近期经济观察 – U.S. Trade Deficits

The Fed increase the federal fund rate and resulting in an increase in the nominal interest rate in the U.S. market. The U.S. dollar becomes more and more attractive to global investors due to mainly two reasons. One is that the U.S. dollar behaves as the safety currency (detailed reasonings are shown in the previous posts), and the other is that the increase in the interest rate attracts money from other countries to be invested in the U.S. market.

U.S. dollar gets appreciated for the above two reasons, and thus the U.S. faces an increase in trade deficits. For the aggregate U.S. market, imports are way more than exports. However, those extra imports are clearly paid through the U.S. dollar or exchanged with other currencies (but shared with the same logic as paid with USD). And that extra amount of US dollar is from the helicopter drops and QE of the Fed. That means the extra US dollars back with nothing, but are used to purchase/import assets from other countries. Right! it do not need to be backed by other in the current economy (Also, MMT advocates even crazy).

I am telling that those facts are equivalent to that the U.S. is getting net imports from other countries for free. Also, the U.S. is sending its “worthless” extra currency to others, exchanging goods and services. Productions are not working in a good way for those exporting countries in the battle with the pandemic.

Due to the fact that the US dollar is the safest currency, the extra printed amount is absorbed by other countries that get net exports to the U.S. Those other countries export goods and services and import back inflation. There are also countries that conduct QE in a similar rhythm to the U.S. would face even higher inflation intuitively, because the US dollar is the safest one and the only one linked with crude oil and commonly accepted in commodities trading but other countries’ currencies are not.

Fed放水，释放美元供给，按quantity theory of money的说法：people hoard money instead of spending them。但是现实中， hyperinflation comes later than the theory tells。原因可以部分可以参考MMT。同时美元作为 1. 最safest的货币，且 2. 与石油挂钩，并未大宗商品交易的主要媒介，仍然有很大的需求。导致虽然市场上美元供给增加了，但是因为紧张的国际关系、俄乌战争、de-globalisation、pandemic的影响，以及上述两条原因，市场上对美元仍有大量需求，导致inflation没有立刻到来。

但是，大量printed US dollar实际上并没有real goods\ productions or services的支持，很多出口商品的他国公司获得美元（or other currencies, but similar as holding USD）交付（美国import，其他国家export），这里的美元只能用来交易且为extra美元。相当于是Fed pays nothing印的钱，买了real goods。这些出口国家失去了商品、产能、and factors，得到了USD，相当于得到了nothing but inflation，由美国extra money printed 带来的 inflation。

同时一些国家与美国同步QE印钱，执行类似的monetary policy降息，为了保证foreign exchange相对稳定。但是这些国家的货币并非如同USD一样highly demanded。所以这些国家的货币难以与美元继续peg，脱钩后会引入even higher inflation。

Implications：自主货币政策（而非peg）的重要性；外汇储备以应对紧急 外汇、国际经济（如利差倒挂）情况的重要性；以及外汇市场中globalisation情况变化下的monetary policy的重要性。

Merrill Lynch Investment Clock

The Merrill Lynch Investment Clocks describe a framework for understanding the business cycle.

The Merrill Lynch clock separates the business cycle into four phases. Each phase is comprised of the direction of growth and inflation relative to their trends.

1. Reflation – 萧条

After stagflation, people are frustrated and have low confidence in investing.

Both the GDP growth and inflation are falling or lower than the trend. The stocks are suffering in a bear market but bonds suppose to be the most welcomed asset because of the generous monetary and fiscal support from governments and central banks (bail-out, cutting rates, and stimulus programs).

Jan 2020 till Apr 2020, the pandemic flowed globally. Governments of each country conducted policies of lockdowns. The economy was blocked, and the unemployment rate increased. A recession began globally.

  • Low Growth and Low Inflation
  • Bonds are attractive

2. Recovery – 复苏

Investors’ confidence has built up / recovered.

