A PP Tweak with some Theoretical and Empirical Logic

[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!

Trying to clarify here... we need to make the duration the same as what?  The same as when the bonds were purchased?  If so, I've done that already by repurchasing 100% of all bonds at the market rate on Jan 1 of each year.

For the 1 year bonds, I simply assume you receive back your principal and repurchase the bonds at par at the prevailing rate.  For all higher duration bonds, I calculate the present value of the bonds purchased 12 months prior, and then buy as many new 10/20/30 year treasuries at the new market rate as possible.  Basically, I'm emulating the sale of the last set of long bonds you purchased at current market prices, and using the proceeds from that sale to buy all new equal duration bonds (at par and market yields) to remove duration issues from the analysis. 

Two other notes:  I do allow fractional shares of bonds (which obviously can't be done outside of ETFs or funds) and, again, this isn't terribly practical in the real world due to transaction costs.  Nevertheless, unless I'm missing something, it does mean we are comparing apples to apples in this case. 

I checked iShares website, and two things stick out at me:

1)  The effective duration of TLH is 10.19 years. 

The duration on my 10 year-treasury-only backtest above would be (more or less) 9.5 years, given the yearly repurchase explained above.  So there is a slight difference in duration between the two, but it's probably close enough for the sake of comparison.

2)  The date of inception of TLH is in 2007. 

Unfortunately, that doesn't give us much room for backtesting actual data using that particular ETF.  Is it not possible the sharpe ratios are skewed by a single downward interest rate trend since its inception?  What else can we envision would explain how you get higher sharpe ratios and I get lower ones based on the same basic idea?

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.

I for one have no problem with that, and I view this thread and others like it simply as an opportunity to learn more about the strategy and investing in general.  I'm a whole lot less concerned with being right than I am learning something and potentially applying what I've learned to my investing. 

I've read your blog and many of your posts and find them all very insightful, so I don't like the idea that you might perceive any of my comments as simply argumentative.  I'm just trying to flesh out whether the historical performance matches our expectations on what I think is a pretty interesting idea....

Also, if anyone has any specific periods they would like to see tested, let me know.  I can put in arbitrary start and ends dates and we can compare the strategies based on different historical economic condition as well.

Thanks,
P2T

[Peak2Trough]

2)  The date of inception of TLH is 2007. 

Unfortunately, that doesn't give us much room for backtesting actual data using that particular ETF.  Is it not possible the sharpe ratios are skewed by a single downward interest rate trend since its inception?  What else can we envision would explain how you get higher sharpe ratios and I get lower ones based on the same basic idea?

Replying to myself here now...   

I was thinking about what I wrote above and decided to test it.  If the results are being skewed by the short history of TLH as I suggested, then the 10/10 year bond portfolio should show a higher CAGR for the period of 2007-present than the 1/30 portfolio.  Sure enough, it does.  Results below.

Start:  01-01-2007
End:  11-20-2012
Reinvest Div/Int:  Yes
Rebalance: 35/15

Portfolio 1: 

Cash:  10 year treasury
Bond:  10 year treasury



Portfolio 2:

Cash:  1 year treasury
Bond:  30 year treasury



This suggests to me that one or the other approach is not better for all economic environments.  For the last 5 years (interest rates sharply down) the 10/10 portfolio has outperformed the 1/30 portfolio.  That makes perfect sense to me.  However the 1/30 portfolio has outperformed the 10/10 over a longer period (1972-2012) containing both rising and falling rates, inverted yield curves, and many other macro economic curveballs.

[melveyr]

BTW, have you two considered that convexity of the barbell is much higher than TLH?

Slotine,

I was thinking about doing my weightings for the portfolio based off of volatility. So, difference in the second derivative of price wouldn't really matter because I would be taking that into account by simply looking at price volatility.

