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<![CDATA[Polaris Capital Management - BLOG]]>Wed, 01 May 2024 21:35:51 -0700Weebly<![CDATA[Another look at Ergodicity Economics]]>Sat, 22 May 2021 07:00:00 GMThttp://polaris-capital.com/blog/may-22nd-2021I came across a lecture notes on Ergodicity Economics: https://ergodicityeconomics.files.wordpress.com/2018/06/ergodicity_economics.pdf. It looks like the whole theory goes far beyond the article in the Nature Physics, we discussed in the previous post. Interestingly, Ole Peters applies his theory to find an optimal leverage which defines the portfolio with the highest time average growth rate. According to his calculations it is equal to:

We thought it might be a good idea to backtest a strategy on S&P 500 Total Return Index to see if the optimal leverage improves portfolio performance. An idea of a non-constant leverage to boost an investment performance is not a new one. There are multiple investment products such as Constant Proportion Portfolio Insurance (CPPI) products and volatility targeting funds. Those products are based upon different portfolio construction principles compare to the ones specified in ergodicity economics theory.

Unfortunately, the author does not specify the way he estimates an excess return of risky assets, which is µ and volatility of risky assets, which is σ in equation (316).
To estimate volatility we use an industry wide approach and calculate historical volatility for the last 500 trading days. For stock market returns, it is more tricky. There is no industry wide standard model to project future expected returns. We use three different indicators to project five-year returns: P/E ratio, Tobin’s Q and the Household Equity Share. P/E ratio and Tobin’s Q are well known measures used in valuations of companies, whereas the Household Equity Share is a relatively new predictor. It was introduced by Yang and Zhang in their paper: https://cba.lmu.edu/media/lmucollegeofbusinessadministration/responsivesite/research/Yang_Household%20equity%20share.pdf
The Household Equity Share represents retail investor positioning and according to Yang and Zhang it outperforms popular forecasters of market returns such as the cyclically adjusted price-earnings ratio, the equity share in new issuances, the consumption-wealth ratio, the term spread, and the Treasury bill yield.

To get an expected return on a five-year horizon we simply regress on a quarterly basis five-year rolling returns on our three indicators. i.e. to avoid forward data contamination we iteratively add an additional quarter of observation when it becomes available. The choice of a five-year horizon is somewhat arbitrary. Since we perform regressions on levels, we have an issue of nonstationary of our variables. Therefore, before we run regressions, we need to make sure that our indicators cointegrate with rolling returns. We have stronger cointegrating relationships between our indicators and five-year returns than between our indicators and ten-year returns. For that reason, a preference was made in favour of five-year return signals. The results of our historical back test are on the figure below. We assumed a zero bid/ask spread for a portfolio rebalancing and our funding rate is 3 month LIBOR. We further assumed, in line with what was described in the article, that in the case of a negative expected returns positions in the market are closed and all funds are allocated to cash, which also pays 3 month LIBOR.

Source: Bloomberg, http://www.econ.yale.edu//~shiller/data.htm

In terms of an absolute performance of different indicators the results are drastically different. A portfolio which uses P/E ratio as a signal (represented by green line and right axis) significantly outperforms a portfolio based on Tobin’s Q and the one based on Household Equity Shares indicators. On the other hand, this portfolio has the sharpest (80%) drawdown. On a risk-adjusted basis, the performance of all portfolios is identical: the Sharpe ratio for all three portfolios is around 0.5.

