A PP Tweak with some Theoretical and Empirical Logic

[melveyr]

I have operated a plain Vanilla PP for almost three years. I like the simplicity and it does feel safer not tinker with Harry Browne's secret sauce. However, I think I have found a change that helps rectify an internal contradiction with the standard recipe.

The PP is actually a leveraged strategy. Yes we all like to bad mouth explicit leverage like literally using margin for speculating, but the PP has leverage embedded within its bond allocation. If you own a bond with a duration of 20 years, you effectively own a leveraged instrument.

Let's say I want to pursue a risk parity strategy and my equities have a 20% standard deviation and my bonds, with a duration of 10 years, have a 10% standard deviation. In order to hold the positions at risk parity, I would have to have 66% bonds and 33% equities. I need to hold twice as many bonds as stocks to get the risks to balance each other out. But let's say I want a higher expected return (presuming stocks have a higher expected return than bonds).

I could...

A) Construct a portfolio of 50% equities + 100% bonds -50% cash (margin is very similar to negative cash position because you borrow at short term rates).

Or I could

B) A) Construct a portfolio of 50% equities + 50% Bonds, this time using bonds with twice the duration. What have I done with B? I have used implicit leverage in the bond market, rather than explicit leverage through margin.

What's strange about the Permanent Portfolio's standard recipe though is that you get leverage with the 30 year, and then dilute that leverage with cash. This is a problem with the standard recipe because the rate at which you pay for leverage with the 30 year is greater than the rate at which you can earn with T-Bills.

Below I created a blend of TLT and SHY that approximated the volatility of TLH, an intermediate term treasury fund. The green line is the blend of TLT and SHY and the blue line is TLH.


Comparing the CAGRs you can see that you are paying for the leverage that you are not using. If you understand Sharpe ratios, just a quick glance will tell you that as well.

This has been true over time as well. If you look at Simba's spreadsheet, Sharpe ratios decline as you go farther out on the yield curve. The sharpe ratio would only decline materially if you were paying a premium over the risk free rate for leverage.

****

I see three actionable points.

1) Holding T-Bills and 30 year Treasuries does not make sense from an expected returns perspective. If your goal is to simply have a higher expected return without changing the underlying risk factors, 50% in an intermediate fund makes more sense.

2) The barbell still may be worth pursuing if your PP overflows your tax deferred space. You can isolate the long end of the curve in your tax deferred accounts and keep money in the bank as your "cash" allocation. Finally, you can exploit subsidized rates with EE bonds (thinking of them as cash with free call option rates remaining low if you decide to wait for it to double) or use I-Bonds to help mitigate some of the leverage expense.

3) You could embrace the leverage you are already paying for and forego the cash allocation.

Bottom line, holding 30 year bonds and T-Bills in a single tax deferred account does not make economic sense. The barbell can be justified for other tax/liquidity reasons, but you are paying for it.

[craigr]

Bottom line, holding 30 year bonds and T-Bills in a single tax deferred account does not make economic sense. The barbell can be justified for other tax/liquidity reasons, but you are paying for it.

You always pay for safety. As your portfolio grows having a large cash cushion becomes indispensable for dealing with life emergencies, etc. I think the portfolio could be simplified into this as you point out:

25% Stocks
25% Gold
50% Intermediate Term Treasuries

Eliminates another asset to track. But the cash is really nice to have around when markets are volatile, you are facing a layoff, need to pay for emergency expenses, etc.

But you know I wouldn't have a huge quibble if someone wanted to simplify things this way and they had sufficient cash to ride out a protracted bad market or job loss (at least a year's living expenses).

Re: Sharpe Ratio/Volatility

Sharpe Ratio and Volatility matching are inherently backwards looking. Volatility itself is highly time dependent and this of course impacts the Sharpe Ratio.

For instance, let's look at the standard deviation of the total stock market the past few years:

2009-2011 12.8%

Not so bad. But let's put in just one more year:

2008-2011 27.6%

So you have with just one volatile down year a more than doubling of standard deviation. Let's look at it from before:

2004-2007 9.2%
2005-2008 23.4%

So things looked pretty calm from 2004-2007. Then we just shift it up a year and it blows up. Volatility is 2.5X. I'm not sure how volatility matching can account for these kinds of swings reliably. The 25% cut seems to work well enough. Ok to match against each others volatility, but not enough that there is a major explosion if a black swan comes along.

