Volatility Targeting - The Asset Level.
What’s up readers, I am sure by now most of you would have checked out the code template. There was a call for putting it in more readable format, so attached below is a Github gist for our paid readers! Today, we go through an essential tactical asset allocation technique called the volatility targeting.
First, I want to highlight the different levels of risk management in a portfolio management schematic, and that is
The Portfolio Level, which focuses on multi-strategy allocation and tactical switching.
The Strategy Level, which focuses on overall exposure of a single strategy.
The Asset Level, which focuses on relative capital allocation within a strategy between different capital assets.
There is in some cases no tenable distinction between the different levels since the hierarchical structure of risk baskets can be mixed. For example, multiple strategies (such as different MA crossovers) can be considered the Moving Average Strategy or it can be the Momentum Portfolio Fund . This can of course depend on the preference of the trader, or depend on quantitative exhibits such as the covariance structure in both empirical and theoretical forms.
In our template provided, we take a look at both the Strategy Level and Asset Level tactical allocations — today we focus on the Asset Level approach (we previously discussed portfolio level too), where we target conditional volatilities as the sole factor behind exposures.
When we mean exposure, we really have no strict definition for it. One may consider exposure from a number of variables, or a mix of them. For instance, we may wish to control portfolio exposure from a
Alpha (expected return) perspective
Nominal value exposure
Risk exposure …
and so on.
We can also further try to expand on these terms. What does risk entail? For a trader, this could be the drawdown risk, (conditional) variance, (conditional) volatility et cetera. Even then, we can unwrap these terms — how do we define our conditional variance, or the choice of modelling behind these figures? Instead of trying to argue and explain the case for what is clearly an immensely large and difficult topic, let us first discuss one of the solutions to such a problem. The reason is simple, there is no singular best model, and the best way to find out is by implementing and testing them out.
The framework of choice, as discussed, is volatility targeting. From a high level view, this means that the capital allocation is inversely proportional to the volatility of the asset. The exposure under consideration is risk, and the risk measure is the volatility of an asset. In particular, we are interested in achieving an equal risk/volatility allocation to all of our positions taken.
Scenario: We have a list of thirty stocks, and a unit-less alpha indicator. We rank their alpha/expected return, indexed 1..30. We ignore a third of the universe, and decide to go long 21..30 and short 1..10 to form a L/S portfolio.
Goal: Identify the smart capital allocation for these 20 stocks.
One of the ways we can do this is by adopting the Markowitz framework, which considers the asset’s expected returns, and cross relationships (the covariance matrix) of asset returns. The inherent issue is the instability of asset’s expected returns and the dynamic instability of asset correlations.
A stylised fact of financial time series is that there are volatility clusters, or that high level of volatility today imply high level of volatility tomorrow and low level imply future low levels. That is, the predicability, or the second moment of returns are considerably easier to approximate. In the Markowitz framework, the only stable approximation are the diagonals of the covariance matrix in the future. The volatility targeting framework ignores all but this aspect of the asset returns; it assigns capital based on the asset volatility, ignoring the expected returns or the alpha size.
Food for Thought: If so, how do you incorporate relative sizing between assets of different alpha strength, such that larger positions are achieved for more confident signals in a volatility targeting framework? (Hint: discussed before!)
The Mathematics
That is essentially what line 76 to line 80 is doing.
The Target Effect
Let us first take a look at the differences between volatility targeting at the asset level against an approach where the capital allocated is nominally equal (size is inversely proportional to the price).
I take some five mediocre-okay strategies and compare their results in the graph above (PAIRS: In BOLD, asset vol target, versus nominal targeting in thinner lines).
I would go and continue to show more numerical statistics, but — I can tell you that the Sharpe and Drawdown, and basically almost all risk-adjusted performance basis favours the vol-targeting approach (except the nominal exposure imbalance, if you consider directional nominal exposure as risk).
So. Let’s round things up: we argued that a volatility targeting approach can be taken to achieve improved performance on risk-adjusted basis. This approach is based upon the volatility as a measure of risk, as well as the belief that volatility can be accurately approximated. Additionally, we considered the difficulty in estimating asset level returns, as well as the dynamic instability in asset correlations and ignored them all together. Next, we formulated the approach, covering but not going into detail the portfolio and strategy volatilities. We look to argue in favour of strategy level volatility targeting based on the stylised facts of volatility clustering, as well as the leverage effect, where the volatility process is anti-correlated with the return process.
We also look to talk about the different volatility estimation techniques, and explore whether they are much different at all.
I shared on Twitter an interesting read on Elastic Asset Allocations. Hope that you go through this and give it some thought.
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2543979