My Unexpected Findings on Backtesting Vanguard ETFs

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FundyInvestor
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My Unexpected Findings on Backtesting Vanguard ETFs

Post by FundyInvestor »

Hi guys, I just started looking into investing last month. I've read "Millionaire Teacher", "The Quest for Alpha", and is moving on to "The New Coffee House Investor" this week. The case for index investing is convincing, and as an international investor, the mutual funds available locally are charging exorbitant expenses. Thus I'm looking towards Vanguard ETFs as an option. I am aware of the 30% dividend withholding tax and the estate tax. I am currently doing my own simulation/backtesting to see if the claims for index investing can be supported by data.

I was not able to find any free stock simulation/backtesting programs that give me the level of detail I want, so I created my own with excel and data from Yahoo Finance. You can find it here (4.7MB). It's large due to the amounts of data and formulas, and my clumsiness with excel. I'm sure the excel pros here will cringe and groan when they see it, so please pardon my fugly work.

The simulated portfolio contains the following ETFS:
VTI
VGK
VPL
VB
VO

The excel simulates two buying approaches over a period of ~9 years (the longest over which data for all the ETFs are available):

1. The balanced approach
On each buy date, amount of each share to buy is obtained by calculating backwards - given the prices of all shares on the buy date, the target share holdings are calculated based on the allocation percentage, the amount of investable cash, and the total value of the current holdings. The amount to buy is the difference between the target holdings and the current holdings. If calculations indicates that shares are to be sold, then we will not sell it. Selling is only allowed on the rebalancing date and is done to reduce turnover.

2. The lazy approach
On each buy date, the entire investable cash balance is split according to the allocation percentage. Each portion is then used to buy the corresponding shares. Rebalancing is done periodically.

The result shows that the two approaches produce almost identical yield (difference between annualized yield <0.001%). Furthermore, removing rebalancing for the lazy approach consistently produced higher yield, though the different is not significant (~0.001%). Since the balanced approach tries to actively balance the portfolio, I was expecting it to produce better yield.

I don't know whether if this is due to my excel algorithm, the short length of my backtesting period, or the special combination of my selected ETFs. Would appreciate if anyone can weigh in on this.

P.S.
I'll write a documentation on the formulas if anyone is interested, and when I have the time.
Refer to the "To buy" column for number of shares bought on a particular day. The "To buy R." column is used to facilitate calculation only.
The buying algorithm is able to handle breaks in trading periods, so if the buy date is on a weekend or holiday, it'll buy once trading resumes.
Given the brokerage and the amount of trading I'm expected to do, I'm setting the monthly brokerage fee to be $10.
Leeraar
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Re: My Unexpected Findings on Backtesting Vanguard ETFs

Post by Leeraar »

You might search this site for Simba's backtesting spreadsheet.

L.
You can get what you want, or you can just get old. (Billy Joel, "Vienna")
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Re: My Unexpected Findings on Backtesting Vanguard ETFs

Post by Peculiar_Investor »

I'll save the OP some searching. Check out the wiki page, Simba's backtesting spreadsheet - Bogleheads
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k66
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Re: My Unexpected Findings on Backtesting Vanguard ETFs

Post by k66 »

Hi FundyInvestor,

I'm guessing by your name that you might also be interested in Vanguard Canada's small selection of ETFs (but really you wouldn't need anymore that what they do provide):

https://www.vanguardcanada.ca/individual/etfs/etfs.htm

and all can be DRIP'ed if that is of use to you as well.

Regarding the "Rebalancing Bonus" (i.e. the notion that rebalancing provides an improved result either as better performance or less volatility), see also Bernstein's excellent piece here:

http://www.efficientfrontier.com/ef/996/rebal.htm

If your two investment streams are yielding exactly the same result (or only trivially different as you note), then I might suspect that it is a programming error.
LOSER of the Boglehead Contest 2015 | lang may yer lum reek
Topic Author
FundyInvestor
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Re: My Unexpected Findings on Backtesting Vanguard ETFs

Post by FundyInvestor »

Thanks for pointing me to Simba's backtesting spreadsheet. Unfortunately, it does not allow me to specify the investment frequency, rebalancing frequency, account for investment of lump sums, and most importantly, it backtests funds, not ETFs.