[melveyr]

Bottom line, holding 30 year bonds and T-Bills in a single tax deferred account does not make economic sense. The barbell can be justified for other tax/liquidity reasons, but you are paying for it.

You always pay for safety. As your portfolio grows having a large cash cushion becomes indispensable for dealing with life emergencies, etc. I think the portfolio could be simplified into this as you point out:

It's not the safety you are paying for, its the leverage of the 30 year bond. You are paying for that elevated risk level at a higher interest than you earn on the short end of the curve.

The Sharpe ratios were not meant to be a signal of future returns, but simply a measurement of how much that leverage has cost an investor. The only reason the sharpe ratios would decline materially as you go out on the yield curve is if you are paying for a leverage above the risk free rate.

[MediumTex]

melveyr,

What about periods during which the yield curve is inverted?

In those cases t-bills are paying more than long term bonds, and you are also enjoying the safety of zero volatility of your cash during such periods.

I'm not afraid to say that during periods of uncertainty that create an inverted yield curve I would like the security blanket of knowing that 25% of my portfolio is protected from market volatility.

[melveyr]

melveyr,

What about periods during which the yield curve is inverted?

In those cases t-bills are paying more than long term bonds, and you are also enjoying the safety of zero volatility of your cash during such periods.

I'm not afraid to say that during periods of uncertainty that create an inverted yield curve I would like the security blanket of knowing that 25% of my portfolio is protected from market volatility.

What it really comes down to is whether or not you think the price you pay for the leverage of a 30 year bond is above or below the risk free rate. I doubt that is below it most of the time. This would be the bond market giving investors free leverage!

I gotta run for now, but I can attempt to run different scenarios later... I just thought of this stuff last night so I might be missing something! 

[Lone Wolf]

I always enjoy insightful PP surgery like this.

I do want to touch on the simplification angle.  What might appear to be a simplification (going to 3 types of securities rather than 4) often isn't in practice.  Most of us will keep some substantial portion of our money in cash-like instruments in order to make sure we have plenty of liquidity for whatever life throws our way.  With a single 50% intermediate hunk, your cash allocation is no longer really part of your PP.  That's not a disaster, just a downside.  One feature of the PP that I like is that it is comprehensive -- you could stick just about all of your financial wealth into it in a very practical way.  That's missing with the "all intermediate bonds" construction.

The PP is actually a leveraged strategy. Yes we all like to bad mouth explicit leverage like literally using margin for speculating, but the PP has leverage embedded within its bond allocation. If you own a bond with a duration of 20 years, you effectively own a leveraged instrument.
...
B) A) Construct a portfolio of 50% equities + 50% Bonds, this time using bonds with twice the duration. What have I done with B? I have used implicit leverage in the bond market, rather than explicit leverage through margin.

How literally do you mean "leverage" here?  Do you mean that 30-year bonds are like a leveraged instrument in that they demonstrate the greater volatility that a leveraged instrument would give you?  Or do you mean something more fundamental?

[craigr]

The only reason the sharpe ratios would decline materially as you go out on the yield curve is if you are paying for a leverage above the risk free rate.

The Sharpe Ratio of course is the difference between the risk-free rate and the asset class return divided by the volatility.

So it is made of some really big assumptions:

1) Risk free rate is a valid figure going forward and not much higher/lower depending on what is going on in the economy. Risk free rate (defined as t-bills) today is 0%. In the early 1980s it was over 10%. That's a big window!

2) The asset class return from the past, which may not continue going forward. A decade back people expected stocks to turn in easily over 10% per annum. Today some authorities have lowered that significantly.

3) The volatility of the asset, which may not be the same going forward as it was in the past. Also very time dependent.

