Risk Parity Investing

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shamino
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Risk Parity Investing

Post by shamino » Fri Feb 23, 2018 2:55 pm

I just noticed that Wealthfront is offering a new mutual fund called Risk Parity Investing. Personally, I think Wealthfront a good brand, since they've been giving sound advice on their blogs. I know there will be opinions that they are just finding ways to charge new fees, but I was wondering if you all had any thoughts on risk parity investing. I looked up some basic articles and YouTube videos, but would love to hear your thoughts.

lack_ey
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Re: Risk Parity Investing

Post by lack_ey » Fri Feb 23, 2018 5:26 pm

For reference, there's a Wealthfront whitepaper and mutual fund prospectus.
===

Risk parity has been discussed a lot previously.

It's nothing new at all and frankly is just a strategy based on repackaging Modern Portfolio Theory (1960s finance) ideas about portfolio construction and efficiency with a certain constraint. One of the big practical issues to MPT optimization is parameter estimation—to build the most efficient portfolio, you need to know not only the volatility of different assets but their forward returns and covariances. The results are very sensitive to those parameters, which are unknown.

Risk parity is something of a practical compromise that doesn't attempt to find the optimal allocation but instead simply uses estimates of risk for each asset, forgetting about the returns and covariances. It builds an asset allocation that takes equal risk in each asset by scaling the weightings inversely to the estimated risk of that asset. That is, the risk is at parity—which is not anything actually special, but quite possibly results in decent diversification. Usually but not necessarily, risk is assessed by volatility, and forward volatility can be estimated in a number of ways (assuming volatility in the coming quarter is equal to volatility in the previous quarter is a reasonable starting point that can be improved upon). Particularly if risk and return are properly priced by the markets, higher-risk assets should have higher return, and ignoring that parameter won't matter much in practice. In any case, an allocation with more balanced risk exposures is likely to be more efficient, and risk parity exploits this.

Risk parity allocations differ in the underlying assets used. Wealthfront's seems to use relatively boring and vanilla assets, just different stocks and bonds. Notably this means that the correlation between some of the assets will be pretty high. Sometimes you see allocations to commodities (futures), precious metals, alternative investments, various liquid alternatives, and so on. In the whitepaper they list US equities, energy stocks, REITs, developed ex-US equities, emerging markets equities, US bonds, and emerging markets bonds. Like the regular allocations from Wealthfront, they are a bit big on emerging markets.

Typically, resulting risk parity allocations end up being heavy in bonds by percentage of capital invested, as the bonds are less risky than the other assets.

Usually but not necessarily, risk parity allocations are thus leveraged, again a familiar concept from MPT. But rather than scale up the capital markets line by leveraging at the risk-free rate, real risk parity investments have to borrow in practice at a higher interest rate, depressing returns. Most risk parity strategies probably access leverage through futures and/or total return swaps, probably paying some 50 bp or so above LIBOR, which is not that bad. But it is a drag. In part because most risk parity allocations are leveraged (and the leverage ratio needs to be managed over time) and also because of the nature of most risk parity managers, most of these strategies adjust positions over time based on forward volatility forecasts as they change, in order to keep the risk taken by each asset more stable over time. In practice, risk parity is somewhat synonymous with volatility targeting, but this is in theory not necessary. You could instead have a vol forecast that is very slow moving or constant, spitting out the same value always.

Leveraging up to about 12% annual volatility in a risk parity fund with those underlying assets is a bit aggressive but not reckless. Overall what you should see is just a balanced allocation that may be typically some 2/3 or so in bonds, varying over time, that is variably leveraged, on average a little bit above 2x. So this is far from safe, and obviously if both stocks and bonds go down simultaneously, this can look really bad. But at least when bonds go down they don't go down as far as stocks do.

Overall this is reasonable enough in the sense that any balanced and diversified allocation is reasonable enough. However, they're charging 0.50% on the mutual fund and then have effective borrowing costs on total return swaps, so it gets a "meh" from me, especially considering what they are using for the underlying assets. I wouldn't be totally frightened off by the leverage, though, but it of course does magnify both the good and the bad of the underlying allocation.

I think some people would have tactical concerns because both stocks and bonds look relatively expensive now, and cash rates look to be heading up (of course, if it bodes poorly for risk parity, it bodes poorly for all kinds of other allocations as well). But I think we are long-term investors here, and of course the market can definitely surprise or do any number of things in the short term.
Last edited by lack_ey on Sun Feb 25, 2018 7:12 pm, edited 1 time in total.

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Re: Risk Parity Investing

Post by nisiprius » Fri Feb 23, 2018 5:49 pm

1) As noted in another post, if the concept of risk parity has been around since 1970, and if Burton Malkiel thinks there is enough value in the concept to structure an important Wealthfront service around it, then I think it is very odd that he says nothing about risk parity in the 2016 edition of A Random Walk Down Wall Street..
2) Unfortunately I haven't been keeping careful track, but risk parity was all the rage just a few years ago, and my recollection is that they suffered a fairly serious blow... which might possibly explain why I can't find very many risk parity mutual funds.
September 2, 2015, Risk parity funds suffer a cruel summer.
“Risk parity” funds seek to give investors equity-like returns with bond-like stability at low cost.
It is, then, reasonable to compare a risk parity fund (AQRIX, blue) with stocks (red) for return, and with bonds (orange) for volatility. AQRIX, blue, has been out for nearly eight years, and AQR is often mentioned as a pioneer in risk parity mutual funds, so I assume it's a reasonable fund to look at and a reasonable example of the "risk parity" strategy.
I took a look. To my eye, AQRIX was definitely not giving "equity-like returns with bond-like stability," but that's a lot to expect, and it would be harsh to say it had done the opposite. It was in between stocks and bonds, in both return and volatility.
So how does AQRIX (blue) compare with another in-between choice, the plainest of all in-between choices: the 60/40 long-only Vanguard Balanced Index Fund, VBINX (red?)
Source
Image
So, there you go. In the eight years the AQR Risk Parity Fund has been available, the dumbest fund in the world, Vanguard Balanced Index, has beaten by quite a lot in return, while, at the same time, has had quite a lot lower volatility. The result is a difference in Sharpe ratio that I can only call stunning: the unsophisticated fund had nearly twice risk-adjusted reward of the risk parity fund.
I see no evidence that AQRIX achieved anything. It basically parallels VBINX except in the two places where it got clobbered and hasn't yet recovered.
I mean, seriously: what's the point?
Last edited by nisiprius on Fri Feb 23, 2018 6:01 pm, edited 7 times in total.
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grok87
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Re: Risk Parity Investing

Post by grok87 » Fri Feb 23, 2018 5:52 pm

Thanks for the detailed post. Lack-ey.

I guess I would say it slightly differently. Here for example is a link to the holdings of Aqrix, the aqr Risk parity http://portfolios.morningstar.com/fund/ ... ture=en_US

Cash -98%
Bonds 106%
Foreign stocks 48%
Other 44%

As you point out it’s a leveraged strategy. The other way to look at it, considering cash as really short term bonds,
Is that there is practically NO net bond exposure. There is exposure to the yield curve. If it flattens the fund benefit. If it steepens the fund gets hurt.

The other is probably commodities, currencies etc.

Looked at this way, things look more risky. The fund does NOT have a lot of bonds, ie there is no cushion there from bonds to protect returns as is the case in say a 60/40 portfolio.

It might be an interesting exercise to calculate what amount of yield curve steepening might make the fund blow up, assuming they cAn’t execute their volatility targeting strategy in time...
Keep calm and Boglehead on. KCBO.