@k66:
Erm...any reason why Canadian ETFs? I'm not Canadian.
It could be a programming error, but I've checked through the formulas and results a few time and couldn't find any discrepancies. Furthermore, if you look at the "To buy" column for an ETF and compare the values across the 2 buying approaches, you will see that while they are similar near the beginning, as expected, they are completely dissimilar afterwards. It's highly unlikely that an error can serendipitously produce almost identical yield with two different buying profiles.
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FundyInvestor
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Re: My Unexpected Findings on Backtesting Vanguard ETFs

Post by FundyInvestor »

@k66:
You're right about the programming error - I checked through the sheet again and found that a formula for VO is indeed erroneous. Also I forgot to multiply by 100 when stating the difference in yields. However, after correction, lazy approach with no rebalancing still produce a higher yield of ~0.1%. However, the article you linked has been most insightful, and holds the key to explaining this supposed discrepancy.

Simply put, and I'm making a gross oversimplification, Berntein pointed out that the amount of rebalancing bonus is inversely proportional to the correlation among a portfolio's component stocks. Using buyupside.com's correlation calculator, I calculated the correlation for all the simulated portfolio's stocks, and the results are telling. With the max correlation being 1, the lowest correlation is 0.6907 - between VGK & VB. The highest correlation is a whopping 0.9945, between VB & VO. To test out Berntein's postulate, I picked a new ETF that has negative correlation with one my current ETFs - BND.

Testing a portfolio with 50/50 BND & VGK, , correlation -0.0112, starting on Apr 10, 2007 (earliest date on which data for both ETFs are available) and ending on Mar 31, 2014, here are the annualized yields:
Balanced approach: 4.51%
Lazy approach, with rebalancing: 4.56%
Lazy approach, no rebalancing: 4.07%

Testing a portfolio with 50/50 VPL & VGK, , correlation 0.9494, starting on Apr 10, 2007 and ending on Mar 31, 2014, here are the annualized yields:
Balanced approach: 6.35%
Lazy approach, with rebalancing: 6.33%
Lazy approach, no rebalancing: 6.23%

Observe that with just two stocks, the lazy approach with no rebalancing underperforms the balanced approach, while it's the opposite for my initial blend of 10%VTI, 30%VGK, 20%VPL, 20%VB, 20%VO. It appears that adding more stocks to the portfolio has a negative impact on the balanced approached. That aside, the results clearly shows that correlation does have an impact on the rebalancing bonus. Of course, this is just 1 sample and I'm still not too confident on whether this is an exception or the rule. Will do more testing.
Leeraar
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Re: My Unexpected Findings on Backtesting Vanguard ETFs

Post by Leeraar »

It's a fairly simple thought experiment.

Prices are composed of a trend plus some noise.

Rebalancing on the trend produces a penalty. Rebalancing on the uncorrelated noise produces a bonus.

L.
You can get what you want, or you can just get old. (Billy Joel, "Vienna")
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Re: My Unexpected Findings on Backtesting Vanguard ETFs

Post by gwrvmd »

Fundy Investor:
I am not surprised that your testing of rebalancing did not show a benefit

Rebalancing your portfolio:

1) A chance to claim that selling winners and buying losers was done on purpose for academic reasons

2) A way for investment advisors to justify poor investment decisions by saying it was done to reduce risk

3) A way to prevent your investments from being so successful they put you in a higher tax bracket

4) An attempt to prevent self directed investors from exceeding industry and academic projections of success.

:) ....Gordon
Disciple of John Neff
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ogd
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Re: My Unexpected Findings on Backtesting Vanguard ETFs

Post by ogd »

Fundy: the lazy approach without rebalancing will become more risky over time as stocks grow. As such, it is generally higher returning. Because what you looked at is a turbulent period, this bonus was probably just enough to match the efficiency of the rebalanced portfolio; over time it will actually be quite a bit larger.

However, it's not fair to compare the returns of a more risky portfolio to the less risky one (otherwise 100% stocks, or leveraged, beats everything). The rebalancing bonus only exists on a risk-adjusted return basis; for example if you found a group of low-volatility stocks and you compared it with a rebalanced portfolio of stocks and bonds of the same volatility, the latter should outperform because of the benefits from low correlation of the components.

To adjust for risk, you could multiply one of the portfolios by the difference in equity allocations at each point in time; for example, if the rebalanced portfolio stays at 50/50 and the lazy one drifts to 60/40, multiply the rebalanced portfolio by 6/5. This in practice corresponds to the possibility of leveraging the first portfolio slightly to match the risk of the second one; this possibility is a simple reason why we always have to keep risk in the picture.

Or, you could just remember that rebalancing is above all a means to control risk, as opposed to letting it fluctuate with the market, and just go with the balanced approach :)
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