13 November 2010

Evaluating the forecasted Yuan-Dollar evolution (2010) (download in PDF)

Last year on 26 November 2009, I try to forecast the evolution of the Yuan-Dollar exchange rate for the year 2010. A very simple long-run model assuming the Purchasing Power Parity (PPP) and a negative relation between the level of prices and the short run interest rate was considered. From this model I derived a long run relationship between the China-USA exchange rate, and the interest rates of China and USA (see my previous report). If the long-run evolution between the two economies in the last years (from 2005 to 2009) maintained, I forecasted a decrease of 5% in Yuan-dollar exchange rate, an increase of 117% in US T-Bills 3 month, and a increase of 27% in the Chinese lending rate for December 2010.
In this year some interest things have happened. US government has asked Chinese government to let appreciate its currency. However, China has tried to maintain the exchange rate at a level almost constant the most of the year avoiding the Yuan appreciation.

Despite the Chinese effort to avoid appreciation, inflation pressures make China consider some measures who appreciate Yuan. In October, inflation climbed to 4% over the annual target of 3%, as a result the central bank raised interest rate last month for the first time in nearly three years and some analyst believe another increase could be around the corner. This week Popular Bank of China launched a slew of tightening measure to fight excessive liquidity, including a rise in the reserve ratio for all banks on top.

While some critics have demanded the Chinese currency should rise up to 40%, China has controlled its pace under the 7% in a year.

But let’s evaluate the levels I predicted with the actual results and let’s try to explain what is going on.

Figure 1 shows the prediction I made last year about the evolution of Yuan-Dollar in blue and the actual values in black. The first thing we observe is that the direction was the correct. In fact, the Yuan is appreciating against the dollar as was expected, however the rate of appreciation is not enough to maintain the long-run equilibrium of the model.
Whereas the model predicted a 5% of appreciation for December 2010, we found almost 3% of appreciation on November 2010. However, this is not a bad result as a prediction considering that I used monthly data making a dynamic prediction staring on November 2009.

Figure 1. Forecasting and Actual Yuan-Dollar Exchange rate (2010)

Let’s focus now on the instruments of both countries, the short run interest rate. Figure 2 shows the predicted and actual US Treasury-Bill 3 Month for the whole year 2010.

Figure 2 Forecasting and Actual US T-Bill 3 Month (2010)

This is an excellent result for who knows that actual values can be divided in long run trend plus shocks. Note how the Actual values oscillate around my long-run Forecasted (last year) trend. It is like the US government is moving considering a similar long-run tendency. Since 2007 US government has been decreasing its short-run interest rate and I predicted an increase of 117% this year. Well, considering Nov-2009 to Nov-2010 it increases 160% over long run trend in a clear policy of avoiding Yuan appreciation against Dollar.

Figure 3. Forecasting and Actual Chinese Yearly Lending Rate (2010)

Figure 3 shows the evolution of the Chinese yearly lending rate for 2010. Note that my long run trend is over the actual values. It is a clear result of the Chinese policy of avoiding the appreciation of its currency. The rate remained constant until September; in October 2010 China increases its rate to control inflation and as mentioned some analysts believed another increase. The model forecasted a 27% of increase in the rate and the actual increase was just 4.7%. The Chinese policy is far from the long-run trend of the last year.

Table 1. Annual Variation of the Exchange rate Yuan/Dollar, US 3-month T-Bills and Chinese lending rate. Actual and Forecasted (in Red)

As conclusion, the forecasting was not bad and the small difference can be perfectly explained by government policies.
According to Table 1 the Yuan-dollar has continued appreciated since 2005, considering the last year the appreciation was inferior to expected values. I forecasted a 5% of appreciation for December 2010 and now (13rd November 2010) it arrived to 3%. This result is explained basically for two reasons in my model. First, even if US government who has cutting the interest rate since 2005 (Table 1) has decided to increase the interest rate this year as expected, the increase was larger than the expected value. This is consequence of a policy avoiding the devaluation of Yuan against dollar, note in equation (1), in our model and increase in the US interest rate (rUS) increase the Yuan-Dollar exchange rate (e).

Long run relationship using data from 2005-2009:  et= 3.399    - 0.827(rChina)t   + 0.055(rUS)t   (1)

Second, there was a more clear policy in China of avoiding appreciation in Yuan against dollar. Increasing just 4.7% the interest rate when the model needs a 27%, of course the secondary effect is an increase in inflation rate over the equilibrium level. For this reason some analysts expect a new increase in Chinese interest rate to maintain the inflation target of 3%.

