Portfolio Strategies

Strategy type & universe

What is the difference between maximum gross exposure and net exposure?

The maximum gross exposure is the sum of absolute positions in your portfolio, while the net exposure is the signed sum of long and short positions. E.g 100% long and 100% short positions would make the gross exposure 200% but the net exposure as 0%.

What is the difference between a benchmark and stock-picking universe?

The portfolio active return is the annualised difference between the benchmark universe return and the portfolio return. The risk controls are calculated relative to the benchmark universe. By restricting the stock-picking universe to a subset of the benchmark, you may induce a desired tilt in your portfolio by only allowing allocations to this subset.

When restricting my stock-picking universe to a subset of the benchmark, would it make sense to also restrict the benchmark to the smaller subset?

Having a common benchmark for a range of different stock-picking subsets will help in measuring performances versus a common ground. For example, you may have a common Europe benchmark, and various sectors within the Europe universe as your stock-picking universes. Information Ratio and other measures will be based on a common reference point.

You may also want to reduce your benchmark to the stock-picking universe in some cases, e.g. if you want to investigate how well an alpha signal performs in a long-short strategy compared to being long in the given stock-picking subset.

Alpha & style factors

What is the significance of the weight field in alpha and style factors? Can it be negative too?

The weight signified scales your effective positions which can increase the net returns you observe in the portfolio. But it also increases the leverage in the case of a long/short portfolio. Negative weights can be chosen, if you want to bet against the sensibility of your construct.

Can I put multiple signals into the alpha and style factors tab?

Yes, you can include multiple alpha signals with an option of choosing static weights for each one of them. There will be a feature of weight optimization that will be coming out soon.

When do I pick Z-transform over the percentile-based normalization?

Use percentiles for a ranking based scoring, while the Z-transform is good for a normal distribution of signal scores and handling outliers, because it employs winsorization.

Risk control

How does “reduce single company exposure” differ from “reduce tracking error”?

Reduce single company exposure will try and minimize the quadratic objective of portfolio positions with respect to the benchmark positions, while tracking error will reduce the covariance matrix based quadratic objective. In other words, the "reduce tracking error" takes into account the correlations between stocks and tries to reduce the volatility of the strategy based on that, whereas "reduce single company exposure" simply tries to stay close to the benchmark positions without considering the correlations and volatilities of each stock.

How does changing the weighting factor for “reduce volatility” affect the overall portfolio? How does this weight interact with the signal weight in the previous tab?

Increasing/decreasing weight on volatility will put stricter/leaner limits on volatility in the objective function thereby allowing to scale the returns of the portfolio. You could choose the correct set of weights according to your risk appetite and leverage constraint, by choosing different weights for signal and volatility.

Which one of “Maximum relative deviation” or “Maximum absolute deviation” takes precedence in “reduce sector exposure”?

The larger range will take effect in the strategy. For example: your current exposure to Industrials is 5%. Setting an absolute deviation of 3% will give an allowed exposure of 2% to 8%. Setting a relative deviation of 100% will give an allowed exposure of 0% to 10%. Hence, the strategy will allow an Industrials exposure in the range of 0% to 10%.

Where can I find more information about Exabel's factor model?

The article Exabel's Factor Model is available on arXiv.

Rebalancing options

What happens if I rebalance every 5 days, and it’s a weekend on one of the rebalance dates?

The rebalance date will be shifted to the next business day

How is trading cost incorporated into the model?

Given in basis points (0.0001%), it is the average cost of buying/selling a stock and bringing it in/out of the portfolio. Higher turnover of your portfolio implies higher transaction costs. So you can choose to minimize turnover if the churn is high.

Backtest results

Why are the resulting long, short, and gross exposures sometimes far off my max exposure limits?

Depending on the strength of the risk controls versus the alpha signals, smaller exposures may result in a better objective goal value. If this happens, try increasing the weights of your alpha signals, and/or reducing the weights of the risk controls.

What are the transfer coefficients?