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Re: Risk Parity Investing

Post by lack_ey » Fri Feb 23, 2018 6:39 pm

nisiprius wrote:
Fri Feb 23, 2018 5:49 pm
“Risk parity” funds seek to give investors equity-like returns with bond-like stability at low cost.
Maybe the best idea here is to not quote bad analysis and hyperbole from the financial press. I suppose some may have pushed that narrative, but that's mostly a straw man.
nisiprius wrote:
Fri Feb 23, 2018 5:49 pm
I see no evidence that AQRIX achieved anything. It basically parallels VBINX except in the two places where it got clobbered and hasn't yet recovered.
I mean, seriously: what's the point?
The point is that when you invest in international stocks and commodities (futures) over a period in which US stocks beat international stocks soundly and commodities drop like a rock*, you tend to do worse than a basic US stock/bond allocation.

*and furthermore where stocks do better than bonds on a risk-adjusted basis and your allocation reduces exposure to equity risk relative to bond risks

Whatever you think about risk parity, you're not really evaluating much of anything with a window like that, especially if not accounting for basic differences in passive exposures.

Also, I think you should pick up more on the differences between the AQR risk parity implementation and Wealthfront's.

grok87 wrote:
Fri Feb 23, 2018 5:52 pm
Thanks for the detailed post. Lack-ey.

I guess I would say it slightly differently. Here for example is a link to the holdings of Aqrix, the aqr Risk parity http://portfolios.morningstar.com/fund/ ... ture=en_US

Cash -98%
Bonds 106%
Foreign stocks 48%
Other 44%

As you point out it’s a leveraged strategy. The other way to look at it, considering cash as really short term bonds,
Is that there is practically NO net bond exposure. There is exposure to the yield curve. If it flattens the fund benefit. If it steepens the fund gets hurt.

The other is probably commodities, currencies etc.

Looked at this way, things look more risky. The fund does NOT have a lot of bonds, ie there is no cushion there from bonds to protect returns as is the case in say a 60/40 portfolio.

It might be an interesting exercise to calculate what amount of yield curve steepening might make the fund blow up, assuming they cAn’t execute their volatility targeting strategy in time...
I don't think it's right to treat cash as basically bonds for these purposes.

Even if it were actually short short-term bonds and not cash, there's still an actual difference between intermediate-term (or long-term) bonds and short-term bonds. Certainly a difference between cash and bonds.

Bond returns and cash returns differ every day, month, year, etc. in just the same way as stocks do, but with a lower standard deviation of the differential. If I gave you an unlabeled time series of bond excess returns and another unlabeled time series of [1/4 stock + 3/4 cash] excess returns, they would not be all that much different in character and you would probably have trouble telling them apart.

In a flight to quality, Treasury bond returns may be significantly better than cash and could "protect return" in the sense that they would in a 60/40 allocation. In fact, with even more bonds you get even more protection. That said, AQR's fund specifically takes credit risk as part of fixed income; definitely not all of that 106% is likely going up. Wealthfront's EM bonds likewise may be a drag under poor equity conditions.

But more in the risk parity paradigm, all assets are risky sources of return. You don't use bonds as a cushion. Everything is equally cushion for everything else, or nothing is a cushion. The equity risk contribution from a risk parity portfolio will be smaller than that of a standard balanced allocation of comparable risk. That said, some of the other assets could be in part related to equity risk, depending on what they are.

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Re: Risk Parity Investing

Post by nisiprius » Fri Feb 23, 2018 7:58 pm

lack_ey wrote:
Fri Feb 23, 2018 6:39 pm
...The point is that when you invest in international stocks and commodities (futures) over a period in which US stocks beat international stocks soundly and commodities drop like a rock, you tend to do worse than a basic US stock/bond allocation...
So is there any risk parity fund older than AQRIX? This article lists eight, and I will add the ticker symbols and inception dates.
  • Salient Risk Parity--now called "Adaptive Growth fund"--SRPFX--07/09/2012
  • Columbia Risk Allocation--CRAAX--06/19/2012
  • Managers AMG FQ Global Essentials--now called AMG FQ Global Risk-Balaced--MMAFX--11/18/1998--ah, that's more like it
  • Bridgewater All Weather (mutual fund)--discontinued? never existed?
  • AQR Risk Parity Fund--AQRIX--9/30/2010
  • Putnam Dynamic Risk Allocation--PDREX--09/19/2011
  • Invesco Balanced-Risk Allocation--ABRZX--06/02/2009
  • RPG Diversified Risk Parity--DRPAX or DRPIX--not found. Bloomberg says "DRPIX was liquidated."
So, we only found one fund older than AQRIX, MMFAX; but it's a lot older, old enough to include two big stock market declines and all kinds of "weather."
It is definitely old enough to get us back before "a period in which US stocks beat international stocks soundly and commodities drop like a rock."
I can't even use VBINX for the comparison, because MMFAX is older than VBINX, and even older than VTSMX (total stock). So I will compare MMFAX (blue) to a monthly-rebalanced 60/40 portfolio of Vanguard 500 Index for stocks, and VBMFX for bonds (red).
Source
Image
And, once again, this time with thirty years of data to look at, the dumb 60/40 portfolio did better than the risk-parity mutual fund...in every way. Higher return. Lower volatility. A better best year and a less bad worst year. A smaller max drawdown. Double the Sharpe ratio, and more than double the Sortino ratio. In fact I only see one period of time on that chart, from about 2003 to 2008, during which the risk-parity fund was outperforming the simple 60/40 fund (i.e. the gap was narrowing instead of widening). And the notches at 2013 and 2015 are visible in this fund, too.
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Re: Risk Parity Investing

Post by patrick013 » Fri Feb 23, 2018 8:36 pm

Image
How can you get more risk/reward with bond yields up and all
estimates for stocks and Intl good but not super ?
So prior stock yields can be cut in half as future estimates.
age in bonds, buy-and-hold, 10 year business cycle

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Re: Risk Parity Investing

Post by lack_ey » Fri Feb 23, 2018 8:40 pm

nisiprius wrote:
Fri Feb 23, 2018 7:58 pm
[*]Bridgewater All Weather (mutual fund)--discontinued? never existed?
Were you expecting a mutual fund? Have they ever run mutual funds? They're known as a hedge fund and institutional money manager.
nisiprius wrote:
Fri Feb 23, 2018 7:58 pm
So, we only found one fund older than AQRIX, MMFAX; but it's a lot older, old enough to include two big stock market declines and all kinds of "weather."

It is definitely old enough to get us back before "a period in which US stocks beat international stocks soundly and commodities drop like a rock."

I can't even use VBINX for the comparison, because MMFAX is older than VBINX, and even older than VTSMX (total stock). So I will compare MMFAX (blue) to a monthly-rebalanced 60/40 portfolio of Vanguard 500 Index for stocks, and VBMFX for bonds (red).

...

And, once again, this time with thirty years of data to look at, the dumb 60/40 portfolio did better than the risk-parity mutual fund...in every way. Higher return. Lower volatility. A better best year and a less bad worst year. A smaller max drawdown. Double the Sharpe ratio, and more than double the Sortino ratio. In fact I only see one period of time on that chart, from about 2003 to 2008, during which the risk-parity fund was outperforming the simple 60/40 fund (i.e. the gap was narrowing instead of widening). And the notches at 2013 and 2015 are visible in this fund, too.
AMG FQ Global Risk-Balanced (MMFAX) has an options overlay, some other oddities, a too-high expense ratio, and some other detractors. The "risk balance" is not exactly risk parity though I guess close enough, looking at the allocation now. More importantly, did you check to make sure that a lot of the old history is actually using a risk parity-type allocation? Fund objectives and style drift over time. It may not have always invested like it does now. I did a spot check of the 2009 annual report and it mentioned losing to its benchmark on account of negative to neutral performance within "equity country selection, bond country selection, and currency," which sounds more like a general-purpose market timing / tactical allocation vehicle than risk parity or what they're doing now.

Ray Dalio and Bridgewater are most credited with popularizing risk parity, and All Weather opened in 1996. I would imagine that MMFAX doesn't predate Bridgewater in running risk parity. For what it's worth, taking Jan 1996-Dec 2013, Vanguard Balanced returned 7.6% and the early 2014 article quotes All Weather as returning 8.9% since inception (maybe the dates aren't quite aligned correctly), though that is obviously cherry-picking an old and successful investment vehicle. That said, I don't know All Weather's risk exposures and volatility over the period. Maybe it wasn't so good.