So the Sharpe Ratio is a really squishy thing. It can kind of get you a feel for the assets, but only in hindsight. If you even use the years I posted above you'll see the Sharpe ratio for 100% stocks goes from over 1.1 to negative very quickly just with one really bad year that blows past expectations. This is the main point of Mandebrot/Taleb is that these statistical tools don't work well in a chaotic investing markets. They are very susceptible to outlier events.

Sharpe Ratio can be used as part of an arsenal to assess risk, but not something I'd put a terribly large amount of faith in for predicting future returns of any particular asset class or asset class mix.

[MediumTex]

What it really comes down to is whether or not you think the price you pay for the leverage of a 30 year bond is above or below the risk free rate. I doubt that is below it most of the time. This would be the bond market giving investors free leverage!

Well, inversion of the yield curve happens periodically.  It's not that unusual, and is a classic recession signal.  Here is what it looked like in 2000:



An inverted yield curve is one of the many things that the PP protects you from.

[Dets]

You can make a case for either approach, but i think for the majority of investors they're better off sticking with the combo of 25% cash and 25% LTT's.  When you combine the two it gives you roughly an equal volatility to what you're getting from each of stocks and gold, so it gives you something very close to "risk parity", while providing the advantages and flexibility of cash.

[melveyr]

Hm.... I don't think the word leverage is appropriate in this case.  TLH has outperformed the barbell in the last while because....

ETF Maturity Coupon YTM Eff Dur DV01
TLT 27.86 4.00% 2.62% 17.29 0.2302 0.1151
SHY 1.88 2.04% 0.26% 1.84 0.0192 0.0096
TLH 14.29 6.23% 1.95% 10.2 0.1614 0.1614

Weighted yield sensitivity for 50%TLT+50%SHY is roughly 0.1247  Compare that with the 100%TLH which is 0.1614.  That accounts for the difference IMO. 

MediumTex's point about the inverted yield curve is also very important.

The blend in the graph was not an even split. It was a blend of TLT and SHY such that its volatility was equal to TLH.

Furthermore any discrepancies about unprecise duration weightings are irrelevant because the discrepancy in Sharpe ratios indicates that there is no blend of TLT and T-Bills that would have had the same risk adjusted return.

Craigr,

I am not talking about absolute predicitions about Sharpe ratios, but rather relative Sharpe ratios of long and intermediate term bonds. Ther is a strong theoretical argument for why intermediate duration bonds will have a higher Sharpe ratio than long bonds because very few individuals can borrow at the risk free rate. Investors bid up leverage, you can see it in the long run poor risk adjusted returns for high beta stocks relative to low beta stocks.

[MediumTex]

What about protection against an inverted yield curve?

That needs to be addressed for anyone wanting to sneak a peek and maybe tweak their PP in order to avoid a leak in returns in the teak of their portfolio, regardless of whether an asset is at a peak or a trough.  If you don't do this, you might find that the tweak of the week will make your PP returns weak and your desire for them to speak in something more than a squeak will be overwhelmed by the fact that the peek you sneaked resulted in a tweak that made your portfolio reek, and you could find yourself up the creek, your outlook bleak, your spirit meek, as you cry out "Eek!--I should have thought more about the effects of an inverted yield curve."

[D1984]

What about protection against an inverted yield curve?

That needs to be addressed for anyone wanting to sneak a peek and maybe tweak their PP in order to avoid a leak in returns in the teak of their portfolio, regardless of whether an asset is at a peak or a trough.  If you don't do this, you might find that the tweak of the week will make your PP returns weak and your desire for them to speak in something more than a squeak will be overwhelmed by the fact that the peek you sneaked resulted in a tweak that made your portfolio reek, and you could find yourself up the creek, your outlook bleak, your spirit meek, as you cry out "Eek!--I should have thought more about the effects of an inverted yield curve."

How long do inverted yield curve situations typically last? Aren't they usually short periods? If an inverted yield curve lasted several years and also hurt your stocks, bonds, and gold simultaneously, then maybe additional protection against them would be warranted. As it stands, I thought the main reason to keep cash in the PP was for tight-money recessions (although I guess that could lead to an inverted yeild curve...it did in 1981). IIRC, the aggregate US bond index returned about 6.2% in 1981 (high rates offset capital losses); an equal mixture of just LTTs and cash (1-3 year Treasuries for the cash) returned just over 10%.