My simple model considering Purchasing Power of Parity between China and US and negative relationships between the short run interest rates and level of prices is not far from the evolution of reality.

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26 November 2009

-Forecasting the Yuan-Dollar exchange rate evolution (2010) (download in PDF)

Appreciation of Chinese Yuan has generated so much discussion in the last period. Some people assert that Yuan has the potential to become a world’s reserve currency. In fact, HSBC predicts that by 2012 nearly $2 trillion of annual trade (over 40% of China’s total) could be settled in Yuan, making it one of the top three currencies in global trade. Even though China has political reasons to have a strong currency, it is also true that depreciation of dollar (in special after the recent crisis) has worried China. In fact, China is the largest creditor of US and having huge foreign exchange reserves, largely dollar-denominated, and the value of these assets may shrink if the depreciation tendency of the dollar continues.   
Yuan currency accelerated its appreciation since June 2005 when the People’s Bank of China instituted a modest floating regime. Yuan-Dollar exchange decreased 2.5%, in 2005-2006, 3.4% in 2006-2007 and 7.02% in 2007-2008. After this acceleration China decided to peg to dollar in 2008. The Yuan has been pegged at about 6.83 to one U.S. dollar since July 2008. Note that in 2008-2009 Yuan appreciated 5.59% and taking October 2008 and October 2009 the appreciation is just 0.13% (see Table 1). However, there are reasons to think that China may have to adjust its policy and increase the flexibility of Yuan, with the almost inevitable appreciation of the Yuan.

Table 1: Annual Variation of the Exchange rate Yuan/Dollar,
 US 3-month T-Bills and Interbank Chinese rate.

On November 17, 2009, US President Barack Obama called on Chinese counterpart Hu Jintao to make good on a commitment to allow the Yuan to appreciate to help prevent trade imbalances that exacerbated the global economic crisis.
China has to evaluate the evolution of the US economy. After the crisis US has depreciated its currency, in particular respect to the currency of emerging countries. US budget deficit has exploded in the last time after the government plan to save the financial system. It is probably that US will apply a fiscal policy increasing taxes and reducing public expenses, it could contract a bit the US economy. The 3-month Treasury bill presents the lowest level in its history 0.07% (at October 2009). There is almost no margin to reduce the interest rate helping to increase production and depreciating even more the dollar. On the contrary, an increase in the US interest rate would be contractive policy but could help to appreciate dollar. Even if it is likely that US increases its interest rate but it is not sure that it will be enough to stop the Yuan appreciation.  

I decided to evaluate a simple model to forecast the evolution of the Yuan-Dollar exchange rate for the next year. This model is a simplification in order to capture just a few variables determining the exchange rate.

Figure 1

Let E to be the exchange rate between Yuan and Dollar, PUS the level of price in US, PChina the level of prices in China, and RUS and RChina, the respective 3 month interest rate in US and China.
According to the purchasing power parity (PPP) hypothesis we know that the following equation should be taken in the long run:

E . PUS = PChina                                                                   (1)

Therefore the exchange rate is determined by:

E= PChina/ PUS                                                                     (2)

As known the US economy uses the interest rate as monetary policy in order to control inflation and China has also used this policy. Defining the level of prices as a decreasing function of the interest rate we obtain the following equations:

PChina=A(RChina)-b1                                                                  (3)

PUS=B(RUS)-b2                                                                         (4)

Substituting (3) and (4) in (2) and taking logarithms, we obtain our econometric model.

et= b0 - b1(rChina)t + b2(rUS)t+ut                                                                 (5)

I take monthly data from January 2005 to October 2009 for the exchange rate, the US 3 Month T-Bill interest rate and the Chinese interbank interest rate. Using the Johansen Cointegration test and the test of weakly exogeneity I obtain the following equation.

et= 3.399    - 0.827(rChina)t   + 0.055(rUS)t                                                     (6)
      [9.979]      [-4.174]                   [3.947]
 

The signs are the expected and the coefficients are significant. Furthermore, the Chi2-statistic of 9.44 shows that the rChina and rUS are weakly exogenous at 1%.

Using the Vector Error Correction model and 10,000 Montecarlo simulations, I forecast the following months until December 2010. Figure 2 shows the results.

Figure 2: Forecasting of Chinese and American interest rate and Exchange rate Yuan/Dollar for the period Dec-2009 to Dec-2010.

