Yaremenko's CAD-gold loop adds at most 11% on its calibration

This paper offers no trade, and its proposed mechanism adds at most 11% to shocks under Yaremenko's own calibration. The empirical evidence offered in support reverses two of the signs the model needs.

Inside Yaremenko's CAD-gold loop

Yaremenko jointly models USD/CAD, spot gold and 3-month gold futures, driven by real rates and a financialisation index. The paper develops a theory and checks it empirically. It proposes no strategy.

Three equations make up the model. The first defines the exchange rate S as USD per CAD: a higher S means a stronger loonie. Its inputs are the US-Canada real-rate gap, log gold and log WTI. Uncovered interest parity is attached to a terms-of-trade equilibrium.

The second equation makes gold depend on the 10-year TIPS yield, the 5-year breakeven, VIX, log S and a financialisation index. The index combines GLD holdings, COMEX open interest and CFTC net non-commercial longs through their first principal component. In the third equation, a constant-maturity 3-month future equals spot multiplied by a cost-of-carry exponential, plus a premium proportional to the index's speculative component.

The feedback between the first two equations accounts for two of the paper's three claimed novelties. Higher gold prices strengthen CAD through Canadian exports. The assumed elasticity α2 is 0.05 to 0.10. The model then treats a stronger CAD as a weaker dollar, lifting gold with an elasticity γ of 0.8 to 1.0. Solve the equations together and every shock is scaled by 1/(1 - α2γ).

For its empirical check, the paper uses monthly observations from January 2000 to December 2024, roughly 300 months. It applies a Johansen test, a sign-restricted structural VAR (SVAR) and an error-correction model. A US real-rate shock lowers gold by 5.8% at three months and S by 3.4%. A financialisation shock raises gold by 7.8% and S by 4.5%. The paper says these results suggest gold "could improve carry trade signal quality". We find no carry-trade test, signal or backtest in those results. The paper also suggests that futures positioning may contain information about spot.

Does a stronger loonie mean a weaker dollar?

The loop depends entirely on ln(USD Index) = -ln S + C. This identity treats a bilateral CAD exchange rate as the broad dollar. Yet a Canadian terms-of-trade shock can move CAD without moving the dollar against the euro or the yen. For a gold buyer in Zurich, metal gets no cheaper unless the dollar also falls against her franc.

The oil channel exposes the problem. In the paper's comparative statics, oil lifts gold by α3γ/(1 - α2γ). Set α3 at 0.10 to 0.20 and γ at 0.8 to 1.0, and a 10% WTI rally raises gold by 0.8% to 2.0% before the multiplier. The entire effect comes from the loonie's rise. Gold accounts for about 3% of Canadian merchandise exports; the paper puts oil at over 20% of total exports.

The paper supplies neither an estimate nor a citation for γ. Its second cointegrating vector gives s a coefficient of 0.05, with the opposite sign.

A multiplier of 1.04 to 1.11

The calibrated α2γ range is 0.04 to 0.10, giving a multiplier of 1.04 to 1.11. Combine the baseline estimate α2 = 0.082 with vector 2's coefficient on s, retaining its sign, and α2γ comes to about -0.004. On those estimates, the loop damps shocks by 0.4%; the multiplier is about 0.996.

The stability proposition is correct for positive α2 and γ, with eigenvalues of ±√(α2γ). Stability is never in question at these parameter values. Even so, amplification leads the conclusions' principal findings.

The cointegration estimates reverse the model's signs

The Johansen trace test rejects zero cointegrating relations: 78.45 against a 5% critical value of 63.88, p = 0.008. It does not reject at most one: 36.32 against 42.92, p = 0.064. Having concluded that there is one relation, the paper reports and interprets two vectors.

Rearranging vector 1 gives s = 0.45 r_US - 0.38 r_CA + 0.08 g + 0.15 oil - 0.06 Φ. This makes a higher US real rate strengthen CAD, contrary to α1 > 0. In vector 2, gold falls as CAD rises, contrary to γ > 0. Nevertheless, the paper says "the signs match those in Equations (1) and (2')" and "the magnitudes are in the expected ranges". The exchange-rate coefficient in vector 2 is 0.05; the assumed γ is 0.8 to 1.0. Although the author describes the validation as preliminary, the abstract says it confirms the principal theoretical predictions. The conclusions likewise describe the estimates as consistent with the theoretical priors.

There are further sign discrepancies. Φ changes sign between vector 1 and the bracket in the ECM. The text gives the ΔrUS coefficient as +0.15, while Table 6 gives -0.152.

The SVAR assumes the signs it would need to establish. In Table 4, the restrictions require a real-rate shock to lower S and G, and a financialisation shock to raise S, G and F. Table 5 reports impulse responses for S and G only. They have exactly the imposed signs.

The magnitudes tell us more, although we did not find a stated shock size. Taken at face value, they also conflict with the structure. The financialisation shock moves CAD by 0.045 and gold by 0.078. Their ratio is 0.58, about seven times the estimated α2 of 0.082. By 12 months the real-rate responses lose significance: CAD is at [-0.019, 0.003] and gold at [-0.042, 0.006].

The futures equation carries gold at the real rate, represented in the data by the 10-year TIPS yield. An arbitrageur funds at a nominal short rate. Annual storage of 0.1% to 0.2% contributes little. The funding term therefore does the work in the carry relation, and the paper assigns it the wrong rate. There is also an unresolved gap in the index: GLD began trading in November 2004, but the sample begins in January 2000. We did not find an explanation of how the index covers that interval.

The paper acknowledges that its results depend on the sign restrictions' validity and are specific to the 2000 to 2024 sample. That caveat addresses sample and identification. It leaves the reversed signs in the vectors unexplained.

A scenario map still has some use

The sign table predicts that a rise in rUS weakens CAD and produces the largest fall in gold, marked by two arrows in the paper's table. It also predicts wider contango. That column relies on the disputed real-rate carry relation above. Across the 3-month TIPS variant and the pre- and post-2008 splits, CAD's gold elasticity ranges from 0.065 to 0.094. The ECM adjustment speeds of -0.124 and -0.082 imply in-sample half-lives of about 5 and 8 months.

We could not test any of this on our data.

A faithful run requires spot USD/CAD, LBMA spot gold, Canadian yields paired with Consensus inflation forecasts, and CFTC and ETF positioning. We hold none of them.

We would change our view if vector 1's error-correction term predicted next-month USD/CAD out of sample, net of costs.