Engineering Targeted Returns and Risk

[MachineGhost]

Except for the corporate credit, all assets share dual economic roles.  Interesting.  The exact risk breakdown is:

Nominal Bonds: 25%
IL Bonds: 20.83%
Equities: 18.75%
EM Bonds: 14.58%
Gold: 8.33%
Corporate Credit: 6.25%
Commodities 6.25%

I separated gold from the commodities due to the former's stronger role in crisis protection.  Growth seems well represented already anyway.  I find it interesting that the nominal bonds are already pegged at 25% risk that I choose to value anchor with my code.  I'm guessing the implication is that risk normalization to nominal bonds would provide the above weights?

Are the nominal and emerging bonds supposed to be Treasuries?  Seems risky, if not.

I think real estate would have a dual economic role.

EDIT: I'm impressed with Schwab's variety.  It can be done all there.

These are the value weights I get to normalize risk to bonds:

Stocks: 6.72%
Bonds: 12.5%
Gold: 2.35%
Junk Bonds: 3.319%
EM Bonds: 3.319% **
Commodities: 8.44%
Real Estate: 8.44%
IL Bonds: 54.91%

I treated IL Bonds (TIPS) as cash as it overwhelms the portfolio otherwise.  ** The data for em bonds only goes back to 1996 so it is extremely limited, missing the 1994 bond market massacre and the Latin American debt crisis, so I used the junk bond risk instead.

[MachineGhost]

Mapping the AWP quadrants to the PP and economic environments:

Rising Growth is to "Prosperity": Inflation, Reflation
Falling Growth is to "Recession": Disinflation, Revaluation
Falling Inflation is to "Tight Money": Inverted Yield Curve, Deflation
Rising Inflation is to "Inflation": Depreciation, Devaluation, Hyperinflation, Negative Real Rates

Quick pop quiz: What environment is Cyprus finding itself under this week?

[D1984]

** The data for em bonds only goes back to 1996 so it is extremely limited, missing the 1994 bond market massacre and the Latin American debt crisis, so I used the junk bond risk instead.

You couldn't use the data for FNMIX for 1/1/1994 to 12/31/1995? Is it because it is actively managed and not an index (come to think of it, I think GMO has an actively managed EM fund as well that dates back to 1994)?

EDIT: If you need emerging markets debt index data before 1996, couldn't you use the JP Morgan EMBI? That dates back to 1-1-1991 IIRC.

[melveyr]

So, I think, it is worth exploring what Ray Dalio's AWP does, trying to repro it and comparing it with the PP performance over the same period and see if AWP provides a better performance with much less risk.

And there is no simple or complex way to do that. We just need to reverse engineer the known/published AWP mechanisms and see where it gets us.

I agree that AWP is a great portfolio. I have attempted to reverse engineer it many times and something always throws me off. Perhaps we can continue to share our thoughts in this thread and when one of us figures out a decent framework we can share with the group 

[melveyr]

I'm not using Excel, but coding this up to be dynamic in real time as part of a trading system, hence I don't have Solver available to brute force an optimal solution with contraints.  For now, I think it works reasonbly well to use 25% as the initial value weight and after normalizing the risk of the three assets, using the adjustment factors to modify the 25% value weight and then using a separate beta factor to manually increase or decrease the resulting value weights to get to the portfolio risk target.  A problem is if I use bonds as the risk to normalize to, then it will always be a 25% value weight in the portfolio unless I use a higher or lower risk that doesn't match the assets.  That doesn't seem elegant.  What also bothers me is I rather have the whole process be adaptive and decide the optimal weights by itself without having to first use a fixed 25% value weight or adjust the manual beta factor.

Hi MG,

I wrote a python script a long time ago that solved the solution. The way I did it might inspire you to find an elegant solution in whatever language you are using. If you are familiar with python I could share the script.

What you do is start off with 1% weighting in each asset. You then write a loop that adds 1% to whatever asset class has the lowest weighted covariance to the overall portfolio. You just have the program keep looping through this action until you get to 100%.

I like this because it also makes sense intuitively. If you have a pile of money and buy a little bit of one asset, the next asset you buy should be the one that has the most diversifying power with respect to your portfolio. You keep doing this until all of your money is invested.

[Stefan]

MG: interesting analysis of the risk breakdown.