Growth starts to back on track while inflation still remains low. Stocks regain attraction with very attractive valuation and improving earnings. It is, of course, the most favorable asset at this stage.

From May 2020 to Feb 2021, the Central Banks and Fiscal Divisions of each country placed monetary policies and fiscal policies, aiming to boost the economy. A huge amount of money was pooled into the market. QE and Helicopter Drops were conducted and resulted in an increase of M2, about 10% in the European market, and 25.7% in the U.S. Meanwhile, the interest rate hit the floor. Banks with extra money reserves holding started to actively search for clients with the demand for money.

The good thing is money went to the market and smoothed the economy. The recession gets reversed a little bit. However, bad things happened at the same time that (1). individuals and firms held extra money. That fact raised people’s expectation of inflation, and thus invested their extra holding of money into stock markets, pushing an increase in the index; (2). Firms with not good financial and operating conditions were also granted credits and debts. Potential default probabilities increased.

  • High Growth, and Low Inflation (but expected inflation increased)
  • Stocks are attractive.
  • P.S. Bitcoins are even more attractive, coz the limited supply and even more sensitive than stocks.

3. Overheat

Growth reaches its peak and slows down and inflation is rising. (does it sound familiar if you follow these days’ headlines?) Both stocks and bonds won’t perform well, but betting on commodities will be a proliferating and profitable strategy.

The economy got overheated, and the economy was still speedily moving until reaching a peak. After achieving the top, growth got slower.

The expected inflation in the recovery stage transferred to a true increase in inflation with high CPI. Investors started to be unconfident and started to pursue safety assets, which are necessities such as commodities (metals and crude oil).

  • High Growth and High Inflation.
  • Commodities are attractive.

4. Stagflation

Inflation is way out of control and that severely hurts consumer confidence. Central banks are forced to hike rates, and stocks, as one of the leading indicators of the economy, have already fallen. However, this stage of the cycle doesn’t happen that often in the last few decades, thanks to Fed’s “remarkable” economic interference policy, which is to print out enormous money to stimulate the economy meanwhile artificially setting interest rates low to control the inflation (however we just don’t know how long it could last). Flying to safety assets, cash is the best choice given the circumstance.

  • The Fed’s policy works not bad because the U.S. dollar links with crude oil, and becomes one of the “safety assets”. However, other countries do not have that “lucky” chance.
  • Low Growth and High Inflation.
  • Even the U.S. Dollar is not safe enough, so people change to hold cash.

Reference

https://www.zhihu.com/question/284396767/answer/1745335386?utm_source=wechat_session&utm_medium=social&utm_oi=774013724896788480&utm_content=group1_Answer&utm_campaign=shareopn

https://medium.com/@richardhwlin/how-does-investment-clock-work-c7d8fbbeb7bd

Hodrick Prescott Filter / HP Filter

We decompose a time series into two parts, one is the trend, and the other is the seasonality.

$$ y_t=g_t+c_t $$

, where \(g_t\) is the trend, and \(c_t\) represents seasonality. Or, one can understand those two components as a low-frequent part, and a high-frequent part.

The filer tells that,

$$\min_{g} \sum_i^N (y_i-g_i)^2+\lambda \sum_i^{N-1} (g_i^2-2g_{i+1}+g_{i+2}^2 )^2$$

$$\min_{g} \sum_i^N (y_i-g_i)^2+\lambda \sum_i^{N-1} [(g_i-g_{i+1})-(g_{i+1}-g_{i+2}]^2$$

,which can be also written as,

$$\min_{g} || y-g||^2+\lambda||\nabla^2 g||$$

We can see the first term represents how far the trend term \(g\) is away from the original series \(y\), and the second term means to smooth the trend term \(g\).

$$ g=argmin_g || y-g||^2+\lambda||\nabla^2 g||^2$$

We replace \( \nabla^2 g \) by \(Dg\).

$$ || y-g||^2+\lambda||D g||$$

$$ (y-g)^T (y-g) +\lambda (Dg)^T(Dg)$$

We take the first gradient (f.o.c.) to solve for the trend term \(g\).