The results shows that in average is expected to have an increase in the interest rates, 117% the US interest rate and 27% the Chinese interest rate from Dec-2009 to Dec-2010. On the contrary, the Yuan will appreciate even more, in fact the exchange rate is expected to decrease 5% in the same period. Of course, the uncertainty increases as the time goes on, note that the confidence intervals growth as the time advances.

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22 April 2009

-Is a Bubble in the Treasury Bonds? (download in PDF)

As known the long-term Treasuries such as the 10-years notes, are subject to all kinds of long-term risks (currency risk for foreign debt holders, inflation risk and even credit risk).
However, it is generally considered as a safe security. After the crisis in the technological sector (DotCom bubble), the real estate sector and the Banking sector, investors have tried to satisfy their appetite for safety moving a growing number of assets into US government bonds decreasing the yield of the bonds and increasing their prices. Remember that bonds prices trade inversely to their yields. Figure 1 shows that after October 1981 the bond yield presents a negative trend and nowadays we are under the values of 1962 (the initial date). The latter is translated in a very high increase in price bonds.
Most of the holders are China, Japan, the petro-powers, and the surplus of emerging Asia. The question is whether the US Government has the capacity of repay all this debt in the future or not.
As it is well known, the US budget deficit has exploded in the last time. Of course, it is because the US Government has loaned, invested and committed around $7.8 trillions after the financial bank crisis ($200 billion to nationalize the world’s two largest mortage companies, Fannie Mae and Freddie Mac, $150 Billion for American International Group, $300 billion for the Federal Housing Administration rescue bill to refinance bad mortages, etc.).

Figure 1: Yield for the 10 years Treasury note (1962-2009)

This seems to be the picture of a new bubble about to burst. Actually, some time ago Warren Buffett (often called the "Oracle of Omaha")asserted the following:
“When the financial history of this decade is written, it will surely speak of the Internet bubble of the late 1990s and the housing bubble of the early 2000s. But the U.S. Treasury bond bubble of late 2008 may be regarded as almost equally extraordinary”
On March the China Premier Wen Jiabao, the U.S. government’s largest creditor, was “worried” about its holdings of Treasuries and wanted assurances that the investment is safe. Wen said to the press: “We have lent a huge amount of money to the United States”. “I request the U.S. to maintain its good credit, to honor its promises and to guarantee the safety of China’s assets.”
Let’s do some calculations on the 10 years treasury notes. I applied a simple GARCH(1,1) model to the percentage changes in yields (gy)and compared it with the computation of the evolution of the entropy.
The following model was estimated for the changes:
gyt=0.000160
s2t=0.0000002+0.9325s2t-1+0.0673e2t-1
Figure 2 shows the evolution of the informational efficiency and the volatility (according to the GARCH model). The results are amazing, the efficiency decreases since November 2007 arriving to a minimum nowadays. On the other hand, the volatility increases after June 2007 arriving to a maximum at the present. Note that they are the global minimum and maximum for the whole period since October 19th,1967 to April 22nd, 2009.
Figure 2: Evolution of the Efficiency and the GARCH volatility (1967-2009)

Kenneth Rogoff, an economics professor at Harvard University and former chief economist of the International Monetary Fund asserted this month that annual inflation in USA could go as high as 8% to 10% within three to five years, and sooner in the UK. That can have a big impact on bond prices.
In order to see if this phenomenon happens only in USA I obtained data from UK. I took the yields of a 10 years security from the British Government. I calculated the entropy and estimate a GARCH(1,1) model.

Figure 3: Evolution of the efficiency and the volatility of the bond in UK (according to GARCH)

The results are similar to the previous one. Since the beginning of 2008 the efficiency decreases and the volatility starts to rise since the middle of 2007.
Of course, since the last year many high powered hedge funds are getting short US bonds and George Soros agreed that there is a bubble in treasury bonds about to burst. He said “That’s the fear that drives people into gold”, however he wouldn’t say whether he’s now actively trading gold.

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27 March 2009

-Predicting the Crash in the Russian Stock Market 27 March 2009 (download in PDF)

In my article “The Informational Efficiency and the Financial Crashes” published in Research in International Business and Finance on 4th March 2008, I asserted that according to my measure, the Russian market was the most inefficient and the probability of having a crash was the largest. Well, looking at the RST index we can observe that my prediction was right, the Russian index arrived to a maximum on 21st May 2008 (2487.9) and then it crashed arriving to a minimum (498.2) on 2nd February 2009, as shown in Figure 1. 

