Optimal Asset Allocation

[HWWProject]

Last year while sitting in lots of cash (finding no value stocks) I developed an Optimal Asset Allocation model.  Articles here: http://healthywealthywiseproject.com/2015/04/optimal-asset-allocation-for-april-2015/

 

and here: http://healthywealthywiseproject.com/2014/04/projected-returns-of-major-asset-classes/

 

It's worked well and I'm growing in confidence in it.  The model takes as input projected future asset class returns and price volatilities, then optimizes the allocations using the Kelly Formula.  I use low-cost Vanguard ETF's to implement.

 

Just thought I'd share and ask how others make overall allocation decisions.  Before this model I was kinda haphazard in my decision-making on allocation, yet as you've likely heard more than 90% of a portfolio's return is attributable to its mix of asset classes.

[frommi]

When you want to learn about asset allocation i would suggest start reading about Ray Dalios All-Weather-Portfolio and the Permanent Portfolio. I don`t think you should optimize asset allocation based on the past or on "current" inflation expectation because future inflation is very unstable and unknowable. So your asset allocation should be robust in every inflation scenario not only one.

[constructive]

I think your TIPS estimated return is unlikely to be correct.

 

VTIP has a 2 year average duration so the effective yield is around negative 1%. To get to your estimated 0.8% return you need inflation to rev up sharply.

[innerscorecard]

The more I think about it, the more I am convinced that the asset allocation approach to investing is fundamentally incompatible with a value-oriented approach. That isn't to say that they both can't work - they can, just that their assumptions are not only different but mutually exclusive, so that it is extremely strange to mix them, except that both are popular and so people want the best of both worlds.

[TwoCitiesCapital]

When you want to learn about asset allocation i would suggest start reading about Ray Dalios All-Weather-Portfolio and the Permanent Portfolio. I don`t think you should optimize asset allocation based on the past or on "current" inflation expectation because future inflation is very unstable and unknowable. So your asset allocation should be robust in every inflation scenario not only one.

 

+1. My current 401k is managed using a loose interpretation of the All Weather philosophy. It's my only real passive strategy and is largely to my limitations in investments and my desire to hedge my ability to manage my own money. It's obviously not a full Risk Parity model because I cant' lever up asset classes to match the volatility of equities, but it's close enough for me.

 

I'd be interested in hearing more about your methodology. How are you coming up with projected returns and volatility and how are you feeding those into the Kelly Criterion to determine a portfolio weight? Also, I'm a little confused by your methodology for determining the forward returns of a bond fund. You said you multiply the duration by the coupon but that doesn't make sense to me. The duration is simply the weighted average timing of the cash flows which means that it would translate to the 50/50 point of a funds life relative to the absolute amount of cash flows to be received. This seems to be it would understate returns and you should simply use the Yield to maturity and multiply it by the average maturity instead of the duration, no?

 

My main two issues with the Kelly formula have been:

1) The Kelly formula assumes you have an edge but we rarely do in investments. I've thought about using valuation and forward expected returns as a proxy for an "edge", but it's hard to figure out how to quantify that unless if you take an approach of assuming mean reversion over a finite period of time like 7 years or 10 years and attach a probability to it.

2) The Kelly formula can be extremely volatile and practitioners can experience massive losses. It's only mathematically the best way to compound, but that doesn't mean anything if you don't stick with it. Investors might find they do better with other systems simply because other systems are easier to stick with in hard times.

 

This is why I chose more of risk-parity type approach for my 401k, but I'd definitely be interested in learning about an alternative.

[vinod1]

The more I think about it, the more I am convinced that the asset allocation approach to investing is fundamentally incompatible with a value-oriented approach. That isn't to say that they both can't work - they can, just that their assumptions are not only different but mutually exclusive, so that it is extremely strange to mix them, except that both are popular and so people want the best of both worlds.

 

+1

 

I spent the first 5 years of my investment life in the asset allocation, correlation, expected returns, portfolio optimization camp and the last 9 years in the value investing camp. I completely agree with innerscorecard.