$$ -(y-g)+\lambda D^TDg =0$$

Therefore,

$$ y=(I+\lambda D^T D)g $$

and,

$$ g=(I+\lambda D^T D)^{-1}y $$

Reference

https://zhuanlan.zhihu.com/p/160243396

资产回报-宏观经济-利率利差-资本流动-汇率变化

1. 经济增长

自微观至宏观的结构。微观层面，公司的资产价值增长或公司的利润增长，而某行业内多个公司总值或均值的增长带来了行业的增长。同理，行业引申至宏观经济体。本质上是weighted average，而意识上是 多个个体增长 带来整体 增长。逻辑简单。

同时，在经济扩张阶段，企业对loanable fund的需求增加反映在财务上往往是负债增加。企业若需继续扩展则 负债增加带来的风险 需要被 企业增长的预期带来的预期收益冲抵，因为如此，理性投资者才原因承担更高的风险。

P.S. Considering the interest rate and saving, lower real interest rates motivate individuals to consume more and save less. Greater consumption enhances capital/money transferring in the whole economy. We may say that a lower interest rate can not just stimulate the economy in a positive way through increase the desire for investment and consumption, but also smooth the economy by pooling liquidity into the market.

2. 宏观经济体之间

假设两个经济体，A和C。C的经济增长快，市场中对goods, services, factors, labours等各方面的需求高，同时对money的需求高。对 money 的高需求，带来了高成本 – higher interest rate。而A增长相对少，甚至Central Bank需要主动采取措施给降低interest rate来降低loanable fund 的成本，刺激需求。

基于以上大背景。A市场中利率水平低，C市场中利率水平高。

Under Globalization, money flows across countries with low fees and less regulation. Without considering others, money would flow into the market with a higher interest rate, pursuing higher returns. However, sovereign risks, frictions, regulations, etc, would block that path.
在全球化的大背景下，如果假设低fees低监管等限制，money会流入高收益的市场。但是现实中往往并非如此，因为投资者会考虑其他因素，如地缘风险，政策变化等等。

继续之前的例子， C国利率高，money流入C国，对于C国currency的需求大，currency appreciates。C国货币升值后，A国再进口C国商品物料或投资的成本变高。对C国货币的需求又会相对减少。Overall, a Dynamic Equilibrium occurred.

当然，以上为理想情况。现实中USD起到全球主要流通外汇的左右，尤其特殊的意义。且经济情况今非昔比。市场或宏观经济体面临不同的环境：如De-globalisation;

3. 加息的传导渠道

https://mp.weixin.qq.com/s/sInT_p-p9ewRYEbt8MMtmg

Reference

https://mp.weixin.qq.com/s/fs-wMetDFe5HmCl3f8tztA

Stock Market Reactions on Taper & the Increase in Federal Rate

Factors affecting stocks valuation are liquidity of the market, Prosperity of the overall market, investors’ preference, etc.

In simply the DCF model, the impacts of those factors would be reflected in the discounted rate. As we consider separating the interest rate into a risk-free rate and the premium for a certain firm, the premium is idiosyncratic. For example, with low liquidity of the capital market, investors would expect a liquidity premium; worse economic conditions and low investors’ preferences would increase the risk premium.

Therefore, we could predict that an increase in the federal fund rate, as what the Fed is doing to face the hyper-inflation, and quantitive tightening would have the following impacts. Firstly, the quantitive tightening (QT) or TAPER means the Fed would actively decrease its balance sheet by sell-out/stoping re-issuing those MBS or Government debts. This conduction would decrease the amount of money available in the market, and thus result in higher costs of borrowing money. The liquidity premium would increase. Secondly, if there is less supply of money, then the higher cost of using money, the interest rate, would increase. Both the increase in the interest rate and the premium would increase the discount rate for a certain company. Applying the higher discounted rate to the DCF model for that firm would end up with a lower valuation.