Melveyr,

How about running a PP backtest for the years from 1968 to 2011 (just do annual results for each year) using 50% of the US aggregate bond index (or an intermediate Treasury index) in lieu of 25% cash and 25% LTTs? How does it affect CAGR and Sharpe Ratio? Is 1981 that much worse? How about 1969, 1973, 1974, 1990, or 1994? Do you lose too much deflation protection in years like 2008?

[MediumTex]

How long do inverted yield curve situations typically last? Aren't they usually short periods? If an inverted yield curve lasted several years and also hurt your stocks, bonds, and gold simultaneously, then maybe additional protection against them would be warranted. As it stands, I thought the main reason to keep cash in the PP was for tight-money recessions (although I guess that could lead to an inverted yeild curve...it did in 1981). IIRC, the aggregate US bond index returned about 6.2% in 1981 (high rates offset capital losses); an equal mixture of just LTTs and cash (1-3 year Treasuries for the cash) returned just over 10%.

Even if the inverted yield curve situation doesn't last that long, the losses it could generate in your portfolio could take a long time to recover from (as would have happened to the PP in 1981 without its t-bill holdings).

[sophie]

What about protection against an inverted yield curve?

That needs to be addressed for anyone wanting to sneak a peek and maybe tweak their PP in order to avoid a leak in returns in the teak of their portfolio, regardless of whether an asset is at a peak or a trough.  If you don't do this, you might find that the tweak of the week will make your PP returns weak and your desire for them to speak in something more than a squeak will be overwhelmed by the fact that the peek you sneaked resulted in a tweak that made your portfolio reek, and you could find yourself up the creek, your outlook bleak, your spirit meek, as you cry out "Eek!--I should have thought more about the effects of an inverted yield curve."

Ha!!!!!!  Whatever you're taking, MT, I want some!

I'm a bit skeptical that the observed difference in returns will hold up over different economic conditions also.  What was the exact split that was used?  And does it have to be adjusted as volatility changes?

A backtest to 1972 of the HB barbell strategy vs intermediate treasuries would be interesting, particularly for those who are stuck with retirement plans that only offer intermediate term treasury funds.  It would be nontrivial because you'd have to take rebalancing of the long bonds/Tbills into account.

[Peak2Trough]

melveyr, great thread, and insightful analysis.  I love the way your analyze this stuff, and you'll win the Browne-e award for best graphs, hands down.   

The PP is actually a leveraged strategy. Yes we all like to bad mouth explicit leverage like literally using margin for speculating, but the PP has leverage embedded within its bond allocation. If you own a bond with a duration of 20 years, you effectively own a leveraged instrument.

Try as I might, I just simply do not understand the italicized (emphasis mine) sentence above.  Can someone explain that to me using monosyllabic words and a crayon?

1) Holding T-Bills and 30 year Treasuries does not make sense from an expected returns perspective. If your goal is to simply have a higher expected return without changing the underlying risk factors, 50% in an intermediate fund makes more sense.

So I did a bit of backtesting on that thesis, and here's what I came up with...

For all Portfolios:

Start date:  01-01-1972
End date:  11-20-1972
Starting capital:  10,000
Rebalance:  35/15 bands
Reinvest Dividends and Interest:  Yes

Notes:  20 year treasuries were not offered between 1987-1994 - backtesting includes swapping 20 years for 10 years during that period.  Also, bond prices are estimated using present value calculations as I'm not aware of any historical pricing data for them outside of coupon rates.

Portfolio 1:

Cash:  1 Year Treasury
Bond:  30 Year Treasury



Portfolio 2:

(attempting intermediate 15yr average duration)

Cash:  10 Year Treasury
Bond:  20 Year Treasury



Portfolio 3:

(attempting intermediate 10 year duration, just because we have better data for those)

Cash:  10 Year Treasury
Bond:  10 Year Treasury



So based on this test, we get a higher return and lower max drawdown for the past 41 years using 1 year treasuries for cash and 30 years (or longest available) for the bond portion.  Note that I'm not claiming these results are 100% accurate, however. 

