allocation through an ingenious exponential scoring function of estimates for return (ri), volatility (vi) and index correlation (ci) as well as applying a portfolio concentration exponent: the non-negative elasticities wR, wV, wC respectively wS.
$\mathit{wi}\sim \mathit{zi}={\left(\frac{{\mathit{ri}}^{\mathit{wR}}\cdot {(1-\mathit{ci})}^{\mathit{wC}}}{{\mathit{vi}}^{\mathit{wV}}}\right)}^{\mathit{wS}}$ , if ri > 0 else wi = zi = 0, for i = 1 ... Nwhere for each asset i in an N-sized portfolio:
- wi is the normalized proportional optimal portfolio weight, where the summation of weights is equal to 100%
- zi is the generalized momentum score
- ri is the average return (total or excess*) calculated over the last 1, 3, 6 and 12 months
- vi is the volatility of total return measured over the last 12 months
- ci is the correlation of total returns with the equal weighted universe index measured over the last 12 months.
The four geometrical weights wR, wV, wC and wS are called "elasticities" due to their relative impact on the three terms (ri, vi, ci) of the EAA scoring function. Remember from math class:
- ${x}^{0.5}=\sqrt{x}$ and
- ${({x}^{0.5}\cdot y)}^{2}={x}^{(0.5\cdot 2)}\cdot {y}^{2}=x\cdot {y}^{2}$.
So when applying exponential values ranging between 1 to 0 the scoring effect is mitigated, while values ranging from 1 to 2 amplify the effect of the said term on the score. Note that with wS = 0 the EAA function will return zi = 1 for each and every asset, independent of ri, vi or ci (provided ri > 0). Put differently, with wS = 0 the asset allocation is equal weighted (apart from the safety net offered by a cash proxy fund, see below).
Different from FAA the proportionality with zi allows the weights wi to be not equal. Next to its exponential scoring function, EAA utilizes an optimal top quantile (TopN) of the portfolio size (N) and a C(r)ash Protection routine (CP) by allocating a proportional fraction of portfolio capital to a cash proxy fund (CPF) for every asset with non-positive return. In accordance with the concept of tactical asset allocation the portfolio is rebalanced at the end of each month.
During a stock market crash, like in 2008, the C(r)ash Protection kicks in. Note the unequal weights too (last column). |