By the way, over the past 30 years, international stocks added risk (past about 20% or so allocation) and detracted from return, relative to all US stocks. All backtests are going to be biased like that. Ideally we just do an attribution to figure out what caused what, rather than try to average over more history to reduce the effect of noise.

Honestly, there just aren't long histories of suitable results that can be quoted for these purposes.

Actually, let's step back a sec. Are you trying to answer something more along the lines of (1) how have risk parity mutual funds done? or (2) what are risk parity strategies like generally? or (3) how would a risk parity strategy like Wealthfront's have done? This is posted in the theory section so I was addressing more like (2). Generally speaking, risk parity results can vary significantly based on which assets are used, costs, how the rebalancing and vol adjustments are done, leverage, etc. Past fund performance doesn't really tell us about what a different risk parity allocation such as Wealthfront's might look like.

As a reminder, Wealthfront is just running a leveraged stock/bond portfolio with a tilt to REITs and energy stocks, and a significant allocation to EM bonds, with time-varying leverage and allocations generally based on vol forecasts.

The relevant questions to really answer there are along the lines of
(1) Does the allocation make sense?
(2) How risky is the fund, and how does the variable leverage fit in? Relatedly, what is the impact of the volatility targeting?

The costs are not much of a question and are known.

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Re: Risk Parity Investing

Post by nisiprius » Fri Feb 23, 2018 10:31 pm

lack_ey wrote:
Fri Feb 23, 2018 8:40 pm
nisiprius wrote:
Fri Feb 23, 2018 7:58 pm
[*]Bridgewater All Weather (mutual fund)--discontinued? never existed?
Were you expecting a mutual fund? Have they ever run mutual funds? They're known as a hedge fund and institutional money manager.
I was running down the list in the article. They chose to list eight "funds." They didn't give ticker symbols or explain what they meant by "funds." There's no law against running both hedge funds and mutual funds, AQR does, so I took a minute to see whether Bridgewater did.
Actually, let's step back a sec. Are you trying to answer something more along the lines of (1) how have risk parity mutual funds done? or (2) what are risk parity strategies like generally? or (3) how would a risk parity strategy like Wealthfront's have done?
I am interested in how risk parity mutual funds have done, because a) mutual funds (and, in theory, Wealthfront) are what I am able and willing to use, and because they are transparent demonstrations of what can be achieved in real life, running real money, with real transaction costs, using strategies that have become widely known to the general public. And I think that's a reasonable anticipation of what might be expected of Wealthfront going forward. Really, AQRIX and MMFAX both showing risk-adjusted return on the order of about half that of a 60/40 balanced fund is pretty impressive... in the wrong way.
By the way, over the past 30 years, international stocks added risk (past about 20% or so allocation) and detracted from return, relative to all US stocks. All backtests are going to be biased like that. Ideally we just do an attribution to figure out what caused what, rather than try to average over more history to reduce the effect of noise.
If you don't like my using a 60/40 U.S.-only portfolio, plug something like LifeStrategy Moderate, or 40/20/40 Total Stock/Total International/Total Bond... or whatever you think is a fair example of "a portfolio without risk parity..." into PortfolioVisualizer, and see how things come out. Yes, I think international is going to add some volatility, but not enough to wipe out a factor of two difference in Sharpe ratio.

What do you suggest is a fair comparison? On the risk parity side, MMFAX, but not starting all the way back, and, if so, starting when? Or AQRIX? On the non-risk-parity side, if not 60/40 Total Stock/Total Bond, then what? Coffeehouse portfolio? The 60/40 "moderate" portfolio published by Larry Swedroe in 1998 and incorporating various factor tilts on both the stock and bond side?
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Re: Risk Parity Investing

Post by lack_ey » Fri Feb 23, 2018 11:18 pm

nisiprius wrote:
Fri Feb 23, 2018 10:31 pm
lack_ey wrote:
Fri Feb 23, 2018 8:40 pm
nisiprius wrote:
Fri Feb 23, 2018 7:58 pm
[*]Bridgewater All Weather (mutual fund)--discontinued? never existed?
Were you expecting a mutual fund? Have they ever run mutual funds? They're known as a hedge fund and institutional money manager.
I was running down the list in the article. They chose to list eight "funds." They didn't give ticker symbols or explain what they meant by "funds." There's no law against running both hedge funds and mutual funds, AQR does, so I took a minute to see whether Bridgewater did.
That's fair enough. I had to look it up myself before. I just thought you might have come across it before and knew that they wouldn't have a mutual fund.
nisiprius wrote:
Fri Feb 23, 2018 10:31 pm
Actually, let's step back a sec. Are you trying to answer something more along the lines of (1) how have risk parity mutual funds done? or (2) what are risk parity strategies like generally? or (3) how would a risk parity strategy like Wealthfront's have done?
I am interested in how risk parity mutual funds have done, because a) mutual funds (and, in theory, Wealthfront) are what I am able and willing to use, and because they are transparent demonstrations of what can be achieved in real life, running real money, with real transaction costs, using strategies that have become widely known to the general public. And I think that's a reasonable anticipation of what might be expected of Wealthfront going forward. Really, AQRIX and MMFAX both showing risk-adjusted return on the order of about half that of a 60/40 balanced fund is pretty impressive... in the wrong way.
I have to disagree here. This is not a category where different implementations will be very similar. Wealthfront's performance in a given year will often not be in line with the others, based on the risk target, lack of commodities (futures), and equity tilts. There should be pretty high correlation between risk parity funds, but there's already high correlation between risk parity and equity funds, and assets with high correlation can have significantly different returns.

I would rather check Wealthfront's backtest in their white paper posted earlier than rely on a different fund's live trading data that uses different assets, weightings, etc. Obviously we need to be suspicious of their methodology and weighting and discount their results a bit, as of course they're not going to show a backtest that performs poorly, but it doesn't look all that contrived so I don't think there are huge problems to looking at their backtest. Then if I really cared a lot about it and were serious in investing in this thing, I would get the data for the asset classes used, grab the LIBOR rate, and do my own backtests using static allocations representing the average weighting of the assets over the period.

There's something to be said for using live trading data, but it doesn't match well here.
nisiprius wrote:
Fri Feb 23, 2018 10:31 pm
By the way, over the past 30 years, international stocks added risk (past about 20% or so allocation) and detracted from return, relative to all US stocks. All backtests are going to be biased like that. Ideally we just do an attribution to figure out what caused what, rather than try to average over more history to reduce the effect of noise.
If you don't like my using a 60/40 U.S.-only portfolio, plug something like LifeStrategy Moderate, or 40/20/40 Total Stock/Total International/Total Bond... or whatever you think is a fair example of "a portfolio without risk parity..." into PortfolioVisualizer, and see how things come out. Yes, I think international is going to add some volatility, but not enough to wipe out a factor of two difference in Sharpe ratio.

What do you suggest is a fair comparison? On the risk parity side, MMFAX, but not starting all the way back, and, if so, starting when? Or AQRIX? On the non-risk-parity side, if not 60/40 Total Stock/Total Bond, then what? Coffeehouse portfolio? The 60/40 "moderate" portfolio published by Larry Swedroe in 1998 and incorporating various factor tilts on both the stock and bond side?
I don't know of any good representation of risk parity we could use as a benchmark. I'd need to check a lot of them to see the average to devise some kind of average or benchmark risk parity. But this wouldn't produce the most appropriate benchmark for what Wealthfront is doing anyway as their implementation doesn't really fall along the average, I don't think.