Re: AC selections for backtests. I think we could use mutual funds up to 1996 for all the AWP ACs.
Here is how I treated TIPs. You are right that its volatility is low and it overwhelms the portfolio. This is because TIPs have short duration. HB recommended T-Bond vs T-Note for the same reason. Fortunately, PIMCO has a 15+ years ETF for IL Bonds - LTPZ. This is great for us as it has about double the volatility of TIPS and closer to TLT.
Now, the problem with LTPZ is that it has been available only since 2010.
My solution for backtesting with IL Bonds since 1996 (when IL Bonds were introduced as an AC) was to synthetically create an LTPZ equivalent from a TIPs mutual fund (which has the same short duration as TIPs) by using a 2X multiplier of returns (equivalent with a Beta = 2). You can play with this beta in the LTPZ/TIPs case but you'll see that, usually, they are almost correlated to 0.9-1 and the Beta is in the 1.8-2 range. Hey, nothing is perfect but I think this is as decent an approximation as is available to us for including this IL Bonds in the backtests.

The other point is about risk calculation. I chose the path of Risk Parity per AC and not per market regime. This is my own departure from AWP (and closer to PP in this respect). I do not know, for instance, how rigidly the ACs will adhere to the quadrants AWP published.
I'll give you an example: HY bonds are usually correlated with stocks. But HY bonds are also "stealth inflation fighters". While stocks suffer in an inflationary environment because their future earnings get eroded by inflation, HY bonds benefit from inflation as the yield burden on the debtor companies is alleviated. The HY bonds prices are mostly sensitive to credit risk and, as the burden of future payments the companies have to deliver is eased by a growing inflation => they get a higher credit => and their junk bonds prices go up. Real Estate is also an inflation hedge.

There is a good paper from Rob  Arnott which analyzes these ACs and their role in the growth/inflation regime shifts. But the AWP paper places corporate bonds only in the growth quadrant, while, if we replace corporates with HY, they have a dual role.
So, we have many ACs with dual roles, as you mentioned. But when will the dual role really materialize and when it won't? My preffered solution to this (and to simplify the model) was to allocate the same risk to each AC.

The last observation is: what formula to use to allocate the same risk to each? Risk Parity traditionally goes with allocating inversely proportional to the AC volatility. Which volatility is measured as the standard deviation of the log of returns over the last N days.
This is important - do not use price returns when calculating volatility, as the ACs have a lognormal distribution. Many miss this key point.

[Reub]

Is it possible that creating a AWP from RD using AC's from ETF's including VTI, TLT, GLD, BND, etc. instead of HBPP could become FUBU?

[cnh]

Is it possible that creating a AWP from RD using AC's from ETF's including VTI, TLT, GLD, BND, etc. instead of HBPP could become FUBU?

Brain...erp...erp...short-circuiting...acronym overload.

[MachineGhost]

I'll give you an example: HY bonds are usually correlated with stocks. But HY bonds are also "stealth inflation fighters". While stocks suffer in an inflationary environment because their future earnings get eroded by inflation, HY bonds benefit from inflation as the yield burden on the debtor companies is alleviated. The HY bonds prices are mostly sensitive to credit risk and, as the burden of future payments the companies have to deliver is eased by a growing inflation => they get a higher credit => and their junk bonds prices go up. Real Estate is also an inflation hedge.

Very good points.  I abhor investment grade corporate bonds and treat them like SNAFU.  They simply don't do anything other than steal from equity at best going back to the 1920's.  I think there is a lot of similarity between high yield bonds and dividend growers in terms of exposure to growth rising and inflation rising.  Back in 2008, while stocks just briefly dipped into the undervalued territory, it was like Toys R' Us for junk bonds in terms of capital gains to be had.  So they complement each other quite nicely.

I'm not convinced that long-term IL bonds have any useful role to play.  Rising inflation is synonmous with a zero to ultra-short duration (note that in high yield lingo, ultra-short is considered 7 years or less maturity which is ridiculously overbroad).  From 1948 to 1981 which was the last rising inflation environment, cash outperformed bonds (4.49% vs 3.83%).  So CD/T-Bill ladders and I-Bonds would be best, but that new short-term TIPS fund might be good too.  I'm open to being convinced otherwise, but I won't be convinced on any purely theoretical grounds.

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EDIT: I can see a use for LT IL bonds in the inflation rising quadrant and ST IL bonds in the growth falling quadrant.  I think bond durations have to be different to serve dual economic roles.

[Stefan]

Yes. That is the AC / quadrants picture!

I'm not convinced that long-term IL bonds have any useful role to play...
I'm open to being convinced otherwise, but I won't be convinced on any purely theoretical grounds.

OK  . Here is a weekly chart of SPY vs LT IL Bonds (LTPZ) returns for 2010 - today.



You can see:

1. LTPZ grew 45%, almost comparable with 51.9% in S&P over the last 3 Yrs. This is a susbtantial gain - for a bond - in the range of equity gains for these bull market times.
2. Most importantly, as you can see from the chart, it was negatively correlated with SPY. So, just using these 2, you would have had a smooth, low volatility ride for this time period.

