Hi all, Could you please help me understand the relation between risk models and trading strategies? Esp. I don't understand the following sentences: "Alternatively, portfolios can be rebalanced with objectives and constraints simultaneously incorporating different risk models. " Any thoughts? Thanks! --------------------------------------------------------------- For the last five years, Axioma has provided portfolio managers with fundamental and statistical risk models that are fully updated on a daily basis. These models can be used within AxiomaÂ¡Â¯s portfolio construction software platform to manage portfolios using multiple risk perspectives. For example, the predicted risk and tracking error of any given portfolio can be measured with both a fundamental and a statistical risk model to provide a range of risk predictions. Alternatively, portfolios can be rebalanced with objectives and constraints simultaneously incorporating different risk models. Research has shown that using multiple risk models for portfolio construction can significantly improve realized performance. In this talk, we consider the possibility of constructing alpha signals by comparing the differences in risk model predictions across both risk model type (fundamental vs. statistical) and across small differences in time (an up-to-date risk model vs. one that is a few days older). These signals exhibit intra-month variations that are essential for extracting a reliable signal. When these intra-month variations are taken into account, the signals found prove to be high quality and reliable. This signal extraction process produces benchmark-dependent, daily alpha signals that can be easily incorporated into an existing portfolio management process. For example, if an existing process rebalances on the fourth trading day of the month, the alpha signals corresponding to the given asset universe and trading day of the month can be used to augment an existing rebalancing process. The signals provide an easy to use and readily understood tool for leveraging the intra-month alpha signals embedded in daily, fundamental and statistical risk models to improve performance.

Risk can be modeled using GARCH (generalized autoregressive conditional heteroskedasticity). Risk = future variance = future volatility. You can predict or estimate or determine likelihood of risk using other methods, so they're talking about combining multiple methods to better determine risk. Whether or not this actually works, who knows. The benefit is, if you're trying to keep your risk/beta/Sharpe ratio low, you can load up on equities and keep cash/bonds portion low, if your model shows that future risk/beta on the equities will be within your risk tolerance. The downside is, in a market downturn or volatile market all of a sudden things (prices, strategies) that weren't correlated and/or weren't risky become correlated and risky.

Risk is the following: *Position Sizing *Portfolio Allocation *Risk may specify a Type of Asset versus another specific type of asset *Duration of risk aversion can be specified Trading Strategies define the behavior of the underlying asset or instrument your risk technique has allotted you to purchase or required to liquidate... Sometimes your risk model is utilizing signals which are also trading signals, so this is where the distinction would get blurred.

The measure of risk one uses in allocation depends on objectives and frequency of allocation. If you re-allocate daily, ATR is maybe appropriate. If you re-allocate yearly, beta is more appropriate. Maybe some people re-allocate portion of the portfolio every few days so they use a mix. This is the point.

Interesting. Have you tried putting GARCH predicted covariance into mean-variance optimization and how good is the performance? When I did mean-variance optimization using historical mean and historical covariance, the backtest Sharpe ratio was horrible.

In the outline of their methods, it says you can generate alpha-signal by inspecting the risk models and their variations. Any thoughts?

I don't personally use GARCH but I've seen papers using GARCH for index funds. I imagine it would work for relatively stable investments like index funds, bonds, currencies. For short time-frame (less than 3 months). What class were your investments? How long was your timeframe? Other keywords concerning portfolio optimization (risk estimation): Markov chain Monte Carlo (MCMC), empirical distributions, extreme value theory, stochastic volatility. Note some models will use Bayesian model whereas other models consider fat tails and extreme values.

I suggest that some reading might give you more education than repeated question and answers on this forum. Trading Risk by Kenneth Grant is good. Also, the Original Turtle Trading Rules might be relevant to your style of trading. It is a good example of a complete and successful trend following strategy: https://www.bsp-capital.com/documents/turtlerules.pdf