If we want to use a non-leveraged asset allocation to benchmark AQR Risk Parity (AQRIX), it should probably include commodities. There's no way to get a good fit without leverage, though, but here's an approximation I came up with:
27% VTI - US stock
18% VEA - ex-US developed stock
9% VWO - emerging markets stock
12% DBC - commodities (futures)
6% TIP - TIPS
6% EMLC - local currency emerging markets bonds (to capture EM currency and then also credit risk)
6% HYG - junk bonds
6% CRED - investment-grade credit
10% BND - US bonds

I think I could imagine a financial advisor using an allocation like that. Looks in the range of reasonable enough to me. How about you?

That comes out similarly to AQRIX since inception, though significantly higher correlation with stocks, as expected:
https://www.portfoliovisualizer.com/bac ... on11_3=100

Looks like AQR's fees pretty much destroyed any benefit (like the higher term risk taken over this period). We'd have to do a more serious attribution to check how the vol targeting impacted things, and also to get the weightings more appropriate. To be honest, 12% commodities is way too low relative to about 54% stocks, even if commodities aren't 100% a category that's supposed to be equal to equity risk by themselves in AQR's formulation. And obviously fixed income exposure is too low here.

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Re: Risk Parity Investing

Post by jalbert » Sat Feb 24, 2018 1:19 am

It is much easier to motivate risk parity by avoiding a discussion of particular risk parity products.

Consider a portfolio of large-cap US stocks and treasuries. If you start at 100% stocks and increase the bond allocation, portfolio risk decreases as bond allocation increases until you reach the allocation where risk has reached parity. At larger bond allocations, the bond risk exceeds the stock risk at the given allocation.

As lack_ey pointed out, you only need a measure of risk, not also of return. This should significantly reduce, but by no means eliminate sample bias in estimating the needed parameters because risk tends to be more stable than return over time.

On the other hand, it appears (see reference below) that it is known that a risk parity portfolio with more than two asset classes lies inside of the boundary of the efficient frontier unless all of the assets have the same expected return, so generally you cannot expect to find the minimum-variance efficient portfolio using risk parity if there are more than two asset classes:

http://www.hillsdaleinv.com/portal/uplo ... ective.pdf
Risk is not a guarantor of return.

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Re: Risk Parity Investing

Post by grok87 » Sat Feb 24, 2018 6:54 am

jalbert wrote:
Sat Feb 24, 2018 1:19 am
It is much easier to motivate risk parity by avoiding a discussion of particular risk parity products.

Consider a portfolio of large-cap US stocks and treasuries. If you start at 100% stocks and increase the bond allocation, portfolio risk decreases as bond allocation increases until you reach the allocation where risk has reached parity. At larger bond allocations, the bond risk exceeds the stock risk at the given allocation.

As lack_ey pointed out, you only need a measure of risk, not also of return. This should significantly reduce, but by no means eliminate sample bias in estimating the needed parameters because risk tends to be more stable than return over time.

On the other hand, it appears (see reference below) that it is known that a risk parity portfolio with more than two asset classes lies inside of the boundary of the efficient frontier unless all of the assets have the same expected return, so generally you cannot expect to find the minimum-variance efficient portfolio using risk parity if there are more than two asset classes:

http://www.hillsdaleinv.com/portal/uplo ... ective.pdf
Thanks. But I think you forgot to mention the leverage?

Looks like an interesting pdf you linked, I will read when i get a chance....
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Re: Risk Parity Investing

Post by nisiprius » Sat Feb 24, 2018 10:26 am

lack_ey wrote:
Fri Feb 23, 2018 11:18 pm
If we want to use a non-leveraged asset allocation to benchmark AQR Risk Parity (AQRIX), it should probably include commodities. There's no way to get a good fit without leverage, though, but here's an approximation I came up with:
27% VTI - US stock
18% VEA - ex-US developed stock
9% VWO - emerging markets stock
12% DBC - commodities (futures)
6% TIP - TIPS
6% EMLC - local currency emerging markets bonds (to capture EM currency and then also credit risk)
6% HYG - junk bonds
6% CRED - investment-grade credit
10% BND - US bonds

I think I could imagine a financial advisor using an allocation like that. Looks in the range of reasonable enough to me. How about you?

That comes out similarly to AQRIX since inception, though significantly higher correlation with stocks, as expected:
https://www.portfoliovisualizer.com/bac ... on11_3=100

Looks like AQR's fees pretty much destroyed any benefit (like the higher term risk taken over this period). We'd have to do a more serious attribution to check how the vol targeting impacted things, and also to get the weightings more appropriate. To be honest, 12% commodities is way too low relative to about 54% stocks, even if commodities aren't 100% a category that's supposed to be equal to equity risk by themselves in AQR's formulation. And obviously fixed income exposure is too low here.
Taking your analysis at face value--that's not a zinger, that's an expression of ignorance on my part--then, when I look at your PortfolioVisualizer backtest...
Image
...and throw into it my intuitions about the amount of variability you get in the real world... this is my "attribution." Do you think it's reasonably fair?
  • As I showed, both of these funds, during the stated time period, had grotesquely lower return and higher volatility than any plain vanilla "Bogleheadish" portfolio.
  • This inferiority can be attributed entirely to these funds' portfolio choices and active management, not to their use of risk parity as such. They were about the same as, not inferior to, your "similar portfolio without risk parity."
  • The use of a risk parity strategy by AQRIX and MMFAX did not have any obvious visible effect; no gain, and no pain. To the eye, it did nothing.
  • Due to the effect of mutual funds that claim to use "risk parity" being actively managed, and making different idiosyncratic portfolio choices, it is not possible to evaluate anything about the real-world value of risk parity, as a component of a strategy, simply by looking at the actual results of funds that use it. Any effect of risk parity is completely swamped and lost in the noise of other choices.
Lower correlation with stocks is irrelevant unless we choose to test these funds as components of a bigger portfolio that also includes stocks. The funds had Sharpe ratios of 0.79 during a time period when Total Stock had a Sharpe ratio of 1.32. 0.79/1.32 = 0.60, so their correlation with stocks would need to be lower than 0.60 for them to improve a portfolio when combined with Total Stock; their actual correlations, 0.59 and 0.56, are so close to 0.60 as to be considered "equal." Furthermore, we would be comparing them with your portfolio which has a correlation of 0.89, not 1.00 with stocks, so it, too, might (theoretically in a crazy-precise calculation over some specific time period) create a hair's benefit itself and... never mind. A correlation with stocks of 0.56 rather than 0.89 is of no practical consequence.
Last edited by nisiprius on Sat Feb 24, 2018 11:11 am, edited 2 times in total.
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Re: Risk Parity Investing

Post by nisiprius » Sat Feb 24, 2018 10:54 am

I don't understand Burton Malkiel's explanation of risk parity. I know it's just a homely analogy, but... I don't understand it. Since he's Wealthfront's Chief Investing Officer, explaining their new strategy, I think it's worth trying to understand it. One problem is that I'm not directly familiar with racetrack betting. Here's what he says:
Imagine you’re at a horse racing track. There are long-shot horses (considered by most to be unlikely to win, but with the largest winning payout), horses that are middle of the pack, and favorites (considered most likely to win, but with smaller winning payouts). What is your optimal betting strategy? Sure, the significant payoff of the long-shots is enticing enough to lure some into throwing their money at them, but a more prudent bet is the favorite. Why? Well, it turns out that over time if you consistently bet the long-shots you lose 40% the amount of your bet to pay taxes and operational expenses since the track takes 20% of each bet. However, over time, if you stuck with betting the favorites, you’d only lose about 5% of your bet over time. Risk Parity aims to give you the probability of the favorites with potentially the larger payoff of the long-shot.
Let's suppose there are only two horses, and that betters choose to bet a total of $99,000 on one and $1,000 on the other. In accordance with Malkiel's statement that "the track takes 20% of each bet," the bookmaker or parimutuel machine or whatever will pay out $80,000, and therefore offers 80:99 odds on one horse and 80:1 odds on the other.

Assume an efficient market, and that the favorite and the long shot actually have, respectively, 99% and 1% probabilities of winning.