The index decreased 79.97% from 19 May 2008 to 21 January 2009; this is an annualized loss of 91.04%!
In my article “The Informational Efficiency: The Emerging Markets Versus the Developed Markets” recently published in Applied Economics Letters but written time before, I show that using daily data for 20 countries from 1997 to 2007 the Russian market ranked as one of the most inefficient (18/20).

The intuition that a bubble was developing in the Russian stock market was not new, some investors warned time before about it. On 14th March 2007, Jim Rogers, co-founded of Quantum Fund with George Soros, warned that the Russian stock market was overvalued. He asserted literally “Everybody in Russia is busy stripping assets. If you ride across Russia, you are not going to see a lot of money being spent on railroads, pipelines or roads”. “It’s outlaw capitalism”.
One year later, on October 2008 when the Russian market accumulated a loss of 71% since the maximum on May 2008, Clifford Levy claimed that many Russian billionaires had done their fortunes by borrowing against the future earnings of their main commodity assets. He says that “Now, as the value of their investment sinks on the stock markets and bankers call in their debts; they’re staying at home to lick their wounds.”

As we can note, this is a very difficult moment for the Russian economy. Some economists suggest that the only thing that could save the country from either disintegration or a massive totalitarian crackdown would be a significant rise in crude oil prices.

Considering the devastating effects of the formation of a financial bubble for the financial market, the economy and even the political stability, I would like to remark the importance of developing measures of financial risk useful predicting or at least detecting these events. On the other hand, I would like to remark again the potential of the entropy as predictor of a crash.

8 October 2008

-Inefficiency in the Financial System (download the article in PDF)

I heard some people to say that now is the moment to invest, is only necessary to have well-taken care of where investing. Thus, I take six important companies which are suffering the financial crisis: AIG (American International Group), C (Citigroup), JPM (JP Morgan), AMD, INTC (Intel) and GM (General Motors), and I applied some statistics.

Most of those companies belong to the Dow Jones Industrial Average; most of them are also important Banks affected by the crisis. In the case of AIG, the US Federal Reserve helped it with $85bn. However, the curious thing I found is that the financial companies starting to present a cluster of inefficiency since 2004 arriving to a minimum in 2006 and 2007. How is possible that the US government did not do anything in order to revert the situation. Of course, now is the market which wildly tries to take to the financial sector to efficiency levels.

The last month, Nobel prize laureate and former chief economist of the World Bank asserted that the crisis in the world financial markets should be less serious than that of the 1929. He highlighted that the America’s financial system failed in its two crucial responsibilities: Managing Risk and Allocating Capital. Well, after doing some calculations I agree with Stiglitz.

The present work is organized as follows. The section 2 presents a performance analysis on the six stocks, taking the S&P 500 index as benchmark. Section 3 presents an analysis of the evolution of the informational efficiency for these assets. Finally, section 4 draws some conclusions.

2) Performance of the six stocks

As mentioned before I wondered if it is possible to invest in any of the important US stocks. I collected daily data from 09 July 1986 to 07 October 2008 (yesterday) for AIG, C, JPM, AMD, INTC, GM and S&P 500. Table I shows some statistics applied to these stocks.

Table I: Performance of the six stocks from 09 July 1986 to 07 October 2008

Note that the S&P 500 index cumulated 310.28% since 1986 until now, with and annualized return of 6.6%. Intel presents the largest cumulated return with 3.905% and an annualized return of 18.26%. Citigroup and JP Morgan also present positive annualized returns of 10.14% and 8.63% respectively. However, AMD, GM and AIG presented a negative cumulated result in the whole period.

The risk statistics show the S&P 500 as the less risky, presenting a Maximum Drawdown of 49.15%, an annualized standard deviation of 17.46% and a Modified Value at Risk of -1.56%. On the other hand, AIG and AMD present maximum draw downs over the 90% arriving to these levels after more than 1900 days. Note also, that only the S&P 500 and JPM have recovered from the maximum drawdown.

When analysing the risk adjusted performance for the whole period (1986-2008), INTC seems to be the best investment with Sharpe, Sortino, Omega and Calmar ratios over the values of S&P 500.

The following figure present the compound growth annual returns (CGAR) rolling 5 years, we just show the evolution in the present year.

Note that in the last 5 years, JPM is the only asset presenting a positive annualized return (6.63% at 08 October 2008). Note that the worst returns are obtained by AIG, GM, AMD and C.

From this analysis we could conclude that INTC is the best option among the assets, when considering all the period. However, note that in the last 5 years it presents a negative annualized return of -9.74%. JPM should be the best option among the stocks but it is riskier than the S&P 500.

