By Helin Gai / January 8, 2017
A picture is worth a thousand words:
After a turbulent start, US large cap stocks ended up returning 12%. Taking some extra risk and moving into small cap helped a lot, returning 21%. Per usual, the riskiest segment of the stock market is not rewarded, with OTC/microcaps returning <4%. Value premium delivered, with value stocks outperforming growth stocks by a large margin. Small cap value did particularly well, returning 32%.
Outside the US, global stocks were generally worse off than US counterparts. World stocks returned 7.9%, and emerging markets returned 7.5%. UK, in spite of Brexit, did astonishing well, returning 19% (of course, British pound depreciated 17% last year against US dollars, so a US investor would’ve suffered investing in UK companies).
Bonds did poorly, as interest rate rose. US government bonds generated just 1% of return.
Inflation expectation rose last year, so inflation sensitive assets did well. Commodities were up 12%, and global inflation linked bonds returned 10%.
Hedge funds continue to do terribly, with the overall hedge fund index up just 0.28%.
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By Helin Gai / December 24, 2016
GDP growth is reported infrequently and with a substantial lag. Fortunately, there are many indices that provide more uptodate readings for the current state of the economy. My favorite amongst them is CFNAI (Chicago Fed National Activity Index), which represents the weighted average of 85 economic indicators (formally calculated as the first principal component of the chosen indicators). However, even CFNAI is published with a delay. For instance, the November reading is not available until late December. To get more timely updates, I have created my own USA Economic Activity Index:
 Like the CFNAI, the USA Economic Activity Index is calculated as the first principle component of a large number of economic indicators (about 50 in my current setup).
 Unlike the CFNAI, I use the Weighted Expectation Maximization PCA approach which can more gracefully handle noises and missing observations. This allows me to continuously update the index as new data becomes available, providing readings at a much higher frequency.
 Since a balanced panel of data is not required by the algorithm, I can extend the time series further back in time, even though some of the constituent series don’t exist until much later.
 I also express the index in GDP equivalent terms (like Goldman’s CAI), making the values more intuitive.
The chart below compares the unadjusted first principle component against CFNAI:
Not surprisingly, the two series are highly correlated (correlation = 0.93).
The next chart compares the final index with realized quarterly GDP growth over time:
As can be seen, the index is fairly capable of capturing major trends in the economy (in sample correlation = 0.75).
The USA Economic Activity Index has been trending upward over the past few months, rising from 2.6% in October to 2.9% in November. The latest reading for December stands at 3.1%.
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By Helin Gai / December 19, 2016
Estimating equity risk premium (ERP) is notoriously difficult. In prior years, I used the dividend discount model (like many other practitioners). The model itself is simple enough – all we have to do is solving for the required return, \(R\), such that the present values of future dividends sum up to the index level:
$$\text{index level} = \sum_{i=1}^\infty \frac{d_i}{(1 + R)^i}. $$
Of course, the challenge lies with projecting future dividends, which typically involves using earnings growth rates forecasted by sellside analysts. This has always been troubling for me:
 First, analysts’ earnings forecasts are notoriously optimistic (which inflates ERP), but it’s not clear how much we need to discount them by on an exante basis;
 Second, the calculated ERP does not forecast subsequent equity returns all that well, making the usefulness of ERP estimates ambiguous;
 Finally, since analyst expectations are not available until 1979, it is difficult to compute ERP that spans the longterm debt cycle.
Recently, I implemented a new model based on Lemke and Werner’s The Term Structure of Equity Premia in an Affine ArbitrageFree Model of Bond and Stock Market Dynamics. Compared with the dividend discount model, the LW framework has several advantages:
 It does not require subjective inputs such as earnings growth. Instead, the model is calibrated based on historical pricing dynamics for bonds and stocks, as well as the evolution of inflation.
 It is capable of jointly pricing stocks and bonds in an arbitrage free framework, producing both equity and bond risk premia estimates.
 Instead of assuming a constant ERP for any investment horizon, the model generates a “term structure” of equity risk premium that varies depending on the investment horizon. (The original paper presents estimates for 3month, 10year, and 100year ERPs.)
 With a few tweaks to the original model, we can obtain ERP estimates with significantly improved forecasting power for futures equity returns.
The details of the model are quite involved and I encourage readers to review LW’s original paper. Here I present the 10year equity risk premium estimates based on my own calibration:
The contour of the series makes intuitive sense. For example, (objective/rational) ERP declined sharply during the dotcom bubble as equity became gross overvalued. It then spiked during the 2008 financial crisis, as investors demanded substantially higher compensation for taking on equity risks.
Using the ERP estimates, we can easily calculate expected equity returns – by adding back expected bond returns. The nominal expected returns, along with subsequently realized 10year S&P 500 total returns (annualized) is presented below:
As can be seen, the model has excellent forecasting power. The correlations between the predicted 10year equity return and subsequently realized return for various start dates are as follows:
 Since 1940: 0.91;
 Since 1950: 0.90;
 Since 1970: 0.89;
 Since 1990: 0.92.