Conclusively, an increase in the Federal Fund Rate and QT/TAPER would generally result in a lower valuation of firms.

Bond Price Approximation

The Price-Yield Curve descripts the relationship between a bond’s price and yield, and they are normally negatively correlated.

We here consider the Bond’s price as a function of the bond’s yield, \(P(Y)\), and study the approximation of the bond’s price.

We firstly apply the Taylor Expansion at \( (Y_0,P_0 \),

$$ P(Y)\approx P(Y_0)+\frac{dP}{dY}(Y-Y_0)+\frac{d^2P}{dY^2}\frac{(Y-Y_0)^2}{2!}+O((Y-Y_0)^3) $$

$$ P(Y)-P_0 \approx +\frac{dP}{dY}(Y-Y_0)+\frac{d^2P}{dY^2}\frac{(Y-Y_0)^2}{2!}+O((Y-Y_0)^3) $$

$$ \triangle P \approx \frac{dP}{dY}\triangle Y+\frac{d^2P}{dY^2}\frac{(\triangle Y)^2}{2!}+O((\triangle Y)^3) $$

Devided by P from both side, then the LHS means the percentage change of Price.

$$\frac{ \triangle P}{P} \approx \frac{dP}{dY}\triangle Y \frac{1}{P}+\frac{d^2P}{dY^2}\frac{(\triangle Y)^2}{2!}\frac{1}{P}+O((\triangle Y)^3) $$

By definition, the Modified Duration \( D=\frac{\triangle P / P}{\triangle Y} = \frac{dP}{dY}\frac{1}{P}\), and convexity \( C=\frac{d^2 P}{d Y^2}\frac{1}{P} \). We replace them into the expansion function. and drop the last term.

$$\% \triangle P \approx D\cdot \triangle Y+\frac{C}{2}\cdot (\triangle Y)^2$$

Finally, we get the approximated bond price curve. Second order Taylor Expansion is applied, and the Duration and Convexity, two important properties of bonds are included. For more accurate approximation, more terms need to be expanded.

Taylor Rule

Developed by John B. Taylor – aims to be a rule of thumb

If the Federal Reserve decides to increase the liquidity, it would then buy bonds and put more money into the market. As there is more money to lend, the interest rate would go down.

The monetary policy aims to target the inflation rate. Considering the Philips curve, there is a trade-off between unemployment and inflation. Unemployment could be replaced by its counterpart, economic growth. We consider the goal of the monetary department to balance GDP and Inflation.

The Fed normally has a target interest rate, the federal funds rate, which is the overnight rate in the interbank market for short term lending. How should the monetary policy set the target interest rate? This is the key discussion of the Taylor rule.

$$i=i^*+a (\pi – \pi^*) – b(U-U^*)$$

By the Philips curve, we replace unemployment with output. As we separate the interest rate to be the real interest rate and the inflation rate.

$$ i=r+\pi^*+a\underbrace{(\pi-\pi^*)}_{Inflation\ Gap}+b\underbrace{(Y-Y^*)}_{Output\ Gap} $$

The output gap could be considered to be by what percentage of the current GDP is below the Potential GDP.

Clearly, the Taylor rule is intuitively to be correct.

If there is an inflation gap the current inflation is greater than the target, which also means there is an extra money supply moving the CPI upward, then the Fed should conduct a contractionary monetary policy, and it should set a higher interest rate.

If the GDP growth is lower than the target (potential), or if the unemployment rate is greater than the target, then the Fed would like to stimulate the market. Thus, it would decrease the interest rate.

For the Taylor rule, John Taylor did not mean the monetary policy should follow it. It is not a law but just a rule of thumb. Normally, we also set the coefficients \(a\) and \(b\) to be 1\2. However, if we think the government would pay more attention to the inflation target, then we could certainly increase the weight of inflation gap.