I have to advise that I just wanted to illustrate the performance of some assets. However, I recommend (of course) to invest in a portfolio, maybe one similar to the proposed by Faber (2007) where we put a part in stocks, part in real state, part in bonds and part in commodities, changing to cash when there is a clear negative trend in any of the components. It was explained also in the work presented in this site on 15 July of 2008 and writing with Stefano Marmi.

 3) The Financial Banks were not Informational Efficient

Some economist believed that the Efficient Market Hypothesis is the clearest law in social sciences. In its weak version it says that prediction in prices is impossible and the formation of patterns in the prices should not appear when there is perfect information. If there is a deviation from efficiency, the market will find the way to come back to efficiency levels. In recent articles I propose a measure of these efficiency in order to check is a particular asset or market is efficient or not (see Risso (2008a) (2008b)).

It was amazing the result when I applied this measure to these assets. The following figure shows the evolution of the efficiency for the S&P 500, AIG, C and JPM (the three financial assets in the group) for the period 27 April 1987 to 07 October 2008, taking a rolling time-window of 200 days.

The incredible results is that since 2004 these financial assets present a cluster of inefficiency, arriving to a minimum of 0.69 (Citigroup on 10 March 2006), 0.73 (AIG on 10 June 2007), 0.81 (JP Morgan on 9 March 2006). Note that in no period the inefficiency is greater than this, nor in October 1987, nor in 2001 after the dotcom bubble. This efficiency is also less than the efficiency of the S&P 500 index.

 Table II presents the average daily efficiency for the stocks and the S&P 500 from 1995 to 2005.

Table II: Average Daily Efficiency from 1995 to 2008

Note that AIG, C and JPM have been clearly inefficient in the last years presenting minimum efficiency in 2006 and 2007. Note that the efficiency of AIG, C and JPM is around 0.95 in 2008 when the S&P 500 presents a level of 0.97 and 0.98 for the technological assets like AMD and INTC.

The following figure shows the evolution of the efficiency in the 2008. Notice that daily efficiency of technological assets such as AMD and INTC has grown in this year. However, efficiency of AIG, C and JPM have tended to decrease, even under the S&P 500 levels.

4) Conclusions

 I analysed the performance of some assets affected by the present financial crisis (AMD, INTC, JPM, AIG, C, GM) and the S&P 500 index. INTC, JPM and C presented a positive annualized return in the period 1986-2008 greater than the return of S&P 500. In the whole period INTC seems to be the best option according to Sharpe, Sortino, Omega and Calmar ratios. However, in the last five years, INTC has presented a negative return and only JPM shows a positive return.

When I analysed the informational efficiency of these assets I found something interesting, the biggest financial companies Citigroup, JP Morgan and AIG have presented a cluster of inefficiency since 2004. These levels of inefficiency are the largest in the whole period from 1986 to 2006. I wonder why the US Government did not act in the period 2005-2007 to revert the tendency. I think that the present crisis is the wild response of the market to revert an inefficiency indicated in the past.

 References:

 Faber, M., (2007), “A Quantitative Approach to Tactical Asset Allocation”, Working Paper available at:  http://ssrn.com/abstract=962461.

Risso, W., (2008a), “The Informational Efficiency and the Financial Crashes”, Research in International Business and Finance, Vol. 22, pp. 396-408.

 Risso, W., (2008b), “The Informational Efficiency: The Emerging Markets versus the Developed Markets” Applied Financial Economics Letters. (forthcoming)

24 August 2008

-WIll the clean energy be the new financial bubble? (Download the article in PDF)

Recently, the US economy has been witness of two big bubbles: the dotcom and the housing bubble. In fact, some people say that the US economy is a “bubble economy”, growing when some sector presents an overvalued trend and entering in recession when the trend disappear and the sector adjusts to reasonable levels. The latter seems to be true in the case of the dotcom bubble, when many investors believed in a “New Economy” where the physical investment was useless. However, the crash in 2000 shows that the fundamental principles of the physical economy still worked. The curious thing is that after the disillusion in a “virtual economy” the investors overreacted investing in the real economy. Thus, a new bubble developed in the real estate, at the first part of the present decade. Again when the acceleration in prices was excessive, the bubble burst and the consequences are palpable.

Now, different analyst and investors are wondering what will be the next financial bubble. That is a very difficult question indeed. In the last months, many candidates have been mentioned: Emerging market, institution specializing in retirement, infrastructure investment, bond market, credit card, oil market and clean energy.