A bettor following a risk parity strategy bets on both horses. He wishes to bet a total of $1,000. According to the principle of risk parity, how much should he bet on each horse? What, exactly, is improved by doing this, and by how much? And how do we get to Malkiel's numbers of 40% versus 5% losses, and his statement that "Risk Parity aims to give you the probability of the favorites with potentially the larger payoff of the long-shot?"

Why is taxation different for winnings on the favorite and the long shot, or is it?
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Re: Risk Parity Investing

Post by lack_ey » Sat Feb 24, 2018 12:55 pm

nisiprius wrote:
Sat Feb 24, 2018 10:26 am
Taking your analysis at face value--that's not a zinger, that's an expression of ignorance on my part--then, when I look at your PortfolioVisualizer backtest...
https://imgur.com/sTUbsi2.png
...and throw into it my intuitions about the amount of variability you get in the real world... this is my "attribution." Do you think it's reasonably fair?
  • As I showed, both of these funds, during the stated time period, had grotesquely lower return and higher volatility than any plain vanilla "Bogleheadish" portfolio.
  • This inferiority can be attributed entirely to these funds' portfolio choices and active management, not to their use of risk parity as such. They were about the same as, not inferior to, your "similar portfolio without risk parity."
  • The use of a risk parity strategy by AQRIX and MMFAX did not have any obvious visible effect; no gain, and no pain. To the eye, it did nothing.
  • Due to the effect of mutual funds that claim to use "risk parity" being actively managed, and making different idiosyncratic portfolio choices, it is not possible to evaluate anything about the real-world value of risk parity, as a component of a strategy, simply by looking at the actual results of funds that use it. Any effect of risk parity is completely swamped and lost in the noise of other choices.
Lower correlation with stocks is irrelevant unless we choose to test these funds as components of a bigger portfolio that also includes stocks. The funds had Sharpe ratios of 0.79 during a time period when Total Stock had a Sharpe ratio of 1.32. 0.79/1.32 = 0.60, so their correlation with stocks would need to be lower than 0.60 for them to improve a portfolio when combined with Total Stock; their actual correlations, 0.59 and 0.56, are so close to 0.60 as to be considered "equal." Furthermore, we would be comparing them with your portfolio which has a correlation of 0.89, not 1.00 with stocks, so it, too, might (theoretically in a crazy-precise calculation over some specific time period) create a hair's benefit itself and... never mind. A correlation with stocks of 0.56 rather than 0.89 is of no practical consequence.
I'm not sure how much of it is the active management. For sure some of the bad performance relative to US 60/40 is the costs and expense ratios. A large portion is about the underlying investments used. Some residual may be from the timing and management, whether it's discretionary or algorithmic.

My passive alternative benchmark didn't have the right exposures, anyway. If you compared the risk parity funds against allocations that had higher levels of commodities exposure (like they did), the risk parity funds would look better. But then that would mean shortchanging the equity or bond risk taken. There's simply no way to cram all those exposures in without leverage, so comparing to unleveraged allocations is never going to work all that well.

You're right that the lower correlation with another asset doesn't really matter. I pointed it out not to say that it means risk parity has some advantage, but that the risk parity funds observed are significantly different from the standard portfolio allocations.


As for Malkiel's example, I have no idea what he's going on about, and it seems there's some information we're supposed to have that is not given in the prompt, regarding taxation and the house's cut in horse racing. Also, I don't really see how this is relevant anyway as a key feature of actual portfoilos and a motivation behind risk parity is that assets are not entirely dependent on one another. Stocks and bonds frequently have low, zero, or even negative correlation. But the outcome of which horse wins a race is completely dependent—one wins and the others lose. Though I suppose there are some bets that are not about 1st place, or...?


Risk parity is better understood with MPT motivations and calculated with simple examples. If we have two assets, A with excess return mean 6% and standard deviation 15%, B with excess return mean 2% and standard deviation 5%, both have Sharpe ratios of 0.4. One is 3x more volatile than the other. Risk parity would say to use 25% A and 75% B, so we take equal risk from both. If they're uncorrelated, the 25%/75% portfolio would have an excess return mean 3% and standard deviation 5.303% if we do the math (sqrt[.75^2 * 5^2 + .25^2 * 15^2]), for a Sharpe ratio of 0.566. If we want to target a return of 4.5%, we leverage up the 25/75 by 50% (to 37.5%/112.5%/-50% cash), if we could actually borrow at the risk-free rate, scaling it up (to vol of 7.955%). The alternative is to use an unleveraged allocation of 62.5%/37.5% with vol of 9.56%. In practice, with borrowing costs above the risk-free rate, the risk parity allocation would not look as good.

In the above, the return figures are arithmetic means. Looking at geometric would be more complicated, and with leverage the relative returns are path dependent and depend on the rebalancing and so on. Also this example doesn't look at vol targeting, assuming A and B vol are constant over time.

That's the ideal case for risk parity, where different assets have equal Sharpe ratios and are uncorrelated. The risk parity allocation becomes less optimal and further off the efficient frontier as those conditions become less true. That said, with more than two assets there's additional room for potential diversification benefits to exploit.

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Re: Risk Parity Investing

Post by nisiprius » Sat Feb 24, 2018 5:00 pm

I know that lack_ey has already rejected the simple-minded approach of looking at the real-world performance of "risk parity" mutual funds, and his reasons have a good deal of justice to them... I do want to finish up with one grand roundup.

This is an overview of six funds, which, regardless of whatever else they are doing, are all said to be using "risk parity." Now, so far, nothing I've read about "risk parity" has said that it is expected to do poorly in bull markets. It is a general approach that can be used on any desired asset allocation. Nevertheless, whatever they have been investing in, every one of these funds did really poorly, not just a little bit, but really poorly compared to Vanguard LifeStrategy Moderate (yellow). And we have over five years which is not very much to look at, but isn't ludicrously short, either. (I used LifeStrategy Moderate instead of Balanced Index, so that I wouldn't be accused of intentionally omitting international stocks in my comparison).

Source
Image

And what's striking is that, unlike Anna Karenina, all six of the funds sucked in just about the same way. They sort of paralleled LifeStrategy Moderate for about a year, and then suddenly all six of them took a sharp dive while LifeStrategy just kept rising, opening up white space between them and never getting it back. But it wasn't just once. That white space stayed constant up to about 2015, and then all six funds started to fall faster than LifeStrategy, continuously widening that white space, falling farther and farther behind, pretty steadily from 4/2015 to 1/2016. They then paralleled LifeStrategy again, not closing the gap but not widening it either, until suddenly, in 11/2016, again, five of the six risk parity funds quite suddenly went down... all together... widening the space even more.

That's really quite unusual to see. In just five years, you have three separate episodes of underperformance--two sudden, one gradual--and, basically, no periods of outperformance. Five of them managed to stumble, badly, three times in five years; one of them, only twice.

Whatever those funds were doing, it went memorably poorly. Now whether this is a result of risk parity itself, or whether it is a consequence of the investment portfolios that traditionally go along with the phrase "risk parity," I don't know.

I'd add that most of these funds look to the eyeball as if they had more volatility than Vanguard LifeStrategy Moderate. According to PortfolioVisualizer, the actual numbers, standard deviation, Aug 2012 - Jan 2018

SRPFX, 13.25%
CRAAX, 13.05%
AQRIX, 8.26%
MMAFX, 8.10%
PDREX, 6.28%
VSMGX, 5.74% <---
ABRZX, 5.70%

So, all of the funds underperformed Vanguard LifeStrategy Moderate in return, but four of them managed to combine that underperformance with higher volatility; two were about the same as VSMGX. Not one of them justified their lower return by combining it with lower volatility.
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Re: Risk Parity Investing

Post by willthrill81 » Sat Feb 24, 2018 5:22 pm

One poster here once said that a "poor man's" risk-parity portfolio is just a bond-heavy one. There's some truth in that I think.

