22. Arbitraging Bond ETFs with Momentum

Can bond ETF be arbitraged? One suspects a “Yes” answer because the underlying bonds of a bond ETF trade infrequently meaning ETF prices are only an estimate of their portfolio. We test this question on four bond ETFs with 10 years of data  using a casual binning method supported by regression statistics.
 The  strategy is:    Buy at 4pm; Sell at 9:45 next morning. 

One predictive factor we study is the ETF’s Premium or Discount (P/D) , defined as ETF price minus NAV (value of the individual bonds) divided by NAV at 4pm. When P/D is positive traders expect the value of the bonds to rise. When it’s negative they expect the bonds to fall. 

A second factor is momentum - but not as defined in this blog series which uses GDP-weighted momentum of world stock prices to estimate SPY. Instead it's self momentum, that is, if a bond ETF rises in the afternoon, does it continue overnight? 

We’ll show the answer is “Yes” Both factors have predictive power although municipals and investment-grade ETFs have inverse momentum. That is when they rise in the afternoon they fall overnight and vice versa. 

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Factor 1. Premium/Discount (P/D). We create 7 bins of P/D ranges containing the avg overnight change for days in these bins.

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P/D levels affect overnight returns although in different directions. International bonds do best with a 4pm Premium. Municipals do best with a 4pm discount.

Seeing the bins without linear slopes suggests a 3 degree polynomial. HYG, LQD and MUB have significant 2nd and 3rd degree coefficients. 

Trading statistically  row 2, column 2 says: Buying EMB every day when its Premium was between 1.5% and 5.0% returned: 187 *.05%= 9.3% (There were 187 days with such a premium; Trading costs of .01% reduce daily return to .05%)

Factor 2: Intraday Momentum, the change in the ETF between 11:45 and 4pm, is a second factor influencing the overnight returns.

EMB (International) follows direct momentum. Examples are .15% when the intraday rise was between .5% and 1.5%;  With intraday drops between -.5% and -1.5% it drops overnight -.06%.

HYG (High-Yield) has a convex effect. It rises overnight after a large afternoon increase; It’s flat with other changes but also rises with large drops, ie rise .17% when afternoon change drops between -.5 to -1.5%. 

LQD (Investment-grade) and MUB (Municipals) have inverse momentum. After afternoon rises they drop overnight. After drops they rise overnight. Negative slopes of -.12 and -.25 with strong T’s confirm this.

A surprise was that LQD, bonds rated high by S&P, Moodys' ... have much stronger coefficients than HYG, high-yield, which is the area of most SEC concern..

Trading statistically row 8, column 3 (blue highlight .17%) says: Buying HYG  when its afternoon change was between -1.5 and -5% profit would be:   58 * .16 = 9.0% . (There were 58 days with such a change; Trading costs of .01 reduce return to .16)

So Momentum and P/Ds produce tradable returns -  but combining factors further improves results. Let’s expand our bins to 7-by-7.

In the matrix for HYG the rows are the P/D as listed above.The columns are the afternoon change. Column 1 represents (-1.5% to -0.5%}  
Col 2: {-.5% to -.3%},   .., Col 7: {.5% to 1.5%}].

Specifically, row 2, col 1 are those days where P/D is between .5% and 1% and afternoon change is between 1% and 1.5%. Content of {4, .59} represents 4 days with an average overnight return of 0.59%.

HYG avg overnight returns by P/D (rows) and by 1145to4pm change (columns)

Those in blue suggest cases for going Long but surrounding cells should be similar.  For instance row7, col1 {29,.23} has similar bins to its right and above it so Buying has good probability. Row7, col4 {20,.10} has losing bins to its left and right so may be just noise.

Col 1 of this matrix says go Long only in rows 1, 2, 6 and 7 for an average return of .23% whereas Table 2, row 7, col 3 with no P/D restriction, has an average return of .20% thus showing the power of combining factors.

Many statisticians are skeptical of binning because it doesn’t fully use the data. The 7-by-7 matrixes have only 49 data points rather than the 2200.

So it’s less than optimal but it’s visually helpful. And it’s consistent with regression which does use the full data set. The blue entries on the left and right are consistent with cells {3,3}, {3,4} and {3,8} in Table 2. Blue in entries in the bottom row are consistent with cell {3,8} in Table 1

Additionally binning has similarities to Artificial Intelligence. Machine learning techniques such as nearest neighbors and k-clustering somewhat create bins - albeit based on heavy computations rather than personal choice as I did. 

Tim Leung, Director of Computational Finance at the University of Washington and an ETF researcher has reviewed some results. Being a Princeton mathematician he’s leary of binning but he did offer a comment: “This is an interesting experiment. As for all ETFs, Premium /Discount  is a natural candidate factor, but combining it with other factors, such as Momentum, can potentially identify good tradable signals. One natural question, which speaks to the broader impact of this research, is whether these factors have similar effects on ETFs of other asset classes ."

Conclusion. 1) Premium/Discount and 2) Momentum at 4pm can predict  overnight returns of bond ETFs. Below is a summary from Tables 1 and 2:

Momentum, the strongest factor, is inverted for investment-grade and municipal ETFs. That is when the ETF rises strongly in the afternoon it falls overnight. When if falls strongly it rises overnight. 

In terms of momentum strength, both the binning method and standard regression coefficients show that all 4 ETF types are arbitragable. Investment-grade being more so than high-yield was quite surprising. 
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Combining factors, shown above for HYG, produces even more powerful returns.