In addition, in a reflationary environment, if the economy slows down, there are not many other things to insure your portfolio outside gold and LT IL Bonds. And they are uncorrelated. This is the theoretical argument.

[MachineGhost]

2. Most importantly, as you can see from the chart, it was negatively correlated with SPY. So, just using these 2, you would have had a smooth, low volatility ride for this time period.

So what does LTPZ and SPY both going up at the same time suggest?

Throw up TLT or EDV and lets see how all three/four compare.

[melveyr]

I have thought about setting up two portfolios and balancing the risk between them. One is the "risk off" portfolio comprised of 30 year nominals, 30 year IL (more implicit leverage than LTPZ!), and gold. The other portfolio would be "risk on" comprised off stocks and HY corporates. The weightings within each portfolio would be a simple 1/n.

To balance these portfolios between each other you would look at the volatility of each portfolio and just do 1/vol weightings.  Of course you could add cash to dial in your risk tolerance, but that is up to the investors discretion.

[Stefan]

I have thought about setting up two portfolios and balancing the risk between them. One is the "risk off" portfolio comprised of 30 year nominals, 30 year IL (more implicit leverage than LTPZ!), and gold. The other portfolio would be "risk on" comprised off stocks and HY corporates. The weightings within each portfolio would be a simple 1/n.

To balance these portfolios between each other you would look at the volatility of each portfolio and just do 1/vol weightings.  Of course you could add cash to dial in your risk tolerance, but that is up to the investors discretion.

Risk On/Risk Off is based on the Equity Bull/Bear performance. Gold is a hedge in Risk Off - up to a point. Look what happend with Gold in the 2008 Risk Off period. TLT did indeed protect you.



In stagflation (economic contraction + inflation), like we had in the 1970s, Gold and IL will be great but TLT will become a drag on teh Risk Off portfolio. So, my point is that the Risk Off portfolio you sugested will only partially act as protection and partially will expose you to risk. 

But I have a question for you: What ETF would you use for 30 year IL?

[melveyr]

I have thought about setting up two portfolios and balancing the risk between them. One is the "risk off" portfolio comprised of 30 year nominals, 30 year IL (more implicit leverage than LTPZ!), and gold. The other portfolio would be "risk on" comprised off stocks and HY corporates. The weightings within each portfolio would be a simple 1/n.

To balance these portfolios between each other you would look at the volatility of each portfolio and just do 1/vol weightings.  Of course you could add cash to dial in your risk tolerance, but that is up to the investors discretion.

Risk On/Risk Off is based on the Equity Bull/Bear performance. Gold is a hedge in Risk Off - up to a point. Look what happend with Gold in the 2008 Risk Off period. TLT did indeed protect you.

In stagflation (economic contraction + inflation), like we had in the 1970s, Gold and IL will be great but TLT will become a drag on teh Risk Off portfolio. So, my point is that the Risk Off portfolio you sugested will only partially act as protection and partially will expose you to risk. 

But I have a question for you: What ETF would you use for 30 year IL?

Stefan,

No single asset (gold, LTT, IL) will always be a reliable risk off asset. It depends on what is happening with the price level. In the risk off portfolio that I proposed, you have an asset that benefits from inflation (gold), is agnostic about inflation (IL), and one that benefits from deflation (LTT). So I think we are total agreement if you look at the propsal more carefully 

There is no 30 year IL fund that I am aware of. I was thinking of buying them directly and then rolling them over once they reach 20-25 years.

[Stefan]

Switching your allocation parameters based on Risk On/Risk Off, in general, is an excellent idea. The concept of these 2 regimes showed clearly after 2008, when it was observed that all risk assets correlated to 1 when the equity market went through turbulent times.
Ray Dalio uses a similar concept, it just defines it differently - "a depression gauge". And it is used to protect AWP in teh same turbulent times.

Now, here is an idea for you: As Risk On/Risk Off is defined by the equity bull/bear regime shifts - and everything else follows - why not using a market timing mechanism - like 200 MA - and switch to Risk On/Risk Off.

Volatility is not a good switch indicator, it is just an indicator of risk. You can have high volatility when something goes up, in a parabolic rise, for instance. It just tells you that it may go down as fast as it went up, but it doesn't tell you when. A switch mechanism like 200 MA tells you when.

Lastly, I wonder if you can backtest your ideas and if you would like to post any results I could look at and try to repro. Backtesting is the key validation for continuing research on any hypothetical systems we discuss here - and maybe implementing it in real time trading. If backtesting gives you good results, it doesn't mean you'll get these same results in the future, but it means there is value in your ideas. But if backtesting fails, you may want to discard that hypothesis.