For those looking for such a fund, Vanguard's Wellesley and the new Global Wellesley funds are worth a long look.
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Re: Risk Parity Investing

Post by jalbert » Sat Feb 24, 2018 5:57 pm

Thanks. But I think you forgot to mention the leverage?
Leverage is used in many investment products based on risk parity, but it is not an inherent property of risk parity. The idea of leverage is that if you have controlled risk using risk parity then you can afford to take more risk with leverage. In modern portfolio theory, if you want a lower risk portfolio than the minimum variance portfolio on the efficient frontier, you add cash. If you want more risk you could slide along the efficient frontier curve toward the more risky end of a higher returning asset, or you could do the opposite of adding cash, which would be to add leverage.

I’m not a fan of leveraged portfolios because leverage drains portfolio liquidity. If a risk parity portfolio includes bonds, then leverage and bonds more or less cancel each other out (not exactly cancel because the bond duration and leverage duration might be different) so that the leveraged portfolio often no longer will in fact be a risk parity portfolio. Perhaps risk parity products factor this into the risk parity determination.
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Re: Risk Parity Investing

Post by lack_ey » Sat Feb 24, 2018 6:12 pm

In an equity bull market, diversification by reducing equity risk exposure = deworsification.
nisiprius wrote:
Sat Feb 24, 2018 5:00 pm
I know that lack_ey has already rejected the simple-minded approach of looking at the real-world performance of "risk parity" mutual funds, and his reasons have a good deal of justice to them... I do want to finish up with one grand roundup.
Nah, that's fair and interesting to evaluate what risk parity funds have done. It just doesn't necessarily generalize well to describing specific risk parity implementations that may fall somewhat away from these six in strategy, such as Wealthfront's. Sticking just with stocks and bonds like Wealthfront would have been better the last six years.
nisiprius wrote:
Sat Feb 24, 2018 5:00 pm
This is an overview of six funds, which, regardless of whatever else they are doing, are all said to be using "risk parity." Now, so far, nothing I've read about "risk parity" has said that it is expected to do poorly in bull markets. It is a general approach that can be used on any desired asset allocation. Nevertheless, whatever they have been investing in, every one of these funds did really poorly, not just a little bit, but really poorly compared to Vanguard LifeStrategy Moderate (yellow). And we have over five years which is not very much to look at, but isn't ludicrously short, either. (I used LifeStrategy Moderate instead of Balanced Index, so that I wouldn't be accused of intentionally omitting international stocks in my comparison).
I don't think these funds did poorly. They all gained nontrivially. Some were pretty decent, others much less so. It's only when we compare performance relative to traditional balanced funds that we would say that they did relatively poorly.

Risk parity is supposed to do worse than balanced funds when stocks are doing well. Isn't that the point? You take less equity risk, you do less well when equity risk is rewarded. Maybe you're surprised by the magnitude of the difference, which is concerning I suppose, but largely explainable by the passive exposures.
nisiprius wrote:
Sat Feb 24, 2018 5:00 pm
http://quotes.morningstar.com/chart/fun ... A%5B%5D%7D
https://imgur.com/3jzckDh.png

And what's striking is that, unlike Anna Karenina, all six of the funds sucked in just about the same way. They sort of paralleled LifeStrategy Moderate for about a year, and then suddenly all six of them took a sharp dive while LifeStrategy just kept rising, opening up white space between them and never getting it back. But it wasn't just once. That white space stayed constant up to about 2015, and then all six funds started to fall faster than LifeStrategy, continuously widening that white space, falling farther and farther behind, pretty steadily from 4/2015 to 1/2016. They then paralleled LifeStrategy again, not closing the gap but not widening it either, until suddenly, in 11/2016, again, five of the six risk parity funds quite suddenly went down... all together... widening the space even more.

That's really quite unusual to see. In just five years, you have three separate episodes of underperformance--two sudden, one gradual--and, basically, no periods of outperformance. Five of them managed to stumble, badly, three times in five years; one of them, only twice.

Whatever those funds were doing, it went memorably poorly. Now whether this is a result of risk parity itself, or whether it is a consequence of the investment portfolios that traditionally go along with the phrase "risk parity," I don't know.
Again, I'd have to say this is really the feature, not a bug. You should expect to see declines in risk parity funds that you don't see in balanced funds. That's evidence that the funds are taking nontrivial risks outside of equities and that these are being punished sometimes. There are some episodes in the graphs shown where the risk parity funds do better than the LifeStrategy fund (or in the very least, [performance - mean] is better for the risk parity fund). It's just not as apparent because the overall mean performance was worse for all the risk parity funds.
nisiprius wrote:
Sat Feb 24, 2018 5:00 pm
I'd add that most of these funds look to the eyeball as if they had more volatility than Vanguard LifeStrategy Moderate. According to PortfolioVisualizer, the actual numbers, standard deviation, Aug 2012 - Jan 2018

SRPFX, 13.25%
CRAAX, 13.05%
AQRIX, 8.26%
MMAFX, 8.10%
PDREX, 6.28%
VSMGX, 5.74% <---
ABRZX, 5.70%

So, all of the funds underperformed Vanguard LifeStrategy Moderate in return, but four of them managed to combine that underperformance with higher volatility; two were about the same as VSMGX. Not one of them justified their lower return by combining it with lower volatility.
I didn't check all of them, but SRPFX targeted 15% vol, and AQRIX targeted about 10% vol, for what it's worth. Volatility overall kind of surprised on the downside over the period, particularly for stocks (also for bonds, really).

Equities were quite tame and returned a lot. Go figure.

Over a full cycle the relative results should probably be closer, though it would certainly help if the cycle included commodities playing quite a bit of catch-up at this point.

jalbert wrote:
Sat Feb 24, 2018 5:57 pm
Thanks. But I think you forgot to mention the leverage?
Leverage is used in many investment products based on risk parity, but it is not an inherent property of risk parity. The idea of leverage is that if you have controlled risk using risk parity then you can afford to take more risk with leverage. In modern portfolio theory, if you want a lower risk portfolio than the minimum variance portfolio on the efficient frontier, you add cash. If you want more risk you could slide along the efficient frontier curve toward the more risky end of a higher returning asset, or you could do the opposite of adding cash, which would be to add leverage.

I’m not a fan of leveraged portfolios because leverage drains portfolio liquidity. If a risk parity portfolio includes bonds, then leverage and bonds more or less cancel each other out (not exactly cancel because the bond duration and leverage duration might be different) so that the leveraged portfolio often no longer will in fact be a risk parity portfolio. Perhaps risk parity products factor this into the risk parity determination.
The leverage is usually through derivatives, though, so effectively very short rate, and not really impacting liquidity. Does it matter so much for these purposes if they're sitting on some futures, swaps, or whatever? There are the usual issues of leverage rebalancing and so on, sure, but most of the risk parity funds are already frequently adjusting position sizes for vol targeting anyway.

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Re: Risk Parity Investing

Post by jalbert » Sat Feb 24, 2018 7:02 pm

Fair enough, but that does not increase my interest level in these products. Presumably they include the derivative assets in the risk parity determination.

