# Interlude: using math to buy cheaper gas

The concept is to buy more gas when cheaper (and vice versa) to reduce average fuel cost.

This simple demonstration assumes a commuter uses 1 gallon per day and fills when the gauge indicates empty.  The rule is as follows:

Add 5 gallons if price is above the 10 day average, otherwise add 10 gallons.

Prices were randomly distributed between \$4 and \$5 and a typical output for 1000 days is shown below:

Running 30 tests of 1000 days yields an average savings of 8 cents per gallon.

This result would vary with the rule used and price range.

For example, testing partial fill quantities:

 Partial fill Savings Savings gallons cents/gal % of stdev 5 8 30% 3 13 45% 1 20 65%

CONCLUSIONS

Significant fuel cost savings can be realized by the application of a simple “gas purchasing quantity” rule (as defined above).

Closing thought

When adding regular money to the market, does adding when price is below an average improve returns?

# Combining value and momentum (HT Asness)

Cliff Asness of AQR recently published a paper entitled “Value and Momentum Everywhere”

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1363476

The main points for me were:

1. Value and momentum are both broad and persistent anomalies.
2. Value and momentum are reliably negatively correlated.

This second effect is rare across asset classes and may be very valuable for portfolio construction.  I will be exploring this further.

A very simple implementation is to take the “small value” (SV) data series from the French data library and add a momentum rule:

Invest when the previous month’s return is positive, otherwise go to cash (3% annual interest).

The result is to increase annual returns by several percentage points, reduce time in market to 67% and increase Sharpe by 50% to 1.2.

Note: the best return of 19.3% CAGR is without using the recession model, only the rule above.

Plotting with the results from the previous post:

 COMP-IBH Buy & hold Sharpe SPX 11.2% 7.4% Low beta 11.8% 11.4% 0.89 High beta 14.1% 6.6% 0.37 Small value 17.7% 15.8% 0.82 SV momo 17.5% 19.3% 1.21

Examining the equity curve shows that SV momo is very robust in recessions.

Plotting the SV return for the current month against the next month shows the degree of autocorrelation present (see upward sloping trendline):

If desired, SV momo could be combined with other asset classes (e.g. gold, bonds, REITs) into a Faber-type tactical allocation :

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=962461

“Small value momo” returns very similar to the “top 3 of 13” asset strategy in that paper.

Another similar momentum switching strategy is COP which has the interesting property of real-time success in the last few years.  Switching allows capital to move to the best performing asset classes without attempting prediction, in accordance with the literature.

Momentum may also be combined with trend-following: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2126478

These addendum items require some more study.

# Market timing: comparing instruments (SPY, value and beta)

I will use Georg Vrba’s recession model to compare timing versus Buy & Hold for the S&P500, low & high beta and value investing:

The buy/sell dates are taken from the COMP-IBH model (above).

Data sources:

Beta series: Falkenstein

Value series: French data library

Results (1970 – 2012) CAGR:

• The timing model increases returns in all cases, although marginally for low beta.
• Return on cash during time out of the market is not included therefore timing results are a conservative estimate.
• Small value is the clear out-performer, both for timing and Buy & Hold.  \$1 returns almost \$1000 over 42 years (30% of that time in cash).

 COMP-IBH Buy & hold SPX 11.2% 7.4% Low beta 11.8% 11.4% High beta 14.1% 6.6% Small value 17.7% 15.8%

# The momentum of beta!

Numerous studies show how low beta investment strategies have outperformed relative to high beta.  Data from Eric Falkenstein’s site illustrates this over the last 50 years:

However, there are clearly periods when high beta returns are higher (for example the 1990s).  What if we switch monthly to the strategy with the highest return in the previous month?

\$1 now returns \$1000, or 15% annually, up from 12%.

This test is frictionless, with switches occurring approximately every 2 years.  (Testing is ongoing).  Currently SPLV and SPHB could be employed; of course these instruments are only recently available.

The next post looks at combining these returns with the RecessionAlert model to see whether they can be improved.