A New Kind of Global Macro

This is going to be kind of esoteric because I'm holding my cards close to the vest.

Imagine:
Since the entire basis of global macro is risk management, what if we could put portfolios together one risk factor at a time? Wouldn't that be interesting? Risk exposure is the beginning and the end of all global macro strategy. So why wait until the end to integrate it? It would be much better to bet on the risk factors right off the bat? Why focus on certain commodities, currencies, and corporation's securities (or the respective derivatives)? That was never the point of global macro. We care about capitalizing on macroeconomic changes anyway. Why get exposure to those changes from a few instruments when you could get right to the source, and just buy the factor itself?

It's simpler. It's more efficient. It's more potent. It's better diversified.

So the answer is to construct portfolios consisting of nothing but a few uncorrelated risk factors selected in whatever relative portion desired. The method driving the prediction of risk factors is not the issue. That is for another time. What we're concerned with is portfolio allocation once the decisions have been made.

And best of all? Portfolio optimization is easy. The risk factors are approximated by baskets of many instruments, and the instruments each have a covariance with each other. But that has already addressed by principal components analysis. We can merely treat each factor as an instrument to be bought. (This is reasonable--because it is like buying a stock, which is a basket of risk factors, only these ones have with non-zero sensitivity to only one risk factor.) Once we have bought these baby, de-facto 'stocks,' we realize that they have no correlation at all. Thus, the terms inside the first sigma in the Markowitz Mean-Variance model are eliminated, and the second one is easily maximized by investing the most money where the highest return is expected. This is similar to setting our risk adversity parameter to zero, (though we have done nothing of the kind,) since it is now trivial.

This may seem dangerous, because the allocation weights are not constrained, but a rule can be added separately, allowing a maximum position size in any given risk factor, as well as a maximum position and/or maximum portfolio variance. On top of that, we can use VaR systems and stress testing like any global macro fund would.

The exact method for predicting factors varies considerably. There are several approaches that could work, including the John Paulson approach, the Soros approach, and the Robert Frey approach.

High Frequency Portfolios

An investment management company must keep track of risk across all positions and strategies used in each of its funds. At high frequency, however, this matters less because the positions are held only a short time, and the strategies can be made market neutral or even componentless (as measured by Principal Components Analysis). Instead, the focus is on transaction costs. How much money does the strategy lose from market impact when entering and exiting the trade? How much of those remaining profits are eaten away at by broker fees? These costs will determine how much of a position may be built in the time available for the strategy to work. Thus, the costs and the time series forecast determine how much may be invested, and the investment is entirely time based. Enter here; wait for the time series' next value; exit here if prediction is unfavorable or if a better post-transaction cost profit is predicted elsewhere--and hold position if it is favorable; repeat.

However, the size of orders should also be limited to a certain percentage of portfolio value, the leverage should remain fixed, and a Value-at-Risk system should also be used to determine whether a trade's marginal VaR is too high to make it a worthwhile investment.

One theoretical (gasp!) price impact model is written as an integral, (from the initial price to the final acceptable transaction price) where the integrand is the price multiplied by the liquidity function, which is a function of the price, and can be derived empirically through experimentation and the use of some statistical regression. Of course, we integrate with respect to the price.

This is intuitive because we have an infinitely small amount we can buy without moving the price. The price moves as we buy, so we have the price times the amount we can buy at that price, for every price between the initial and the final one. (And this works in reverse if selling--the top term of the integral will just be lower than the bottom.)

If there is a certain largest absolute price impact that the investor is willing to allow, he can simply set that impact equal to the integral described above, and solve for the upper term. Then, he can see how many shares he will be buying by integrating the liquidity function with respect to the price, and using the earlier boundaries for the new boundaries of integration. Conversely, if an investor wants to see how much of an impact will be made by a trade of a certain size, the later expression can be set equal to a certain number of shares, and the upper bound of the integral can be solved for. In that case, we plug the upper bound into the former expression, and integrate to find the market impact of the trade.

From there, the investor can construct a search heuristic (particle swarm optimization, cuckoo search, etc.) to search for the optimal trade size. From there, we can use a sort of execution algorithm that allows for transactions across time--something that minimizes (if buying) or maximizes (if selling) the VWAP or TWAP.