 

To those of us with a math or an engineering background or mindset, we tend to take to portfolio optimization like a moth to a flame. Portfolio optimization tends to exist only in spreadsheets.

 

To optimize a portfolio you not only need to get expected returns right, but you need to get correlations right and volatility right. The portfolio is also very sensitive to small changes in returns and correlations. Even with a six asset class portfolio, you need to get 42 variables right (30 correlations, 6 expected returns and 6 volatility estimates). What is the chance you would get all of these even roughly right? If you cannot get these roughly right, you are way better off with a simple allocation approach.

 

Vinod

 

[HWWProject]

When you want to learn about asset allocation i would suggest start reading about Ray Dalios All-Weather-Portfolio and the Permanent Portfolio. I don`t think you should optimize asset allocation based on the past or on "current" inflation expectation because future inflation is very unstable and unknowable. So your asset allocation should be robust in every inflation scenario not only one.

 

Thanks will look into the Dalio AWP and how easily applied.

 

The Cleveland Fed publishes an 'expected future inflation rate' based on TIP prices among other things.  I use that for the inflation rate and compare bonds/stocks against it at the proper duration for each asset class.

 

 

 

[HWWProject]

VTIP has a 2 year average duration so the effective yield is around negative 1%. To get to your estimated 0.8% return you need inflation to rev up sharply.

 

True, but maybe not 'sharply'.  Current inflation is at 0%.  We're not a country where 0% inflation usually lasts long.  When I add my expected future inflation (from Cleveland Fed) to the -1% I get a positive 0.8% real yield on TIPS, same as Rob Arnott's website here:  http://www.researchaffiliates.com/AssetAllocation/Pages/Core-Overview.aspx

[HWWProject]

The more I think about it, the more I am convinced that the asset allocation approach to investing is fundamentally incompatible with a value-oriented approach. That isn't to say that they both can't work - they can, just that their assumptions are not only different but mutually exclusive, so that it is extremely strange to mix them, except that both are popular and so people want the best of both worlds.

 

That depends on how you allocate.  I use to follow a few 'Couch Potato' portfolios that simply rebalanced each year.  They don't consider valuations and I agree its not true value investing.  In fact its because these don't consider valuations that I wanted to use a model that does.  I'm specifically 'value-weighting' the asset classes and putting more money into those with higher prospective returns (risk-adjusted, real returns).  I'm sure there are other asset allocation models that do this too.

 

[frommi]

The more I think about it, the more I am convinced that the asset allocation approach to investing is fundamentally incompatible with a value-oriented approach. That isn't to say that they both can't work - they can, just that their assumptions are not only different but mutually exclusive, so that it is extremely strange to mix them, except that both are popular and so people want the best of both worlds.

 

+1

 

I spent the first 5 years of my investment life in the asset allocation, correlation, expected returns, portfolio optimization camp and the last 9 years in the value investing camp. I completely agree with innerscorecard.

 

To those of us with a math or an engineering background or mindset, we tend to take to portfolio optimization like a moth to a flame. Portfolio optimization tends to exist only in spreadsheets.

 

To optimize a portfolio you not only need to get expected returns right, but you need to get correlations right and volatility right. The portfolio is also very sensitive to small changes in returns and correlations. Even with a six asset class portfolio, you need to get 42 variables right (30 correlations, 6 expected returns and 6 volatility estimates). What is the chance you would get all of these even roughly right? If you cannot get these roughly right, you are way better off with a simple allocation approach.

 

Vinod

 

From what i know about asset allocation is that you truly only need 3 different assets (stocks->prosperity,long term bonds->deflation,gold->inflation) to get a portfolio with very low drawdowns (based on the last 45 years of history) and an equity like CAGR. This is because for example REIT`s and stocks (regardless if international/midcap/smallcap etc.) are all so closely correlated that you get no benefit from the diversification in it. And when you lever that allocation up to match equity volatility/drawdowns you get returns that are similar to value investing. I can see a benefit of using some money in such a system and the rest in value investing strategies, especially because its not very easy at the moment to find good value investments and the returns of the system should be uncorrelated to stock returns.