Bernoulli’s Inequality

$$lim_{x\rightarrow 0}(1+x)^n ~ 1+nx$$

Proof:

Taylor Expansion at x=0

$$ (1+x)^n\approx (1+x)^n|_{x=0} + \frac{d (1+x)^n}{d x}|_{x=0} \times (x-0) + \frac{d^2 (1+x)^n}{d x^2}|_{x=0}\times (x-0)^2 + O(x^3) $$

$$ \approx 1 + nx + \frac{n(n-1)}{2} x^2 + O(x^3)$$

$$ \approx 1 + nx + O(x^2)$$

George Soros & the Japan Market

The story began in the third quarter of 2012 when the Japanese Yen depreciated until the beginning of 2013 as the rising Blue curve shows.

As we all know, Japan has been getting into a negative interest era for a long time, partially because the terrible economic condition makes its government have to raise debts (I haven’t studied the Japanese problem. Once do that, I will update it.).

Since 2008 when the US saved the market through QE, the Japanese CB chose to conduct a similar monetary policy to boost its domestic market after Aben won the presidency.

Intuitively, Abenconomics applied QE would result in an excess supply of the Japanese Yen. Unlike the US dollar that backed with the Oil price, the excess money supply of the Japanese Yen would make it depreciate. Soros estimated that opportunity and shorted the Yen, and meanwhile took a long position of Nikkei stocks and bonds in the Japan Market.

QE would result in an extra money supply as we all know, investors who get that extra money would try to invest that money into the financial market, both the stock market and the debt market. As we can find that stock market increased with the depreciation of the Japanese Yen. Soros won the gamble.

However, there is a Winner and there must be a loser, which is the Japanese Central Bank. The failure of the monetary policy of the Japanese CB made worse its domestic economic condition.

In the current world, the CB of each country has to rigorously implement its monetary policy. QE might not be an ideal way to stimulate the market, because not every currency has the ability, like the US dollar, to back up with commodities and oil prices. Also, countries especially those that are in the EU are facing a conflict of interest in conducting monetary policy.

US Dollar Index & Federal Fund Rate & Stock Market Index

QE & Federal Fund Rate

Let’s see from the figure. During the crisis, Fred conduct QE, pooling money into the market, and reduce the federal fund rate, trying to activate the market. As in the shaded area, which represents the crisis period, the green line jumps with the dropping of the blue line.

US Dollar Index & Federal Fund Rate

In the last post, US Dollar & Commodity Price, I discussed the fact that increasing the interest rate in the U.S. market would result in appreciation of the US dollar because the US dollar would be more attractive for investors. Meanwhile, in the crisis especially, unsafety concerns and greater demand for necessitates such as commodities and energy (oil), would also increase the demand for US dollar, as they are traded by US dollar, and thus result in appreciation of US dollar. The conflicts emerge during the crisis period, the shaded area, that Fred reduced the federal rate to activate the market, but the US dollar index increased instead. It seems the demand for necessities dominates the effects of decreasing the federal rate in the crisis.

$$ Federal Rate \downarrow \Rightarrow US Investment \downarrow \Rightarrow US Dollar Index \downarrow $$

$$ Crisis \Rightarrow Uncertainty + Demand for Commodity \& Energy \uparrow \Rightarrow Demand for US Dollar \uparrow \Rightarrow US Dollar Index \uparrow$$

In the crisis, demand for necessities pushes up the demand for the US dollar and thus lifts the US dollar index. However, those two indices work in the same way (positive correlated) in the non-crisis period.

Stock Market Index & Federal Rate

I would use the Wilshirefred 5000 index as the stock market index as it is available in a longer period range in FRED.

While including the stock market index, it seems the stock market grows at a similar path to M2. Although no data is presented about the GDP, it is easy to imagine that the stock market would grow on the same path as the GDP as well. A spurious relationship exists clearly.

Could we explain the growth of the stock market cap as people hold more money and invest in stocks? Maybe right or wrong.

The Figure below shows the nearly random walk of the stock market growth. Presumably, if draw a histogram of the stock market return, it would most likely to be normally distributed and the mean might be positive because the market cap keeps growing (extreme value affects).