I would like to talk about the possibility of developing a bubble in the clean energy due to two reasons. First, as know, nowadays there is an important debate about the feasibility of solving the energy problems with the existing technology without the necessity of breakthrough innovations. In fact, given the high cost of petroleum, some people think that there is a necessity of using new technologies using alternative energy sources. However, many persons suggest that the change would be highly expensive, and is not feasible in the short term.

The second reason is that some analysts such as Eric Janszen suggest that there are many reasons helping the developing of a bubble in the clean energy sector: 1) bubble is forming as the previous bubble deflates; 2) There is a favourable tax treatment and other protections and advantages; 3) is popular, “its name is on the lips of government policymakers and journalists”.

On the other hand, a revolution in the technology sometimes facilitates the developing of a bubble, that was true in the internet revolution and some people believe that electricity also played an important role in the bubble of 1920s. However, we cannot talk about a real clean energy revolution at the moment. There are only seeds of a possible revolution. In fact, according to the Energy Information Administration  (www.eia.doe.gov) the total consumption in renewable energy increased 7% between 2005 and 2006, at the same time the total US energy consumption decreased 1%. This implies that the renewable energy’s share of total US energy arrived to 7% from 6% in 2005. On the other hand, some companies working in the sector such as First Solar present a cumulated annual return of 167.11% (from 03/08/2007 to 04/08/2008), when the financial markets are falling down!!

Let us start analysing the S&P Global Clean Energy Index which recovers the weighted performance of 30 companies working in the clean energy sector (such as First Solar Inc, Solarworld AG and Sunpower Corp). Daily data from 21 Nov 2003 to 14 Aug 2008 was obtained from S&P (www2.standardandpoors.com). Figure I shows the evolution of this index.

 Figure I: Evolution of the S&P Global Clean Energy Index

In figure I we can recognize two important Drawdowns, at first not that from 9 May 2006 to 13 June 2006 the index passed from 2425.93 to 1739.57 losing 28.29%. However, the maximum drawdown was present between 26 December 2007 and 7 February 2008 (from 3911.68 to 2771.08) losing 29.16% and note that the index did not recover from the maximum peak on 26 December 2007. Actually, note that the index seems to be presenting a decreasing trend in the present time.

Let us analyse now, the level of informational efficiency in the sector. As I suggested in some articles the entropy seems to be a good indicator of the efficiency in the financial markets, playing an important role in the proximity of a crash (see Risso (2008), “The Informational Efficiency and the Financial Crashes”, Research in International Business and Finance, Vol. 22, pp. 396-408.).

Figure II: Evolution of the informational Efficiency for the S&P Global Clean Energy Index

Figure II present the evolution of the informational efficiency for the index, from 13 April 2004 to 13 August 2008. The dashed line is a polynomial trend of the efficiency and the red line is a limit of efficiency for finite samples according to 2,000 Monte Carlo simulations. Note that according to the trend there was only a clear cluster of inefficiency between 22 January 2008 and 9 June 2008. However, nowadays seems to be not signs of inefficiency in the market, actually the efficiency is growing up.

Let us compute the impact of the efficiency in the probability of a crash. Defining a crash as the negative tail of the empirical distribution of the returns (actually I take 1% as limit) and applying a logit model such as equation (1) where H is the entropy and y is a variable taking 1 when there is a crash and 0 when there is not.

                                                                                                                                                 (1)

Table I: Logit Model for the S&P Global Clean Energy Index

Table I summarize the results. Note that the model is significant and a negative relationship is found between the entropy and the probability of crash.

Therefore we can conclude that the clean energy market is efficient nowadays (at 13 August 2008) and presenting a growing efficiency. On the other hand, the probability of having a crash is decreasing given the negative relationship between the two variables.

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15 July 2008

-Tactical Asset Allocation Using Daily Data  (written with Stefano Marmi at Scuola Normale Superiore di Pisa). Download the article in PDF

Introduction

A portfolio combining different assets can produce larger return and less volatility. However, this is not a new idea; the Talmud even mentions the advantages of asset allocation (real estate, commodities and cash) approximately 2000 years ago[1].  One can think about many strategies that combine these assets. Recently, Faber (2006) proposed a very simple quantitative market-timing model. In words, it consists in portfolio composed by US assets, foreign assets, commodities, real estate and bonds in equal parts. The strategy is to study the trend of each element, maintaining the position the asset if the trend is growing. However, if the trend is going down we sell the asset and buy cash.

The purpose of the present work is to apply the strategy developed in Faber (1996) using daily data of US stocks, European stocks, commodities, bond funds and cash for the period March 1st, 1994 and May 25, 2008.

