Risk-based allocation of Trading Mate portfolio
When a portfolio invests on different markets there is always the problem of deciding how much capital to allocate to each given market. Most of the time, this is done based on personal preferences or sometimes based on performance.
We will discuss here a risk-based approach that could also be followed to decide how to allocate your trading capital.
As a reminder, Trading Mate invests in the following markets:
The metrics we will use to decide the allocation is the Value at Risk (VaR). If you go to our results page you will find this value reported in the title of each plot. It represents the loss that you expect will be exceeded on the following day only with a very small probability (in our case 1%). In other words, you are 99% confident that during the next trading session your strategy won’t lose more than the VaR.
In the plot title we also show the Expected Shortfall. This number is very important because it tells you: ok, I’m 99% confident that I won’t lose more than the VaR during the next session, but how much can I lose in that 1% of cases when the loss will be exceeding the VaR? The answer is that your expected loss in those cases is equal to the Expected Shortfall. So, really, VaR and Expected Shortfall are two important risk measures that should always be read together.
In the following we will use only the VaR numbers of each markets to decide our allocations, but the same approach could be followed by using the Expected Shortfall. You will see that with some simplifying assumptions this approach will easily give us a VaR for the whole Trading Mate portfolio. The next step then is to set our own risk tolerance and change the allocations to maintain the portfolio VaR within the risk limits we set to ourselves.
An example
Let’s assume that our trading capital is 100,000. This is the amount of money we are willing to risk in the market in order to have the opportunity to achieve higher returns.
In the example below, we are assuming that the trading capital is equally split across all markets we trade. This can be seen in the “max allocation” column. For example, we will allocate 7.7% of our trading capital, so 7.7k, to our trading on S&P500. In this example, we assume the same allocation is given to all other markets.
The column “VaR” shows the market loss that we expect will be exceeded over the next 1 day only with a 1% probability.
Finally, the column “exposure” shows the suggested exposures that we publish everyday in the portfolio page. But for allocation purposes, let’s assume that we have a 100% exposure on each market.
Given the VaR, the expected loss in the last column will be obtained by multiplying our exposure to a given market by the corresponding VaR. So, for example, our 7.7k exposure on S&P500 would experience a loss higher than $455 only with a 1% probability.
By simply summing all the expected losses we make the assumption that there is a perfect correlation across these markets, at least when things go bad. This is clearly a conservative assumption but non necessarily a stupid one.
In this example, our VaR (in dollar terms) over the next 1 day is $5,983.
The VaR limits
The table above also shows a VaR limit. This is the part where personal risk tolerance will need to be factored in. For example, I might feel comfortable with a loss of 5% that I expect to experience only with a 1% probability. More risk-adverse investors might prefer to have a VaR limit of 3% instead, i.e. risking more than 3% only with a 1% probability.
In the example above we have set the VaR limit to 5% but given the equal allocation across all markets, we see that our portfolio VaR is 5.98%. This tell us that this allocation is too risky for our risk tolerance.
To reduce our VaR we can start re-allocating some of our capital from higher risk markets to lower risk ones.
We can, for example, reduce our max allocation to VIX, XLE and Silver from 7.7% to 3%. This would result in a portfolio VaR of 4.66% (so within our limits).
Having reduced the allocation on these 3 markets, we have now part of the capital that is not allocated. This is displayed above as “buffer” and, in this example, is about 14k.
To stay within the VaR limits of 5%, we could allocate part of this buffer to markets with lower VaR. Below we decide to increase our max allocation to Treasury Bonds and Gold.
Portfolio VaR is now 4,94%, so within the VaR limit of 5%. We would have about 6.4k as cash (buffer).
Market VaR vs Strategy VaR
The goal of Trading Mate is to generate superior risk-adjusted returns so it is natural to expect that risk metrics like VaR and Expected Shortfall will be lower when computed based on our strategy returns rather than market returns.
The example below shows our portfolio VaR assuming, again, an equal allocation of the trading capital but using the VaR of our strategies rather than market’s.
Instead of a loss of 5,983 we now can expect not to lose more than 2,478 with 99% confidence. This is well below our VaR limit of 5% so we have more freedom to increase our exposure to more risky assets, if we want to.
So what VaRs should we use, market or strategy? Well since Trading Mate actively manages the exposures based on these strategies it would make sense to use the associated VaR when deciding how to allocate the capital. Clearly, using market’s VaRs would be a more conservative choice in this case.
To understand why using the strategy VaRs makes more sense it is useful to think about each strategy as a single actively-managed fund investing exclusively in that particular market. So, for example, our strategy on S&P500 can be seen as an active fund investing on S&P500 and dynamically changing exposure between cash and index based on perceived risk in the markets. By using the strategy VaRs we are basically assuming that we are allocating part of our trading capital to this active fund which will then change the exposure day by day as the market moves.
How to use the file
At the link below you can download the file that has been used for these examples. Feel free to use it to see how the allocation would change based on your risk tolerance.
Please note that not all the markets have to be used (set the allocation to 0% if you want to ignore that market) and that the assumption to have an exposure of 100% is only made to understand what could be the portfolio VaR should we be fully invested in those markets.
In reality, Trading Mate only has full exposure for limited periods of time as long as favorable conditions persist. So, to have a more realistic portfolio VaR on a given day it is better to update the column “exposures” with the actual exposure we have published in the portfolio section.
Access the updated portfolio here
One last point to remember is that VaR measures change everyday. We provide updated figures on a weekly basis in the section where we publish recent results. Please monitor this section and update the “VaR” column should the VaR of a given market have changed significantly.