Another point about pure risk parity is it does not by itself protect you from choosing assets for the mix that have highly correlated drivers of risk. A risk parity portfolio consisting of a mix of an S&P500 fund and total US stock index fund is not very interesting as an extreme example.
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Re: Risk Parity Investing

Post by grok87 » Sat Feb 24, 2018 8:06 pm

jalbert wrote:
Sat Feb 24, 2018 5:57 pm
Thanks. But I think you forgot to mention the leverage?
Leverage is used in many investment products based on risk parity, but it is not an inherent property of risk parity.
interesting point.
jalbert wrote:
Sat Feb 24, 2018 5:57 pm
I’m not a fan of leveraged portfolios because leverage drains portfolio liquidity. If a risk parity portfolio includes bonds, then leverage and bonds more or less cancel each other out (not exactly cancel because the bond duration and leverage duration might be different) so that the leveraged portfolio often no longer will in fact be a risk parity portfolio. Perhaps risk parity products factor this into the risk parity determination.
i would be curious to know this as well. i suspect they don't. leverage seems to be particularly ill-suited to the standard deviation framework that risk parity funds seem to use. for example the behavior in 2008/09
https://fred.stlouisfed.org/series/USD1MTD156N
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Re: Risk Parity Investing

Post by jalbert » Sun Feb 25, 2018 4:38 pm

If we want to use a non-leveraged asset allocation to benchmark AQR Risk Parity (AQRIX), it should probably include commodities. There's no way to get a good fit without leverage, though, but here's an approximation I came up with:
27% VTI - US stock
18% VEA - ex-US developed stock
9% VWO - emerging markets stock
12% DBC - commodities (futures)
6% TIP - TIPS
6% EMLC - local currency emerging markets bonds (to capture EM currency and then also credit risk)
6% HYG - junk bonds
6% CRED - investment-grade credit
10% BND - US bonds

I think I could imagine a financial advisor using an allocation like that. Looks in the range of reasonable enough to me. How about you?
I don't personally find a benchmark that was determined empirically by backfitting to the product to be measured using the types of asset classes held by the product to be very useful, but some may find it helpful.
Nevertheless, whatever they have been investing in, every one of these funds did really poorly, not just a little bit, but really poorly compared to Vanguard LifeStrategy Moderate (yellow). And we have over five years which is not very much to look at, but isn't ludicrously short, either.
You can see 7 years of data if you just compare AQRIX to VSMGX:

https://www.portfoliovisualizer.com/bac ... ion2_2=100

Not a terrible result, but AQRIX had a larger max drawdown, significantly higher volatility, and significantly lower return.

I suspect Asness et al. would suggest that we have not had an equity bear market in those years, and that may be when AQRIX will overperform a conventional portfolio. They may also consider that the reduced equity correlation makes AQRIX a good portfolio diversifier. I can't dispute those points, but the fact that AQRIX had a larger drawdown than VSMGX (LifeStrategy 60/40) in the market corrections we have had during AQRIX's existence is potentially an ominous sign.
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Re: Risk Parity Investing

Post by nisiprius » Sun Feb 25, 2018 6:12 pm

jalbert wrote:
Sun Feb 25, 2018 4:38 pm
...I suspect Asness et al. would suggest that we have not had an equity bear market in those years, and that may be when AQRIX will overperform a conventional portfolio. They may also consider that the reduced equity correlation makes AQRIX a good portfolio diversifier. I can't dispute those points, but the fact that AQRIX had a larger drawdown than VSMGX (LifeStrategy 60/40) in the market corrections we have had during AQRIX's existence is potentially an ominous sign...
Conveniently, for the premise that AQRIX might have outperformed a conventional portfolio in an equity bear market, AQRIX didn't exist in 2008-2009.

However, MMAFX (blue) AMG FQ Global Risk-Balanced Fund Class did.
And it didn't outperform the conventional portfolio, represented by VSMGX, Vanguard LifeStrategy Moderate (60/40, and includes international)

During 2008-2009, the dumb Vanguard fund dropped 36%, the sophisticated "risk-balanced" fund dropped 44%.

The risk parity fund underperformed both during the bull market and the bear market that preceded it.

Source
Image

Now, I take lack_ey's point that we don't know (with any of these funds, all being actively managed), exactly what there were doing at any point in the past. Not without doing a lot of digging, much of which I don't actually know how to do. But given that since, as shown below, since inception AQRIX has been reasonably similar to MMAFX, and quite different from VSMGX, I think it is likely that MMAFX and AQRIX have been following reasonably similar strategies, and that the performance of MMAFX during 2008-2009 is probably a fair test of how "risk parity funds" did during a bear market.

Source
Image
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Re: Risk Parity Investing

Post by lack_ey » Sun Feb 25, 2018 7:08 pm

nisiprius wrote:
Sun Feb 25, 2018 6:12 pm
jalbert wrote:
Sun Feb 25, 2018 4:38 pm
...I suspect Asness et al. would suggest that we have not had an equity bear market in those years, and that may be when AQRIX will overperform a conventional portfolio. They may also consider that the reduced equity correlation makes AQRIX a good portfolio diversifier. I can't dispute those points, but the fact that AQRIX had a larger drawdown than VSMGX (LifeStrategy 60/40) in the market corrections we have had during AQRIX's existence is potentially an ominous sign...
Conveniently, for the premise that AQRIX might have outperformed a conventional portfolio in an equity bear market, AQRIX didn't exist in 2008-2009.

However, MMAFX (blue) AMG FQ Global Risk-Balanced Fund Class did.
And it didn't outperform the conventional portfolio, represented by VSMGX, Vanguard LifeStrategy Moderate (60/40, and includes international)

During 2008-2009, the dumb Vanguard fund dropped 36%, the sophisticated "risk-balanced" fund dropped 44%.

The risk parity fund underperformed both during the bull market and the bear market that preceded it.

Source
https://imgur.com/lURTqh7.png

Now, I take lack_ey's point that we don't know (with any of these funds, all being actively managed), exactly what there were doing at any point in the past. Not without doing a lot of digging, much of which I don't actually know how to do. But given that since, as shown below, since inception AQRIX has been reasonably similar to MMAFX, and quite different from VSMGX, I think it is likely that MMAFX and AQRIX have been following reasonably similar strategies, and that the performance of MMAFX during 2008-2009 is probably a fair test of how "risk parity funds" did during a bear market.

Source
https://imgur.com/w552fzf.png
AMG FQ Global Risk-Balanced Fund is more similar now to the average risk parity fund and something like AQR's than it was back in 2008-2009.

For reference, that was apparently two fund name changes ago. It was AMG FQ Global Alternatives Fund then, and the annual report covering through the end of Oct 2008 talks about its currency selection strategy and market timing different equity and bond markets, being long some and short others. That's closer to a generic actively managed go-anywhere, multi-asset fund like PIMCO's All Asset All Authority (PAUIX) run by Rob Arnott (Research Affiliates).


That said, I imagine that a number of risk parity type allocations could have done relatively poorly in 2008-2009 depending on risk targets and assets. If a fund included allocations to most foreign currencies, credit risk (especially high yield), commodities, etc., these were all bad in 2008-2009 too. So even if equity market beta were significantly under say 0.6 for the fund, it might do worse than balanced funds with 0.6 market beta. Or at least not much better. The vol targeting most risk parity funds do would have helped, for what it's worth, so this is part of why I'm not that sure about what the performance would have been. Equity and different market vols all went up around that period prior to the steepest declines.

Some of the risks taken by many risk parity strategies are at least somewhat related to equity risk, at least in certain equity bear markets. That's a valid criticism overall—you may not get as much value from diversifying into these other things when times are tough. That said, a significant portion of equity market declines are not credit crises and do not necessarily have commodities and other assets going down.

I also think generally that there is too much emphasis on bear markets. Reducing reliance on equity market risk for returns could be usefully diversifying under flat or middling equity market returns as well (of course it would detract in equity bull markets).

As usual, a lot of the debate around risk parity strategies seems to go around the underlying investments and not as much the risk parity aspect itself. The Wealthfront risk parity fund should be a bit different, being stocks and bonds only (though this includes EM bonds).

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Re: Risk Parity Investing

Post by stlutz » Sun Feb 25, 2018 7:31 pm

FWIW, Salient has back-calculated a Risk Parity index back to 1990: http://www.salientindices.com/risk-parity.html

They began calculating for real in 2012, but the back-history strikes me as being reasonable even though nobody was really doing this back in 1990. They do include implementation costs.

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Re: Risk Parity Investing

Post by nisiprius » Sun Feb 25, 2018 8:27 pm

So, I'm trying to wrap my head around the risk parity concept itself, which lack_ey and jalbert have described. I was trying to understand what would be the difference between a simple traditional stock/bond portfolio, with and without risk parity.