So for example:
TLH volatility: 10.2%
GLD volatility: 18%
VTI volatility: 19%

Would lead to the following allocation being the "balanced" allocation:
TLH weighting: 48%
GLD weighting: 27%
VTI weighting: 26%

I'm sure the convexity effect will have small differences, but I think by balancing volatility I am capturing the essence of the PP. On a somewhat separate note, remember how we discovered that gold dominated the PP in the gold bubble? My analysis shows that the PP actually had a drawdown of 30% when the gold bubble popped. I think this could have been mitigated by changing what you consider to be the "balanced" portfolio by taking into account volatilies. Gold was far more volatile than the other components before the bubble popped, so by holding an equal amount of it you were actually not at "balance."

[Peak2Trough]

BTW, have you two considered that convexity of the barbell is much higher than TLH?

I have not, primarily for two reasons:

1)  I don't even know what "convexity" means in this context - I certainly don't consider myself a student of bonds.

2)  My analysis is only concerned with the data.  Eg, what the portfolio has done, not what it theoretically should have done.

[Peak2Trough]

My analysis shows that the PP actually had a drawdown of 30% when the gold bubble popped.

Interesting.  Can you give some more specifics on this? 

- What was the period of the drawdown? 
- What rebalancing was assumed? 
- Were dividends and interest reinvested? 
- What was the granularity of the price data (daily, monthly, yearly) ?


I ask because the highest drawdown I see using 35/15 bands from 1972 - 2012 is 17.66% starting at a peak of 01/20/1980 and ending on 03/27/1980.

If we change the parameters to annual rebalancing for the same period, the max drawdown 20.23%, also from 01/20/1980 to 03/27/1980.

The back of the napkin math on a standard deviation of 6-7-ish percent support that.  To get a 30% drawdown we'd need to have a standard deviation in the 9 percent range, would we not? 

[melveyr]

My analysis shows that the PP actually had a drawdown of 30% when the gold bubble popped.

Interesting.  Can you give some more specifics on this? 

- What was the period of the drawdown? 
- What rebalancing was assumed? 
- Were dividends and interest reinvested? 
- What was the granularity of the price data (daily, monthly, yearly) ?


I ask because the highest drawdown I see using 35/15 bands from 1972 - 2012 is 17.66% starting at a peak of 01/20/1980 and ending on 03/27/1980.

If we change the parameters to annual rebalancing for the same period, the max drawdown 20.23%, also from 01/20/1980 to 03/27/1980.

The back of the napkin math on a standard deviation of 6-7-ish percent support that.  To get a 30% drawdown we'd need to have a standard deviation in the 9 percent range, would we not?

Annual rebalancing, dividends and interest were reinvested, daily price data, and I included an inflation adjustment (i broke out the monthly data and distributed it on a daily basis). I wonder if the leftover discrepancy between our data is mostly differences in our synthetic bond data that we created?

[melveyr]

Here is my drawdown data:

[melveyr]

Because there's almost no reasonable spread of data going back beyond 2007, I tried using zero coupon curves to validate this (back to 1995, from the ECB).  I'm still using a barbell, but with a 10yr zero it pretty much gobbles up most of the 50% allocation anyways.  It adjusts the zero allocation to match a traditional 25/25 split duration.

I get the overperformance Peak2Trough verified since 2007 too, but I also notice underperformance between 1997-2001.  It closed the gap at 2003 and tracked the traditional split 25/25 barbell up until 2007.  For the entire period 1995-2012, I get 8.64% vs 8.36% in favor of the intermediate.  It's also a tad smoother, at 1.26 vs 1.17 Sharpe.

I tested against Canada's PP as well since they have a better selection of zero curves going back all the way to 1985.  The same thing appears there, although the 2007 is far less pronounced and there's no difference between either.

Barring any stupid errors on my part trying to calculate total returns on a constant maturity zero yield, I don't think the market has mispriced things or embedded any sort of implied leverage into these bonds.  Sure, there's some minor deviations which can be attributed to interest rate risk shocks/convexity/etc - but nothing sustained or long term.

Thanks for crunching the numbers Slotine! Retroactively making the bond data can be a serious pain in the butt 

Also, thank you to Peak2Trough for exploring this with me as well. The PP is a tough beast to improve upon, but I am going to keep trying