The work is organized as follows. In the next section the methodology developed by Faber (2006) is briefly explained. Section 3 shows the results of the tactical asset allocation compared with the assets and the simple asset allocation. In section 4, we analyze the statistics of the portfolio in case we decide to withdraw a monthly percentage of the gains. In section 5 we study the sensibility of two strategies, the simple asset allocation (AA) and the tactical asset allocation (TAA). In particular, we start the AA portfolio in 255 different days and the TAA portfolio in 21 different days, analyzing different statistics such as the maximum in the set of 21 maximum drawdowns. Finally, we draw some conclusions.

2) Methodology and Portfolio construction

Faber (2006) proposed a portfolio aiming to reduce the risk measured as volatility and drawdown. As mentioned, the portfolio is composed with 25% of US stocks, 25% of European stocks, 25% commodities and 25% bond funds. The strategy is described by two rules.

The buy rule is the following:

We buy the asset when the daily price is larger than the 10-month (200 days) Simple Moving Average (SMA).

The sell rule is the following:

We sell the asset and move to cash when the daily price is less than the 10-month (200 days) SMA.

Three considerations should be mentioned:

1)      All entry and exit prices are on the day of the signal at the close.

2)      All data series are total returns including dividends.

3)      Cash returns are estimated with the 13-weeks treasure bills.

We check the portfolio every 21 days. The evolution of the cumulated returns for the Portfolio is measured using daily data. We consider S&P 500 (US stocks), Eurostoxx 50 (European stocks), CRB Index (Commodities) and Treasure Bonds (Bond Funds). In order to estimate the Treasure Bonds we consider two Bond Funds titles the BTTNX and the BTTTX using the first until December 31, 1999 and then using the BTTTX, Table I shows the annual returns, variance and drawdown of the bond funds.

Table I: Treasure Bonds Proxies

3) Tactical Asset Allocation (TAA)

 Figure 1 shows the cumulated returns of the TAA portfolio, the AA portfolio and the assets (S&P 500, Eurostoxx 50, CRB and Bond Funds).

Note that the bond Fund presents the largest cumulated return in the period and the TAA portfolio has the second best. On the other hand, the S&P 500 and the Eurostoxx 50 present the worst cumulated returns in the period 1994 and 2008.  

Figure 1: Comparison among Portfolio and the other assets

Table II shows a series of statistics in order to compare the performance of the portfolio with the different assets. Note that the TAA portfolio has the second best annualized return (14.21%) after the Bond Fund with 14.77%. On the other side, the simple AA portfolio is in the fourth position after the CRB, according to the annualized return. Note also that the worst day in the TAA is the least comparing the group of asset.

Analyzing the risk, we note that the TAA widely reduces the drawdown. As known, the maximum drawdown (MDD) is the largest percentage drop in your account between equity peaks. In other words, it's how much money you lose until you get back to breakeven. According to this measure, S&P 500 presents a MDD of -49.15% in the period; however, the TAA portfolio presents the lowest MDD with -15.78%. The annualized standard deviation and the annualized downside deviation (it means, considering only the negative returns) is also the minimum in the group, with 6.74% y 6.53%, respectively.

Table II: Performance of the Portfolio and the different assets

As known, the Value at Risk (VaR) is a limit loss in a determined interval of time (a day in this work). If we give a confidence of 5%, a loss equal or greater than the VaR happens 5 times over 100 days. The Modified VaR (MVaR) considers kurtosis and skewness, measuring the risk of a portfolio with nonnormally distributed assets. According to this statistic, our TAA portfolio has the second best MVAR (-0.53%) after the Bond Fund (-0.37%).

In order to measure the risk adjusted performance we use four different statistics. 1) The classical Sharpe ratio, measured as the ration between the average return discounted by the free risk asset return (13 weeks Treasure bonds) and the standard deviation; 2) The Sortino Ratio is similar to the Sharpe Ratio, considering the downside standard deviation; 3) The Omega ratio is defined as the ratio of probability-weighted gains to probability-weighted losses; 4) The Calmar Ratio is the ratio between the annualized return and the maximum drawdown. Note that according to all these statistics, the TAA presents the best performance in the group. For three statistics the second place is obtained by the AA portfolio, giving some evidence that asset allocation is a good strategy in order to improve return and risk.

The Table III presents the number of switches realized every 21 days according to the rule described above. Note that for each asset, we have switched approximately the 50% of the total number of controls.