[melveyr]

melveyr, great thread, and insightful analysis.  I love the way your analyze this stuff, and you'll win the Browne-e award for best graphs, hands down.   

The PP is actually a leveraged strategy. Yes we all like to bad mouth explicit leverage like literally using margin for speculating, but the PP has leverage embedded within its bond allocation. If you own a bond with a duration of 20 years, you effectively own a leveraged instrument.

Try as I might, I just simply do not understand the italicized (emphasis mine) sentence above.  Can someone explain that to me using monosyllabic words and a crayon?

Here is the thought experiment.

Portfolio A:
100% Bond with duration of 10
Portfolio A's weighted duration = 10

Portfolio B:
200% Bond with duration of 10
(assets over 100% financed by margin)
Portfolio B's weighted duration = 20

Portfolio C:
100% Bond with duration of 20
Portfolio B's weighted duration = 20

***

Notice how portfolio B, and C are two different ways of getting higher duration. One through explicit use of leverage (margin), and one by buying a high duration bond. I am proposing that holders of high duration bonds are paying for this implicit leverage at a rate that is higher than the risk-free rate. So holding high duration bonds in conjunction with cash does not make sense.

I am having a hard time finding good intermediate term fund data going back and it would be very difficult to find out the exact durations so going back further than the ETFs allow is proving to be more difficult than I thought. However, I think merely looking at the Sharpe ratios illustrates my point decently because the Sharpe ratio is very useful when talking about leverage at the risk free rate. The lower Sharpe ratios for high duration funds appears to indicate that you pay for the increased duration (leverage) at a rate higher than the risk free rate.

We can see this cost of implicit leverage when looking at high beta stocks as well. Check the paper related to high beta:
http://www.advisorperspectives.com/comm ... 111811.php

It explains how leverage embedded in a financial product as opposed to explicitly through the use of margin comes at a higher cost to the investor. Ultimately if my thinking is correct, high duration bond holders are paying up for implicit leverage (the luxury of never losing more than 100% of your portfolio). Paying up for leverage that you are not actually going to use (because you put the difference in cash) wouldn't make sense.

[melveyr]

Melveyr, this might be interesting to you.  I think the inflation risk premiums are what you're currently seeing as sharpe differences and calling leverage.  These work their way into yield and thus the calculations above. 

www.bis.org/publ/qtrpdf/r_qt0809e.pdf

I do think you're on to something interesting though, as premiums do seem to rise around crisis, which also happen to be when we'd want the full power of the bonds, not a diluted version.  It's not as simple as there being an implicit leverage borrowing cost.


On a side note: there is a documented leverage play to take advantage of the higher sharpe at shorter terms.  I don't think anyone has done it because you needed something like leverage ratios of 7 and you're just taking on the inflation risk.

Slotine,

Thanks for the paper. I am sure there are tons of complicating factors to my simple analysis 

[melveyr]

Some supporting evidence:
http://www.cbsnews.com/8301-505123_162- ... r-returns/

"Just like investors are compensated for holding 10-year bonds over T-bills, they are also compensated for holding one-year bonds. Our finding is that the compensation per unit of risk is in fact larger for the one-year bond than for the 10-year bond. Hence, a portfolio that has a leveraged long position in one-year (and other short-term) bonds and a short position in long-term bonds produces positive returns. This result is consistent with our model in which some investors are leverage constrained in their bond exposure and, therefore, require lower risk-adjusted returns for long-term bonds that give more "bang for the buck."

I feel pretty strongly about this because it just makes too much sense to me. I am not going to pay for leverage that I am not going to use. I will probably shift to an intermediate term fund with the same duration as the barbell.

[Peak2Trough]

I feel pretty strongly about this because it just makes too much sense to me. I am not going to pay for leverage that I am not going to use. I will probably shift to an intermediate term fund with the same duration as the barbell.

Thanks for the links and explanation, melveyr.  I haven't had an opportunity to read it all yet, but I do intend to do so as soon as I can get rid of all this family

Whether the thesis is sound on paper or not, I will not debate.  It is obvious to me that you have studied this to a much greater extent than I have (or probably ever will).