How does that compare with the performance of a very naïve strategy that goes 100% long if expected return is positive and stays in cash when expected performance is negative? The results are on a figure below:

Source: Bloomberg, http://www.econ.yale.edu//~shiller/data.htm

Although, this chart looks different compare to a previous one the risk-adjusted basis a performance of the naïve Long/Flat strategies is almost identical to the performance of portfolios with the leverage derived from ergodicity economics theory.
One can obviously argue that the indicators we used are not the perfect ones and one can perform much better if indicators were more precise. For that, reason we decided to test a performance of the optimal leverage strategy where long term return is known in advance. Specifically, we use 8% as a yearly expected total return rate which is roughly the rate of return of S&P 500 Total Return Index for the last 30 years. The results are on a figure below:

Source: Bloomberg

The portfolio had more than 90% drawdown and it took almost 20 years to get back to the High Water Mark. The Sharpe ratio for the strategy is 0.46. Both Sharpe ratio and drawdowns for this strategy are inferior to the Sharpe ratios and drawdowns for the strategies that used Tobin’s Q, P/E ratio and Household Equity Shares as indicators.
Curiously, upon further reading it appears that the author argues that an optimal leverage should always be equal to 1!

In our view, this statement is not entirely consistent with equation (316) and even more importantly, it contradicts to the volatility scaling technique, which is a founding block of modern risk management approach both on a buy-side and on a sale-side. To get things into perspective it would make sense to look at the performance on the Nikkei index on the figure below:

Despite negative interest rates, Abenomics and multiple rounds of quantitative easing the index today is almost 30% lower than it was back in 1989!

To conclude, we found very little evidence that ergodicity economics gives results consistent with the empirical market data. The optimal leverage recommended by the theory does not give much of an added value. It does not improve risk-adjusted return and significantly increases risk of potential drawdowns.

]]><![CDATA[A Practitioner's take on Ergodicity Economics]]>Sun, 09 May 2021 07:00:00 GMThttp://polaris-capital.com/blog/may-10th-2021In a recently published article (The ergodicity problem in economics | Nature Physics), Ole Peters introduces a novel approach of looking at century-old problems of decision-making under uncertainty. Peters highlights a difference between time average and ensemble average. He argues that time ensemble average is a poor measure for non-ergodic processes of assessments of future payoff/investment returns. By carefully addressing the question of ergodicity, the article attempts to resolve many puzzles besetting the current economic formalism in a natural and empirically testable way.

The author proposes to maximize expected growth rate, where growth rate is ergodic variable. He estimates that playing with an entire fortune a game described in the equation (2) of the original paper not an optimal investment decision.

This game/investment provides investors a negative rate of growth when carried out in a multiplicative format. Therefore, the author argues, one should not accept a bet described in the equation (2) on the entire wealth. That confirms market wisdom: playing a game with a significant probability to lose practically all one’s wealth is never a good idea for a rational investor.

Ole Peters’s approach provides readers an interesting framework to analyse different investment opportunities and benefits of diversification between different strategies.

While playing a game described in (2) with one’s whole fortune does not make good sense, it does stand to reason to allocate part of a portfolio to uncorrelated strategies with the payoff described in (2). This will provide an investment return with lesser volatility.

Hedge funds and high frequency traders operate in this fashion. It is arguably difficult to find a standalone scalable strategy with a high Sharpe ratio, but it is possible to construct a portfolio with relatively high Sharpe ratios from standalone strategies carrying low Sharpe ratios.

The table below put this into perspective. It shows risk-return characteristics for game (2) and S&P 500 total return index over the last 30 years.

The game (2) displays attractive risk/return characteristics compared to the stock market.

It would be difficult to argue that people should abstain from investing in risky assets. Those who have not invested a part of their wealth and remained long cash, have typically regretted these decisions later on.

This leads to the conclusion that it does make sense to play the game (2) with proper risk scaling and portfolio diversification.

Ergodicity theory confirms this logic: a strategy with 90%/10% allocation has a positive rate of growth and is therefore a preferable choice compared to the alternative of remaining 100% in cash. The theory tells us interestingly that an optimal investment is game (2) is 25% of the fortune.

All in all, ergodicity theory confirms the benefits of portfolio diversification which was first proposed by Harry Markowitz[i].

One glaring question is: Will diversification help on the downside? Today risky assets are driven by one main factor: excess liquidity provision by Central Banks. The question is valid but it’s outside of the scope of this discussion.

