Main factors in deciding between whether to hedge or not: returns, volatility, and correlation. Very briefly:

Cost of hedge: interest rate differential + any FX basis

Volatility or underlying vs currency: check if a hedged position can give a better Sharpe; sometimes the currency is more volatile than the underlying

Correlation between underlying and currency: some assets are better left unhedged i.e. JPY-denominated equities; denomination has a tendency to rise in times of equity stress

Typically, bonds are hedged while equities are left unhedged, but this 'typical' does not apply to everyone at every time - you have to see if it applies to your case.

Also, always do the analysis with your home currency in mind.

I recently did an exercise on analyzing the limit order book for predictors of the first event that will occur in the next 1 second. There are 3 events: bid level retreating, ask level retreating, and no change in the top of the book price.

The result was that the log of (Bid/Ask) gave the strongest prediction.

Below is a scatter plot for a small sample that shows the relationship between the bid and ask quantities, and the corresponding colours indicate the outcome (grey = no change, blue = bid retreated, red = ask retreated). Contours indicate the probability estimated by multinomial logistic regression.

Here's the full version using tick data of the entire day (about 127,000 data points). White = no change, for better visibility and truncated at size=300.

Below is the full version, without the ax truncation.

Continuing from Part 1 where we concluded that the costs of hedging will almost certainly outweigh the benefits, we now look into detail as to the return drivers of the hedge, and why they amount to nothing.

Correlations

Currency hedging typically works well when the foreign currency is negatively correlated with the foreign asset, as this means that the currency hedge gains when the asset is falling and vice versa, with a net effect of reducing the volatility of the hedged portfolio.

In this case, the Pearson correlation between the returns of SPX and the hedge (short USDSGD) is +0.235 (slightly positive), and so that does not help in reducing volatility.

From the scatter plot we can see that the returns are rather evenly clustered around the origin. The R-squared value for the linear regression is a mere 0.055 - suggesting that linear relationship of the two returns are very weak.

Taking a look at rolling correlations, the monthly returns of SGD (short USDSGD a.k.a. the hedge) have been more positive than in earlier periods (1990s and ~2005).

Notably, the 2008 crisis caused the SGD to be rather highly correlated to the SPX for several years. It has more recently subsided to the ranges of 0.30 but this is still positive and this means that leaving it unhedged actually provides some diversification benefits, as the USD strengthens (against SGD) when the S&P is not doing well, and vice versa.

Thus, in the short term, we don't expect to gain much from the hedge.

Fundamentals and regime shifts

Taking a longer-term perspective, it is unlikely that the SGD can repeat such a dramatic ascent from its levels of 2.0 USDSGD to present levels of 1.35, representing a 48% increase in value (SGD terms). This rise can be attributed to Singapore's rapid development which brought her into the ranks of developed countries, which is an unrepeatable event.

Thus, in the long term, we don't expect to gain much from the hedge either.

Altogether, it continues to argue for the case that we should leave the USD unhedged.

2018 performance for the 3 A.I. stock trading strategies at trade-ideas.com

I recently paid for a membership to take a detailed look at the strategies, and having trawled through the historical data,I present my findings below.

The very short conclusion is that you cannot simply follow the A.I. signals regardless of Risk On or Risk Off method.

Major edit to this article: I'd like to stress that while I present Risk On on a statistical basis, the underlying data that was presented to me has a fundamental flaw and so the results are biased and misleading (more details in post).

The Risk Off method remains a true reflection of 2018 performance.

Expectations vs Reality

The strategy itself seems good - taking every single trade (at standard lot size of 100 shares) would have earned you $69,829 for the Risk On method, and $27,463 for the Risk Off method.

If you have the S&P 500 as part of your portfolio, should you hedge your USD exposure by regularly converting it to SGD? Doing this will remove the currency risk from your foreign (US) investment. But does it produce better returns?

The short answer is: No

This article compares between two portfolios:

Unhedged - an investment in the S&P

Hedged - an investment in the S&P, hedged monthly

The unhedged portfolio is one we all have to bear as the starting point, as the investment is in USD but we have to account for our wealth using SGD.

The hedged portfolio uses a simple method of hedging - hedge the exact amount of USD exposure based on month-end values. For example, if the month-end value is 2,200 we will simply sell 2,200 USDSGD. The result is the undhedged portfolio, plus any gains/losses from the currency hedge.

Results:

Chart 1b (below, middle) shows that the absolute dollar-value difference between the Hedged and the Unhedged portfolio is negligible. Chart 1c shows the cumulative outperformance of the Hedged vs the Unhedged portfolio, and shows no clear trend of outperformance.

Chart 2 below compares the outperformance of the Hedged portfolio vs the Unhedged portfolio in their monthly returns, percentage terms.

The percentage outperformance shows no distinct bias, and its average is indeed near zero (0.02%). Together, the results from charts 1 and 2 suggest that outperformance is random and close to zero.

If the difference in the returns are negligible, what about the standard deviation of the returns? Perhaps the hedged portfolio can give us a more predictable monthly return?

Unhedged (SGD)

Hedged (SGD)

Average monthly return

0.64%

0.66%

Standard deviation

4.17%

4.62%

Sharpe

0.155

0.144

Unfortunately, wWhile the hedged portfolio has marginally better monthly returns, the variance of the hedged returns are also higher, leader to a lower risk-adjusted return measure.

Thus, if we include transaction costs and effort/time spent for hedging, it is likely it will not be worthwhile to hedge.