[Stefan]

I think this is overkill.
You can introduce the assumption that PP assets are uncorrelated - as they mostly are - by portfolio design.
Then:
NNR(i) = Sum(j=1 to N, COVAR(i, j) * w(i) * w(j)  )
NNR(i) =Sum(j = 1 to N, Correlation(i, j) * StDev(i) *StDev(j) * w(i) * w(j) );
NNR(i) = w(i)^2 * StDev(i)^2
Now, you want to equalize risk contributions:
NNR(1) = NNR(2) = … = NNR(n).
This results in this set of equations:
w(1) * StDev(1) = w(2) * StDev(2) = … = w(n) * StDev(n).
add to this the constraint  that
Sum(i=1 to N, w(i)) = 1
And you have to solve a linear system of n equations with n unknowns
And this is the solution:
w(i) = 1/StDev(i) / Sum(j=1 to N, 1/StDev(j)).
Which is actually the traditional Risk Parity allocation.

[MachineGhost]

Overkill in what sense?  I simply presented melvyr's idea in closed form equations.  Why make an assumption that isn't true if you don't have to?

Thanks for the formula.  I don't agree with using covariance because the portfolio should be fundamentally constructed according to the economic quadrants.  As Ag alluded to, covariance, beta, correlations, etc. are simply too unstable to build a strategic portfolio around, but for a portfolio like the PP/AWP with its built-in fundamental correlations, it could possibly play a minor, secondary role in tilting.  Only backtesting would tell for sure.

[Stefan]

I think this is overkill.
You can introduce the assumption that PP assets are uncorrelated - as they mostly are - by portfolio design.

Overkill in what sense?  I simply presented melvyr's idea in closed form equations.  Why make an assumption that isn't true if you don't have to?

In any case, melvyr would be the best one to comment on the appropriateness of your assumption.

Overkill in the sense that melveyr formula, while perfectly correct, requires a very complex process to get to an approximate solution. And this makes that solution unsuitable for real time trading, while a simplified formula, based on the assumption I made, does the same job and can be used in real time.

Now, you question the assumption. But HBPP is designed with uncorrelated asset classes. It is its foundational premise: ACs are selected to be uncorrelated. This is by design - so I just used this premise to generate a practical approach.

This means that in practical applications, the rather complex numerical solvers can be avoided. Investors can construct robust risk parity portfolio for arbitrary large asset universes with simple spreadsheet formulas.

So, I hope I clarified what I meant by overkill.

[melveyr]

I agree that on a forward looking basis trying to use the covariance formula to define risk contribution is probably ill advised. Most PPers are aware that correlation coefficients are pretty unstable, and thus we rely on Harry Browne's framework of causation. Stefan's suggestion of assuming zero correlation for the HBPP assets is very practical, and I think we all do that implicitly.

However, exploring the covariance formula conceptually is still rewarding. Additionally, I think it is a great tool for looking backwards to help understand where the risk in a portfolio was coming from. Historically gold has had the highest covariance to the PPs returns, indicating that critiques of the PPs returns being somewhat gold centric are not without merit.

[Stefan]

@Stefan: idk if it's just me, but none of your dropbox images appear in your posts

I think all the others were able to see them... Let me know what I could do to help with that.

[Stefan]

A backtest of a reverse engineered AWP vs PRPFX

[melveyr]

Would you mind sharing what asset classes were used and the weighting criteria?

[Stefan]

Would you mind sharing what asset classes were used and the weighting criteria?

As per our discussion here, illustrated by MG's 4 quadrants diagram:
stocks,HY, emerging market bonds, real estate, commodities, gold, LT IL bonds, T-Bonds, Tbills.

As for the weighting, I mentioned the methods here in all my posts: volatility weighting and target volatility control. In the case showed here I capped max portfolio volatility at 8% (the grey line you see in the volatility pane).

Finally, like RD does in practice with AWP - an extra mechanism for risk management - I overlayed a "my depression gauge" - in this case a technical indicator.

[MachineGhost]

Interesting.  What is responsible for the lesser max drawdown of the AWP vs PP in 2008?  Your tactical allocation or the asset composition?

I'll have to backtest my own AWP soon and post the results, but I'm rather burned out at the moment.

[MachineGhost]

I managed to finally implement the simple weighting formula (like the one Stefan outlined) as a dynamic process.  I had tried to do it before, but the numbers just weren't coming up sensible.  I like it alot better than the other method I had mentioned using a 25% starting weight.  Anyway, to get the risk down to what I am comfortable with, I had to reduce the weights proportionally by 65%!

Before AWP, I was gonna go strategic PP with 15% dollar weight each, the rest in cash but I decided I rather not have any regrets later on, especially as 15% is rather difficult for me to rebalance down to at the moment.

So score one for "risk parity" and "targeted volatility"!