When it comes down to a choice of an optimal strategy under uncertainty we are less convinced that an optimization of growth rate, which is an ergodic process, indeed provides a best possible solution among all alternatives.
In certain cases, it gives the results well in line with empirical observations (see above), but in others, the results are less convincing. A multiplicative growth process, for example, gives results, which are not necessarily consistent with investors’ preferences.

Specifically, according to the ergodic theory, an investor should prefer playing a game making 1% on a daily basis but losing 99.9% twice a year instead of playing a game as described in equation (2). It also says that, instead of staying in cash, an investor should play a game where she gets daily return of 1% but once every three years she loses 99.9% of her wealth in one day.

It is not certain that individual investors will reveal preferences in line with the predictions of ergodic theory. There are many option underwriting strategies and negative gamma programs, which indeed deliver superior returns at the risk of a 90% loss of capital. However, strategies, which lead to these loss percentages, are not recommended for retail investors.

It might be a different story for institutional investors though. The concept of “skin in the game[ii]” for some of these investors is a foreign concept, and many might happily accept such a huge tail risk playing with investors’ money instead of their own.

The author makes another bold statement claiming that the whole idea of utility function maximization is an error in the foundation of economics. Peters writes that people are not all that different, and the only thing which differentiates people are circumstances i.e., wealth.

Wealthy people subsequently maximizing their growth via an additive process would appear to be brave, whereas less well-to-do people maximizing their wealth via a multiplicative process would appear to be scared.

There are no doubts that wealth is one of the key components in both portfolio allocation and investment analysis, but it is only one of several parameters as shown by different portfolio allocations for investors similar wealth and consumption buckets. Human nature means that people are prone behave spontaneously and irrationally based upon hopes, fears, and beliefs.

Downside risk can be assessed differently by different people within the same wealth bracket. An anecdotal, and somewhat sad example can be drawn from the people’s preferences during the process of the so-called “Russian privatization” of the 1990s. During this period certain people were willing to accept a game with rather drastic extremes:

a 90% probability of centupling their wealth and
a 10% of ending up on in the graveyard.

Moreover, they played multiple rounds of this game. Some of the winners are known to us now as the “Russian oligarchs”. The second group remains silent and unknown.

One can argue that probabilities, and perception of probabilities, in this game were different for different people. While certainly true, it does not change the fact that some people in the same wealth bracket were willing to play the game with infinite downside while others were not.

On balance, it seems that ergodicity economics is definitely an interesting concept, which explains certain aspects of investors’ behaviour. The results of these predictions do not necessarily fall in line with empirical observations in certain cases.

Yet, the same can be also said about many models- not just in Economics. A less dismal science, such as Physics, can provide a fine example. Space satellite engineering and construction use principles of Lagrangian formalisms and application of Newton’s laws. However, applying the same principles to construction of a nuclear reactor will lead to catastrophic failure.
Therefore, it should be acknowledged that models in ergodicity economics, like many other models, do carry certain limitations.

[i] Harry Markowitz. Portfolio Selection. The Journal of Finance, Vol. 7, No. 1. (Mar., 1952), pp. 77-91.

[ii] Nassim Nicholas Taleb Skin in the Game: Hidden Asymmetries in Daily Life (2018)

]]><![CDATA[ECB Rate Cut]]>Fri, 13 Sep 2019 07:00:00 GMThttp://polaris-capital.com/blog/ecb-decisionAs was widely expected by the market, Mario Draghi came up with a 10 bp rate cut and brought out a bond-buying bazooka, citing a “shortfall in inflation” and “muted inflationary pressures”.
We have already discussed the ECB’s inflation estimates and the unintended consequences of ultra-accommodating monetary policy a few month ago (https://www.zerohedge.com/news/2019-07-03/how-monetary-policy-leads-destruction-middle-class-and-rise-populism).