The transfer coefficient of an alpha signal is defined as the average correlation between the alpha score values and the active positions of the strategy (the strategy allocation minus the benchmark allocation, if any). This is a measure of how well the alpha scores are reflected in the actual positions of the strategy. If there was only one alpha signal and no risk controls beside “reduce single company exposure”, then the positions taken would be proportional to the alpha scores. The correlation between signal value and position would thus be 1.0. However, the various risk controls distort the positions. Furthermore, when there are several alpha signals, they will be affecting the positions differently. The transfer coefficient is then a measure of how purely each alpha signal is reflected in the resulting portfolio.

Optimization routine

What is the mathematical formulation of the optimization problem?

For each rebalancing date, we solve a quadratic optimization problem, with linear constraints. The different parts of the configuration are handled in the following way:

Linear terms in the optimization objective to maximize the alpha exposure:

The alpha factors enter into the optimization objective as linear terms, multiplied by the given weights, and optionally normalized with a winsorized z-transform or as percentiles.

Quadratic terms in the optimization objective to minimize the risk exposure:

"Reduce single-company exposure relative to benchmark" gives a quadratic term per stock in the optimization objective, that minimizes the difference between the portfolio's allocation and the benchmark allocation.
"Reduce absolute volatility" adds the estimated volatility to the optimization objective. The estimated volatility of the portfolio is calculated from the historical covariance matrix of the share prices, and takes the form of quadratic terms in the optimization objective.
"Reduce tracking error" adds the estimated volatility of the difference between the portfolio and the benchmark to the optimization objective. This estimated volatility is calculated from the historical covariance matrix of the share prices, and takes the form of quadratic terms in the optimization objective.
"Reduce sector exposure relative to benchmark": For each sector, a quadratic term is added to keep the portfolio's sector exposure close to the given target exposure.
"Reduce country exposure relative to benchmark": For each country, a quadratic term is added to keep the portfolio's country exposure close to the given target exposure.

Quadratic terms in the optimization objective to reduce trading costs:

"Minimize turnover": If enabled, quadratic terms are added to keep the allocations close to the allocations from the previous rebalance date.

Linear constraints for factor exposures:

"Reduce sector exposure relative to benchmark": For each sector, there is a constraint that the net allocation to that sector needs to stay within the given lower and upper bound.
"Reduce country exposure relative to benchmark": For each country, there is a constraint that the net allocation to that country needs to stay within the given lower and upper bound.
"Control style factor exposure": For each style factor, there is a constraint that the net exposure to that style factor needs to stay within the given lower and upper bound.

Linear constraints for allocation limits, for long only strategies:

"Maximum long allocation": For each stock, adds a constraint that keeps the allocation below the given threshold.
"Maximum overweight": For each stock, adds a constraint that keeps the allocation below the given threshold plus the benchmark allocation to that stock.
"Maximum underweight": For each stock, adds a constraint that keeps the allocation above the the benchmark allocation to that stock minus the given threshold.
"Maximum benchmark deviation": Adds a constraint that keeps the aggregate benchmark deviations (summed over all stocks) below the given threshold.

Linear constraints for allocation limits, for long/short strategies:

"Maximum long allocation": For each stock, adds a constraint that keeps the (long) allocation below the given threshold.
"Maximum short allocation": For each stock, adds a constraint that keeps the short allocation below the given threshold (if the threshold is 5%, the allocation must be higher than -5%).
"Net exposure": Adds a constraint that keeps the net allocation (sum of long allocations minus sum of short allocations) at exactly the given desired net exposure.
"Maximum gross exposure": Adds a constraint that keeps the total long and short allocations below the given threshold.

In addition, there's a setting for "Maximum positions", specifying the maximum number of stocks that the portfolio is allowed to take positions in. Since this is a discrete constraint, it is handled outside of the optimization routine itself, through an iterative process. First, the portfolio is optimized with all stocks included. Then, the stocks with the smallest allocations are removed, and the portfolio is optimized again. This process is repeated up to 10 times, where the last optimization will include no more than the desired number of stocks.