 

 

[HWWProject]

 

I'd be interested in hearing more about your methodology. How are you coming up with projected returns and volatility and how are you feeding those into the Kelly Criterion to determine a portfolio weight?

 

 

For bond indexes I use the Yield to maturity of the Vanguard ETF's, and subtract fees/expenses and current premium/discount.  For credit sensitive indices (corporate, high yield, EM) I also adjust for the default risk spread. (you can google a paper - Bond prices default probabilities and risk premiums.pdf).

 

For stock indices I use methods John Hussman has written about including dividend-discount, then average in published estimates from Jeremy Grantham and Rob Arnott.

 

For index standard deviations (volatility) I use historic averages, Arnott's estimates and add a premium for the current duration. (I believe longer durations lead to greater volatility). 

 

The returns are compared to the expected future inflation rate (and each other) to see if there is a positive expected future return.  Then use the Kelly Formula to weight the assets according to return/risk.  I'm a big fan of the Kelly formula it's fundamentally about betting more when the risk-adjusted odds are in your favor.  I do 'soften' the Kelly formula results with a 'diversification' factor which Kelly reportedly used in his hedge fund (to account for multiple opportunities) (some people just use 1/3/ or 1/4th the Kelly result).  Last step is a correlation adjustment.

 

Not thinking I found a holy grail.  I needed to better manage my cash position and 401k accounts.  Wanted a system that I believe weighs value (instead of simple rebalance).  I've been burned by the 'Couch Potatos' they tend to do very poorly in bear markets.  At least if I get burned here its my own fault.

[vinod1]

The more I think about it, the more I am convinced that the asset allocation approach to investing is fundamentally incompatible with a value-oriented approach. That isn't to say that they both can't work - they can, just that their assumptions are not only different but mutually exclusive, so that it is extremely strange to mix them, except that both are popular and so people want the best of both worlds.

 

+1

 

I spent the first 5 years of my investment life in the asset allocation, correlation, expected returns, portfolio optimization camp and the last 9 years in the value investing camp. I completely agree with innerscorecard.

 

To those of us with a math or an engineering background or mindset, we tend to take to portfolio optimization like a moth to a flame. Portfolio optimization tends to exist only in spreadsheets.

 

To optimize a portfolio you not only need to get expected returns right, but you need to get correlations right and volatility right. The portfolio is also very sensitive to small changes in returns and correlations. Even with a six asset class portfolio, you need to get 42 variables right (30 correlations, 6 expected returns and 6 volatility estimates). What is the chance you would get all of these even roughly right? If you cannot get these roughly right, you are way better off with a simple allocation approach.

 

Vinod

 

From what i know about asset allocation is that you truly only need 3 different assets (stocks->prosperity,long term bonds->deflation,gold->inflation) to get a portfolio with very low drawdowns (based on the last 45 years of history) and an equity like CAGR. This is because for example REIT`s and stocks (regardless if international/midcap/smallcap etc.) are all so closely correlated that you get no benefit from the diversification in it. And when you lever that allocation up to match equity volatility/drawdowns you get returns that are similar to value investing. I can see a benefit of using some money in such a system and the rest in value investing strategies, especially because its not very easy at the moment to find good value investments and the returns of the system should be uncorrelated to stock returns.

 

Asset allocation also tends to go through fads. After the 2000 bubble, the mantra was slice and dice because REITs and Small Value performed very well compared to large cap indices. After the 2008 crash, the fad was to go with a more broader asset classes as all sub asset classes (large, small, growth, value, REIT) have performed poorly in 2008.

 

If it is not easy to find good value investments, what does it tell about the expected returns from asset classes? I think asset class returns are going to be even worse then fairly valued "value stocks".

 

Vinod

[rpadebet]

I tend to agree with vinod.

I still do this in my professional life. In my personal portfolio I value invest.

My clients always ask for new asset allocation "technologies" and even though I am quite aware of these risk parity/risk factor stuff, having seen all the backtests over the years and followed by real live results of these "technologies", I have come to the following conclusion,

 

1. Concentrated investments in few select stocks is the best for people with an aptitude to learn about businesses and the discipline to handle the volatility.