One can well argue that the way the ECB’s inflation target will never be met. We might even end up in a situation when consumption might be suppressed because of the negative yield on assets. Economics is called a dismal science for a reason: it is challenging to come up with a comprehensible model and to make robust estimates of all the parameters in the system. However, contrary to all expectations, I think it may be feasible to end up in a positive feedback loop scenario where:

·       narrowly defined inflation would go down because of the negative rates on fixed income assets
·       further rate cuts
·       new rounds of quantitative easing.
·       a further asset price appreciation leading to a bubble

All the while keeping narrowly defined inflation (the one ECB is monitoring) very low.
Albert Einstein came up with a good definition of insanity:    Doing the same thing over and over again and expecting different results.
One can be reasonably certain that the end result of rates cut and quantitative easing won’t be any different this time as well. We’ll still be left with “no inflation”, but even higher systematic leverage and inflated asset prices.

With $16,000,000,000,000 of bonds trading at negative yields, which is roughly 20% of the global tradable bond universe, pension fund and insurance company deficits are putting pressure on pension funds to match assets and liabilities. At the same time, an aging population means that pension funds’ allocations are likely to shift towards fixed income instruments as the ability to withstand larger drawdowns on capital diminishes as people age. The ECB’s official inflation projections for the Eurozone CPI were downgraded to 1.2%, 1% and 1.5% in 2019, 2020 and 2021 respectively. This means that a purchase of a five year German government bond at issuance would lead to a guaranteed loss in the investor’s purchasing power of greater than 10% upon maturity, if indeed the bond is held in a buy and hold portfolio. Further extension in duration doesn’t really alleviate the problem since 30 year German bonds trade at negative yields- even on the primary market.

Such destruction of returns on investment will obviously land a heavy blow to the pension fund system and wreak havoc on the solvency of insurance companies.
Mario Draghi seemed blatantly unconcerned at Thursday’s press conference when he was asked about the potential side effects of negative interest rates policy. However, in the Netherlands, where an official inflation runs at 2.8%, lawmakers are very much concerned about side effects of unconventional monetary policy.

The Dutch civil servants’ pension fund, ABP, with 451 billion euros of assets under management, will be forced to cut pensions next year on current forecasts.

The States General of the Netherlands is keenly aware of the consequences of such unorthodox policy which run contrary to the kingdom’s national interest. Dutch lawmakers sent a formal letter on Wednesday to the European Central Bank expressing the parliament’s concerns. Pieter Omtzigt, author of the motion, said that tiering would effectively unduly benefit the southern Europeans, traditional bank savers, at the expense of Dutch retirees. “The negative interest rates of the ECB disproportionately hit the Dutch pension funds,” he told Reuters.

We have previously discussed the rise in populism, the destruction of the middle-class, and the divide between rich and poor as a result of negative interest rates and quantitative easing. Now there’s a new dimension in the discussion: a conflict among European Member States on the distributive effects of any policy steps. It will neither help cement the fundament of the European Union nor create an atmosphere of trust in the European nation-state family.

There is a glimpse of hope though.

There was an unprecedented revolt which took place during a fractious meeting according to Bloomberg despite the upbeat demeanor of Mr. Draghi. Bank of France Governor, Francois Villeroy de Galhau, joined more traditional hawks such as De Nederlandsche Bank president, Klaas Knot, and Bundesbank President, Jens Weidmann, in resisting an immediate resumption of bond purchases. Those three governors alone represent roughly half of the euro region as measured by economic output and population. Other dissenters included, but weren’t limited to, their colleagues from Austria and Estonia, as well as members on the ECB’s Executive Board including Sabine Lautenschlaeger and the markets chief, Benoit Coeure.

There is a chance that Christine Lagarde will be able to normalize the policy and deflate the asset bubble without too many side effects. Otherwise, I am afraid we will see many more of those infamous “25-standard deviation events, several days in a row.” Earlier this week we saw how sensitive risk premia factors are to the steepness of the interest rate curve after a decade of quantitative easing and negative interest rates. After yesterday’s cut in interest rates, and a new round of quantitative easing, these premia have become even more sensitive.]]>