 Table III: Number of Switch made for each asset

 Figure 2 shows the 5-years cumulated returns from 1994 to 2008. Note that the 5-years cumulated returns oscillate between less that 160% to more than 40% in all the period. It means that in the worst period the TAA portfolio produced an annualized return larger that the 6.96%, whereas in the best period it produced an a.a. less than 16.65%. 

Figure 2: Total Cumulated Return of the TAA portfolio rolling 5 years.

4) Imposing a monthly withdrawal to the TAA Portfolio

 In the present section we assume that we decide to withdraw a certain percentage over the monthly returns (0.10%, 0.20%,…1%). Therefore, we study the feasibility of this strategy in terms of returns and risk.

 Table IV: Performance of the TAA portfolio assuming different monthly withdrawals

Note in Table IV that even withdrawing 1% of the monthly returns, we obtain a positive annual return of 1%. Of course, as we take a larger percentage from the returns the statistics get worse. In particular, note that for a withdrawal of 0.9% the Sharpe and Sortino ratios are negative. However, for a withdrawal of 0.6% the two ratios are still larger than in the case of the S&P 500.

5) Starting the portfolio in a different date

In this section we conduct an analysis of sensitivity in two strategies. First, we suppose that we start the AA portfolio in 255 different days and compute the different statistics. In second place, we conduct the same analysis for the TAA portfolio taking 21 different days.

1) Asset Allocation Portfolio

Figure 3 shows the evolution of the 255 AA portfolios and the Figure 4 shows the drawdown evolution of the portfolios.

Note in Table V that in average the strategy generates an annualized return of 10.34% which is still larger than the annualized returns of the S&P 500 and Eurostoxx 50 (see Table II), even the worst portfolio generates a annualized returns larger that the two assets (9.79%). On the other hand, in average, the maximum drawdown is -23.04% moving form a minimum of -23.54% to a maximum of -22.59%. These values are still less than the values corresponding to the S&P 500, CRB and the Eurostoxx 50 (see Table II). Considering the Modified VaR note that in the worst case we have a -0.63%, which is better than the AA, S&P 500, Eurostoxx 50 and CRB.

Figure 3: The 255 different AA portfolios

Studying the performance, we note that the Sharpe, Sortino and Calmar ratios are positive and larger than the corresponding ratios for S&P 500, CRB and Eurostoxx 50.

Figure 4: The 255 different drawdowns

Table V: The performance of the 255 AA portfolios

2) Tactical Asset Allocation

In the present subsection we generate the Tactical Asset Allocation portfolios starting in 21 different days. Note, that the average annualized return is 12.83% with a minimum of 11.28% in the worst scenario and a maximum of 14.72% in the best scenario. In all the cases, the return is better than the S&P 500 and the Eurostoxx 50.

The maximum drawdown is in average -11.67% with -7.35% in the best scenario and -16.76% in the worst. Note that even in the worst scenario, the maximum drawdown is better than the corresponding MDD of AA, S&P 500, Bond Fund, CRB and the Eurostoxx 50 (see Table II).

 Figure 5: The 21 different TAA portfolios

Note also that the TAA portfolio is very stable, in terms of annualized standard deviation is the best strategy. In the worst case the annualized standard deviation is 6.92%, however the S&P 500, Eurostoxx, CRB and Bond Fund have a standard deviation larger than the 14% (see Table II).

Figure 6: The Drawdown of the 21 different TAA portfolios

Due to the high performance in return and risk note that the risk adjusted statistics in table VI are the best. Note that if we consider the Sharpe, Sortino, Omega and Calmar ratios in the worst case, they are larger that the corresponding statistics in the case of S&P 500, Eurostoxx 50, CRB and the Bond Fund.

Due to the high performance in return and risk note that the risk adjusted statistics in table VI are the best. Note that if we consider the Sharpe, Sortino, Omega and Calmar ratios in the worst case, they are larger that the corresponding statistics in the case of S&P 500, Eurostoxx 50, CRB and the Bond Fund.

Table VI: The performance of the 21 TAA portfolios

 Conclusions

Faber (2006) considers a portfolio composed by different kind of asset and a strategy which takes care of the trend. We apply this strategy to a portfolio composed by US and European Stocks, bond fund and commodities using daily data. We show that even in the worst scenario the strategy produces a better portfolio than the stocks, bond funds and commodities, separately.

 Reference

Faber, M. (2006), “A Quantitative Approach to Tactical Asset Allocation”, Working Paper available at: http://ssrn.com/abstract=962461.