 

2. If you struggle with allocating your bets, i suggest equal weighting is as good as any "technology" out there

 

3. If you can't do that, the best course of action is a simple broad stock index fund with the lowest expense ratios. (I do this is in my 401K because the time horizon is the longest there and stocks beat anything and everything with a long time horizon)

 

4. If you really want to go the multi asset approach, go for the standard 60/40 stock/bond allocation (I dont know with where bonds are currently why anyone would want anything but long term bonds in there though)

 

5. If you want gold, cash etc in there, the permanent portfolio approach of equal weighting asset classes gives you pretty good risk/return characteristics.

 

 

To be honest anything else is just leverage or concentration by another name.

[HWWProject]

Had missed this but apparently Buffett said in February: ""The last asset I would want to buy is a 30-year government bond"

 

He must not be in US long-term bonds at the moment:  http://dailyreckoning.com/warning-warren-buffett/

 

Original interview was early February 2015 Fox Business News: http://insider.foxnews.com/2015/02/04/what-we-learned-warren-buffetts-sit-down-fox-business-liz-claman

 

[HWWProject]

Rob Arnott on buying inflation hedges (April 2015) [ie. TIPS]:

 

https://investments.pimco.com/insights/External%20Documents/Arnott_on_All_Asset_April_2015_PCAAA035.pdf?utm_source=subscription_email&utm_medium=email&utm_campaign=website_subscription_email

 

"Inflation expectations are now 24 months into a severe bear market,

having fallen by nearly 40% from more than 2.5% in March 2013 to

a low of 1.5% in January 2015. I’ve previously said that in such an

environment, a conventional response – especially from those who

are anchored on mainstream stocks – is to question the need for

inflation hedges. The correct response is the opposite. "

 

[frommi]

Had missed this but apparently Buffett said in February: ""The last asset I would want to buy is a 30-year government bond"

 

He must not be in US long-term bonds at the moment:  http://dailyreckoning.com/warning-warren-buffett/

 

Original interview was early February 2015 Fox Business News: http://insider.foxnews.com/2015/02/04/what-we-learned-warren-buffetts-sit-down-fox-business-liz-claman

 

Warren is an optimist with a pretty bad history of making forecasts. If deflation really hits like it did in the thirties and Prem is right, than long term bonds are the only asset that will appreciate in value. And when you look at japanese, german, swiss or denmark long term yields, the us long term rates look not so bad.

 

[merkhet]

Don't most people have a pretty bad record of making forecasts?

[wachtwoord]

Don't most people have a pretty bad record of making forecasts?

 

It's the thing humans suck most at.

[Jurgis]

I'd go with reversion to mean and "cure for low prices is low prices" to predict that medium term we will revert to some inflation. So I hope that Watsa finds a good time to sell deflation positions.

 

This does not mean that we won't see deflation shorter term.

 

But, yeah, I am no expert and I'll defer to Buffett being wrong about inflation for the last 15+ years. ;)

[constructive]

Rob Arnott on buying inflation hedges (April 2015) [ie. TIPS]:

 

https://investments.pimco.com/insights/External%20Documents/Arnott_on_All_Asset_April_2015_PCAAA035.pdf?utm_source=subscription_email&utm_medium=email&utm_campaign=website_subscription_email

 

"Inflation expectations are now 24 months into a severe bear market,

having fallen by nearly 40% from more than 2.5% in March 2013 to

a low of 1.5% in January 2015. I’ve previously said that in such an

environment, a conventional response – especially from those who

are anchored on mainstream stocks – is to question the need for

inflation hedges. The correct response is the opposite. "

 

TIPS are priced based on inflation expectations but valued based on inflation reality. If you buy very short term TIPS the potential for inflation expectations to rise doesn't matter that much. The inflation actually has to show up for you to make money. If you are betting on inflation expectations to rise you need to get longer term TIPS.

[mcliu]

 

I'd be interested in hearing more about your methodology. How are you coming up with projected returns and volatility and how are you feeding those into the Kelly Criterion to determine a portfolio weight?