I started with a 60/40 portfolio of Total Stock/Total Bond, VTSMX/VBMFX, rebalanced annually, using the data available in PortfolioVisualizer, i.e. 1985-2017. The standard deviation was 14.53% for VTSMX, 3.56% for VBMFX. After brooding about it, I came to the conclusion that I could do anything creative like leverage the bonds without leveraging the stocks--the loan doesn't know what asset you're buying with it. Risk parity means you determine the stock/bond allocation from the standard deviations alone. Unlike MPT, the allocation no longer depends on the rate of return from the riskless asset, or the correlation between the assets, or their return.

The standard deviation is 14.53% for VTSMX, 3.56% for VBMFX, and that's it. Your asset allocation is 3.56/(14.53 + 3.56) = 19.7% stocks, 80.3% bonds, and that's it. Based on the standard deviations and nothing else. You then use either leverage, or an allocation to the riskless asset, to adjust the portfolio risk as desired.

And my first impression was that "risk parity" portfolio, 19.7/80.3 leveraged up, was in fact far superior to 60/40. And it is.

The problem is that the MPT optimum allocation over that time period is not 60/40. It's not even close to it.In fact, it's 15.5/84.5. And if we plug that in, we get a very slightly higher return for the same risk than we do with the risk parity allocation.

As, of course, we'd expect. Over a stated historic period, with known historic values, the MPT-based allocation is the value that would have been the optimum over that time period.*

If we actually know the six MPT parameters--two returns, two standard deviations, the correlation of the two assets, and return of the riskless asset--then the risk parity allocation is some kind of rough shortcut that throws out four pieces of data. In our specific example, the risk parity allocation is quite close to the MPT allocation, and both are miles away from 60/40. But in general, the risk parity allocation is not going to be the same as the MPT allocation, and if it's different, it won't be quite as good.

So how can I make sense of risk parity? Why would one want to use risk parity instead of traditional MPT? It seems to me that I can only make sense of it if I assume two things:

a) The risk parity allocation, for known parameters, will always be "close enough" to the actual optimum MPT allocation.

b) In a prediction situation, where we want to predict an allocation that will be good over a future time period, it turns out that, of the six MPT parameters, two of them--the past standard deviations--are reliable predictors of future standard deviation, and that the other four are not.

If we believe that, then we would believe that the risk parity allocation based on past data is a decent predictor of what the risk parity allocation over the forthcoming years will be, but that the past MPT allocation is not a decent predictor of what the future MPT optimum will be. Therefore, it's better to work from a good predictor of a good enough allocation, than a bad predictor of an optimum allocation.

Offhand, I think assumption (b) is really unlikely to be true. But perhaps the point is that the kinds of exotic assets that traditionally go into things called "risk parity funds" are too volatile in everything, to even pretend to estimate MPT parameters, so maybe the fund managers throw up their hands and say "well, at least risk parity is something we can use other than gut feeling to calculate an allocation?"

*In a sense the optimum for a past time period is simply the highest possible allocation--leveraged if possible--to the specific asset that that had the highest return. But the MPT is the optimum if you assume that you have to bet on the result of a randomly selected year from within the time period.
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Re: Risk Parity Investing

Post by tranquility » Sun Feb 25, 2018 9:18 pm

Any financial instrument or approach that’s relatively not easy to understand to us and needs extensive research is out of the question.

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Re: Risk Parity Investing

Post by jalbert » Mon Feb 26, 2018 6:19 am

So how can I make sense of risk parity? Why would one want to use risk parity instead of traditional MPT? It seems to me that I can only make sense of it if I assume two things:

a) The risk parity allocation, for known parameters, will always be "close enough" to the actual optimum MPT allocation.

b) In a prediction situation, where we want to predict an allocation that will be good over a future time period, it turns out that, of the six MPT parameters, two of them--the past standard deviations--are reliable predictors of future standard deviation, and that the other four are not.
First, the risk parity portfolio does not have to be particularly close to the optimal MPT allocation and often is not. When doing a traditional MPT allocation, If you don't care about the having the entire efficient frontier curve so you you can pick the point most suited to your needs on it, but just want the minimum volatility point, a minimum-variance optimization may be done from the covariance matrix of the assets without having to estimate expected returns of the assets.

Second, I think risk parity was originally proposed as a mechanism of constructing stock portfolios. Instead of using a market cap weight, or equal weight, you would weight each stock in proportion to the inverse of its volatility. A variant is to weight as the inverse of the stock's beta with respect to the portfolio as its market domain. This is much less computationally intensive than trying to do a minimum-variance optimization using a very large covariance matrix.

Subsequently, risk parity started being used for asset allocation, which generally means 2 or more asset classes up to some small number like 12. In this case, if some of the assets are lower risk assets like bonds, and some are higher risk assets like stocks, the risk parity portfolio will have a low allocation to the riskier asset and will generally not be a high return portfolio. I think quant folks decided they could soup it up with leverage to bring the returns back to being more competitive with portfolios that have a higher allocation to the riskier, higher return assets, but with a lower correlation to equities than a conventional portfolio that has a higher equity allocation. The idea is that it would be a good alternative investment to use as a diversifier. So far, any results I have seen have been less than impressive. I'm sure risk parity experts would make corrections and fill in details to the above, but that's the gist of my understanding of it.
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Re: Risk Parity Investing

Post by nisiprius » Mon Feb 26, 2018 9:20 am

stlutz wrote:
Sun Feb 25, 2018 7:31 pm
FWIW, Salient has back-calculated a Risk Parity index back to 1990: http://www.salientindices.com/risk-parity.html

They began calculating for real in 2012, but the back-history strikes me as being reasonable even though nobody was really doing this back in 1990. They do include implementation costs.
Since there was a question about my using the MMAFX fund as an indication of "risk parity" results, here's what we get if we compare the Vanguard LifeStrategy Moderate Growth (60/40, includes international) fund to the Salient index. Before I show it: usual carping, if the index wasn't calculated "for real" until 2012, then the back calculations don't really count because they never would have done it if the backtesting hadn't shown promising results. I'm using "since inception of Vanguard LifeStrategy Moderate," which only goes back to 1994, but still is a generous sampling of the index history, including bull and bear markets.

The volatility looks about the same to the eyeball--whatever is meant by "risk parity" didn't give a smoother ride--and the calculated, annualized standard deviation (monthly times sqrt(12)) were 9.73% for the Salient Risk Parity Index, 9.50% for Vanguard Life Strategy Moderate.

Image

I would call that pretty underwhelming. It's, you know, different from plain old VSMGX, LifeStrategy Moderate. But is it better, and, if so, by what criterion? Yes, it did drop quite a bit less in 2008-2009, -28% versus -38% for VSMGX. But, nothing magic going on, a bit less total return over the total time period shown, a bit more volatility.

Now, although you say the index includes implementation costs, it doesn't include the expense ratio.

Given that Salient's own "Adaptive Growth" fund, SRPFX, has a 1.39% for institutional (!) (SRPFX), that's going to make a difference. And, of course, the fund is not stated to be an index fund tracking the Adaptive Growth index, raising questions of its own. I'd hoped the prospectus or the semiannual report for SRPFX would compare the fund to the index, but I can't find any reference to the index. Oddly, IMHO, the Prospectus compares it to: the MSCI ACWI (i.e. stocks) index, the Bloomberg Barclay's U.S. Aggregate bond index, and a "60/40" index.

In any case, they say that the annualized return since inception (7/9/2012) "For the period ended December 31, 2016" was 2.75%, 1.47%, or 1.50% for Institutional, class A, and class C. The comparable number for their risk parity index is 589.76 on 7/9/2012 to 684.54 on 12/30/2016 = 3.39% per year, so their fund underperformed their risk parity index by -0.62%... and, of course, far underperformed the "60/40 index" they present.

Image
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