The only issue I have at this point is that 41 years of actual data do not support the thesis.  If you'll look at my portfolio 1, 2, and 3 above, you'll note that we not only get higher returns, but also higher risk-adjusted returns with the 1/30 bonds as per Harry Browne than we do with 10/20 or 10/10 over the same period.

Those returns were calculated by importing 50 years of FRB H.15 yield data across available durations, over 100 years of S&P500 daily closing prices and (monthly) dividend rates, and closing gold spot back to 1968.  The returns and drawdowns are then calculated by running through each daily close over the entire period, substituting the present value of the bonds for its price (again because historical market bond prices seem to be unavailable), reinvesting dividends and interest, and rebalancing at 35/15 bands.  In short, as close to the Harry Browne recommendations as I could manage.

Regarding the bond pricing, one could argue there are periods were the present value of treasuries will skew from the market value, but I suspect over time they are equivalent.  The only other assumption is that all bonds are repurchased at the start of each calendar year in order to keep the duration as close to the original as possible.  Obviously, in a real portfolio, the transaction costs will likely override that benefit.

I have no dog in the hunt, so to speak, so I'm just as happy to be proven wrong as right on this, but my current research says that the Harry Browne allocation outperforms the 50% intermediate allocation.

Happy Thanksgiving everyone!

Best,
P2T

[MediumTex]

Peak2Trough,

Can you resize (or remove) the images in your post above so that they don't make the screen appear too wide on the whole page?  They don't look that wide, but apparently they are.

Thanks.

(Great discussion.)

[Peak2Trough]

Thanks MT.

The pics in my post are only 455 pixels wide.  I think the culprit is actually the gmo.com link above... when long URLs are posted, the forum software doesn't know where to split them because there are no spaces.  Let me know if you find that's not the case.

Best,
P2T

[MediumTex]

Thanks MT.

The pics in my post are only 455 pixels wide.  I think the culprit is actually the gmo.com link above... when long URLs are posted, the forum software doesn't know where to split them because there are no spaces.  Let me know if you find that's not the case.

Best,
P2T

Of course.  I don't know how I missed that.

I fixed the link and it looks like it fixed the width issue.

[melveyr]

Thanks MT.

The pics in my post are only 455 pixels wide.  I think the culprit is actually the gmo.com link above... when long URLs are posted, the forum software doesn't know where to split them because there are no spaces.  Let me know if you find that's not the case.

Best,
P2T

I changed the link. Sorry about that!

Peak2Trough,

I think the real complicating factor with your analysis is that we need the duration to be the same.

So we would have to make sure that the duration of the 30/1 portfolio is the same as the intermediate portfolio. As interest rates change, the duration of the intermediate/long bonds does change which makes this trickier. Reflecting this would probably take a ton of work!

I guess the theoretical argument and the recent (although limited) empirical evidence that I found, plus the research I have found on the topic is enough to sway me. This is by no means a big deviation from the PP. I simply see this as eliminating a hidden expense while maintaining a nearly identical exposure 

It kind of feels like opening the pandoras box of tweaking, but I am okay with that. The PP is not a religion to me, but an inspiration. I think it is pretty important for us to remember that Harry Browne has revised the "Permanent Portfolio" a couple of times.

[buddtholomew]

It appears as if there is some support for a 4x25 PP with 25% ea. held in Equity and Gold with the balance in IT treasuries. I personally would consider this option as long as the shorter duration bonds can buoy the overall portfolio during periods of economic deflation. Is this composition sound enough for me to consider seriously?

[melveyr]

It appears as if there is some support for a 4x25 PP with 25% ea. held in Equity and Gold with the balance in IT treasuries. I personally would consider this option as long as the shorter duration bonds can buoy the overall portfolio during periods of economic deflation. Is this composition sound enough for me to consider seriously?

If you go for the ITT you are entering a world even lonelier than the PP. It will probably function almost exactly like the PP, but you will be doing something that not many other people are. Something to think about.

For recent backtesting, I am looking at 25% VTI, 25% GLD, and 50% TLH.

Another thing to think about is that I am not a financial advisor and all of my posts are meant to be read purely for entertainment value