The natural question is where we stand today. This is where it gets depressing. The current ERP reading is a paltry 0.35% per annum for the next ten years, and the corresponding expected nominal equity return is just 3% per year. The comforting news it that the 95% confidence interval is rather wide, ranging from 1.5% to 7.5%. One can always hope for more inflated market valuation going forward to get us to 7.5%!
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By Helin Gai / December 15, 2016
Many years ago, when strategists calculated Fed hiking/easing probabilities from market instruments, the first step was to adjust all the forward rates down to account for term premium. After all, forward rates are (were) upward biased estimates of future rate expectations.
Circa 2011, this adjustment had been abandoned. If you have the next 12 Fed funds futures all priced at 10 bp and you start subtracting 1–2 bp of term premium per month, you quickly end up with negative nominal rates. Clearly, term premium is no longer a thing at the front end of the yield curve.
At this stage of the cycle though, I get this sense that the market is not prepared for the upcoming repricing. (Practically speaking, if you graduated from college after 2012, you’ve probably never heard of the “archaic way” of doing rates strat.)
The chart below shows the priced number of hikes in 2017:
We are still far from the three hikes “communicated” by the Fed. Sure I’m in the camp that believes they probably can’t and won’t do three, but given the increased political uncertainty and market volatility, there should be more term premium. And yet, the market is not asking for it:
 Assuming that the Fed delivers only two hikes, we’d be left with just 6 bp of realized term premium (or +0.5 bp per month).
 If the Fed delivers three hikes, our realized term premium becomes 19 bp (1.6 bp per month).
It’s hard to be long with this risk/reward.
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By Helin Gai / November 27, 2016
I have been watching 5y yields very closely, primarily because it’s interesting from a technical perspective. My thinking is that if it broke above resistance, it would signal something has fundamentally changed. Well it did happen (see below), so it’s worthwhile thinking about the implications of this pricing.
The chart below shows the 2y forward 3y real yield & BEI (closely linked to the pricing of 5s, but I want to strip out Fed activities over the next two years):
Frankly speaking, the current pricing is not particularly outrageous:
 Forward BEI is priced at 1.94% – more than reasonable given the Trumpflation rhetoric;
 Forward real Treasury yield is 49 bp. But keep in mind that at this tenor, OIS is about 5060 bp less than Treasuries. So the implied real forward funds rate is not far from zero.
While both real yield and BEI contribute to the selloff, it really is the BEI move that’s pushing the overall yield above the peak. Forward real yield is well within the trading range.
The dynamics of 2y3y, combined with the fact that the Treasury market is discounting 100bp of hikes for the next two years, makes me feel that the current level is about right and likely represents a new equilibrium level for rates to bounce around; i.e., the likely trajectory (all else equal & until the next shock) might look something like this:
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By Helin Gai / August 14, 2016
I ran into this DB chart that has subsequently been annotated by other bloggers:
The implications of the annotations are:
 German bond yields went negative in the early 1920s;
 Hyperinflation ensued.
In reality, neither are true.

Until recently, longterm German bond yields have never turned negative. In September 1923, some bonds traded up to 23 million marks, with an implied yield close to 0, but still slightly above 0. So why does it look like a negative value in the chart? Because the creator of the chart used a very thick line in poor software (Excel?).

As said, the low point in yield happened in September 1923. By then, Germany was already experiencing the full force of hyperinflation. Bonds were trading at 2–3 million marks in price and yields declined to 0 precisely because speculators believed that the government would rebase the debt and repay them on an inflationadjusted basis. Of course, the government was all too happy to have its debt wiped out. When this harsh reality finally set in, bonds quickly lost value and yields skyrocketed.
So what does this tell us? One, there’s no causation or even correlation between negative yields and hyperinflation. Two, drawing inference from poorly drawn charts is incredibly dangerous. For completeness, here’s my own compilation of German bond yield:
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By Helin Gai / August 8, 2016
… because all is well with Spanish finances.
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By Helin Gai / August 7, 2016
Bank of England policy rate since 1700:
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By Helin Gai / June 17, 2016
The Diamond Sutra is one of the most important Buddhist texts. Alex Johnson provides a very accessible English translation for this magnificent text. Here are a few verses from the closing chapter:
“So I say to you –
This is how to contemplate our conditioned existence in this fleeting world:”
“Like a tiny drop of dew, or a bubble floating in a stream;
Like a flash of lightning in a summer cloud,
Or a flickering lamp, an illusion, a phantom, or a dream.”
“So is all conditioned existence to be seen.”
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By Helin Gai / April 2, 2016
Pandas’s Timestamp
currently has a lower bound of 16770922 and an upper bound of 22620411. If a date falls outside of this range is used, the following nasty error is returned:
OutOfBoundsDatetime: Out of bounds nanosecond timestamp: 16770922 00:00:00
To construct very long time series that stretch back hundreds of years, I’ve been using using Period
:
data = {pd.Period('15001231', 'D'): 100,
pd.Period('16001231', 'D'): 200}
df = pd.Series(data)
This generates a Series
object that works with all the usual datetime operations, such as resampling.
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