 

 

For bond indexes I use the Yield to maturity of the Vanguard ETF's, and subtract fees/expenses and current premium/discount.  For credit sensitive indices (corporate, high yield, EM) I also adjust for the default risk spread. (you can google a paper - Bond prices default probabilities and risk premiums.pdf).

 

For stock indices I use methods John Hussman has written about including dividend-discount, then average in published estimates from Jeremy Grantham and Rob Arnott.

 

For index standard deviations (volatility) I use historic averages, Arnott's estimates and add a premium for the current duration. (I believe longer durations lead to greater volatility). 

 

The returns are compared to the expected future inflation rate (and each other) to see if there is a positive expected future return.  Then use the Kelly Formula to weight the assets according to return/risk.  I'm a big fan of the Kelly formula it's fundamentally about betting more when the risk-adjusted odds are in your favor.  I do 'soften' the Kelly formula results with a 'diversification' factor which Kelly reportedly used in his hedge fund (to account for multiple opportunities) (some people just use 1/3/ or 1/4th the Kelly result).  Last step is a correlation adjustment.

 

Not thinking I found a holy grail.  I needed to better manage my cash position and 401k accounts.  Wanted a system that I believe weighs value (instead of simple rebalance).  I've been burned by the 'Couch Potatos' they tend to do very poorly in bear markets.  At least if I get burned here its my own fault.

 

I thought Kelly Criterion was used for bets with binary outcomes. How did you adjust it to feed in data where thr outcome is a distribution and the time period is continuous?

 

I've been looking into using Kelly for my portfolio as well but have struggled to come up with a good system. Would love to hear any details if possible.

H

[HWWProject]

 

Warren is an optimist with a pretty bad history of making forecasts. If deflation really hits like it did in the thirties and Prem is right, than long term bonds are the only asset that will appreciate in value. And when you look at japanese, german, swiss or denmark long term yields, the us long term rates look not so bad.

 

Buffett has probably made many poor forecasts over the years, but with his money I believe he's looking for consistent earnings power (stocks) or real (inflation-beating) returns for bonds.

 

My thinking around LT bonds vs TIPS is:

 

For Vanguard Long-term bond ETF, VGLT:

 

YtM 2.5% and 17.2 year Duration

subtract 0.12% fees

subtract 1.9% expected future inflation (at 17 year duration)

Leaves 0.5% real return

VGLT has about 15% price volatility.  Investing for 0.5% return on 15% volatility is hardly worth it.  There's just no margin for error.

 

For Vanguard short-term TIPS fund, VTIP:

 

SEC yield -0.87% (includes fees) and 2.4 yr Duration

Add 1.6% expected future inflation (at 2.4 yr Duration)

Gives 0.7% real return

VTIP has about 3% price volatility.

 

VTIP gives a higher real return at lower Duration and price volatility.  Better value, more margin for error.  Therefore VTIP is currently offering a better value than the long-term bond ETF.

 

 

[frommi]

VTIP gives a higher real return at lower Duration and price volatility.  Better value, more margin for error.  Therefore VTIP is currently offering a better value than the long-term bond ETF.

 

Thats only true if the next 10 years have a constant inflation rate that matches the current inflation expectation. Long term bonds in an asset allocation have only one purpose and that is to protect you against deflation. Otherwise you can just take stocks, they will nearly always have the higher expected future return.

[wachtwoord]

There will never be deflation. Not in the true definition anyway.

[HWWProject]

I thought Kelly Criterion was used for bets with binary outcomes. How did you adjust it to feed in data where thr outcome is a distribution and the time period is continuous?

 

I've been looking into using Kelly for my portfolio as well but have struggled to come up with a good system. Would love to hear any details if possible.

H

 

I use the Kelly Formula to determine individual stock allocations and address some of these issues in this article: 

 

http://healthywealthywiseproject.com/research-offers/the-kelly-formula-for-stock-investing-growth-optimized-money-management/

 

In part I adjust Kelly for the time value of money, and use an Ed Thorp adjustment he wrote about in a 1997 paper for a situation like the stock market where there are multiple opportunities at same time.  Not saying I've perfected 'Kelly for the stock market' but the results make sense to me and give more confidence with my allocations.