Portfolio-asset class beta/correlation in risk report

[VMatthijs]

Hi Rob (and others),

Do you think it would be useful to implement a feature in the risk report that calculates the recent beta and/or correlation between portfolio returns and the long-only returns of various asset classes (the main ones of importance being bonds and stocks)? I suspect a lot of folks are using trend following to diversity a long-only stock/bond portfolio, so perhaps the correlation between the trend portfolio and such other investments are a relevant metric of risk? Currently, the risk report shows - if I understand it correctly -, for each asset class the beta between the position in that asset class and the long-only returns for that asset class, which is a bit different from what I'm proposing.

I am bringing this up now partly because of the recent discussion by PIMCO on TTU where they explain that their trend product caps portfolio-equity beta for precisely this reason. The other reason for my timing is the strong downturn in both equities and multi-asset trend in the last few days.

If this you think this could be useful, I am happy to implement it!

Best wishes,
Matthijs

[VMatthijs]

Another interesting risk metric that I could imagine including in the risk report would be the diversification ratio: sum_{i in instruments} |w_i| * sigma_i / sigma, where w_i is the position size (as percentage of total exposure) for instrument i, sigma_i is the standard deviation of instrument i and sigma is the portfolio standard deviation. The motivation would be to detect scenarios where the portfolio is secretly not very diversified and is mostly making one big bet. That sort of moment could be risky if it's combined with very high vol. At the same time, I can also imagine that this happens precisely at times that trend strategies make a lot of money: if you have a massive trend in a single sector, I can imagine you simultaneously load on risk and that that sector starts to drive the risk of your whole portfolio. What you do you think about the value of this sort of diversification ratio for risk management?

[ChrisAllisonMalta]

Interesting idea, for it to be effective though you would need to have some sort of adjustment in the system to reduce that risk otherwise with a systematic investment process it will just be a red flashing light in a corner.

PS on your earlier point about equity risk, CFM have a similar product (ISTEC) I think it will become more popular personally

[VMatthijs]

I agree! Eventually, if you really care about this, it needs to be more than a red flashing light in a corner. Monitoring it could be a first step though towards implementing functionality that actually does something with it, if anyone cares enough and trusts these indicators enough.

[robcarver17]

It makes no sense to limit the diversification ratio (it could be very high when total risk is actually very low), but you could limit one of it's components: Sum of abs(annualised risk % capital)

And in fact the risk overlay already does that.

[VMatthijs]

What I meant is rather the opposite, but I don't think that makes much sense either. My sense is that situations where the diversification ratio is very low and the system is piling on a lot of risk are a bit suspect. I am saying that because my intuition is that the expected risk-adjusted return is better if the diversification ratio is higher. Not sure if that's actually true in practice though. I'm trying to think of good ways to test that. Of course, we could look at historical data, but that feels like a risk of in-sample fitting. I wonder if there's some good way of testing this with synthetic data.

[robcarver17]

Happy to see more stuff in the risk report. Make sure you follow the existing paradigm for reporting.

[VMatthijs]

Great! I had a stab at the portfolio betas in PR#1049. I did my best to follow the existing paradigm for report.

I'll do the diversification ratio in a later PR.

[VMatthijs]

@robcarver17 , question: do you think it's a good idea to use a one-year look back when calculating these betas and correlations between the portfolio and various asset classes? Currently, you seem to be using a one year lookback to calculate the betas in the risk report. Shall I follow that example, or do you think a shorter lookback would be better as a risk signal? And similarly, for the diversification factor, do you think a 1-year lookback is appropriate?

[robcarver17]

I think to calculate the diversification factor if I understand the thinking correct you just need to divide two numbers already in the risk report: Sum of abs(annualised risk % capital) divided by risk (actually this only exists by strategy, but you can easily work it out across the whole book).

Generally for correlations 6 months is about right as a lookback, probably the same for betas.

[VMatthijs]

Thanks, Rob! I'll work with 6 month for the betas and correlations then.

I just had a look at the code that generates the two measures of risk you mentioned and I agree that their ratio should be essentially the diversification factor. When I calculate it manually myself, I find a slightly different number, but it's pretty close. These calculations depend a lot on the precise lookback for the volatilities and correlation matrix, of course, so I'm not surpised that they do not give exactly the same number.