Multi-Armed Bandit Approach to Portfolio Choice Problem

Finance master project by Güneykan Özkaya and Yaping Wang ’20

Image by bibblio

Editor’s note: This post is part of a series showcasing Barcelona GSE master projects. The project is a required component of all Master’s programs at the Barcelona GSE.


Historically, there have been many strategies implemented to solve the portfolio choice problem. An accurate estimation of optimal portfolio allocation is challenging due to the non-deterministic complexities of financial markets.  Due to this complexity, investors tend to resort to the mean-variance framework. If we consider the mean-variance framework, there are several drawbacks to this approach. The most pivotal one could be normality assumption on returns so that we could depict the behavior of returns only by mean and variance.  However, it is well known that returns possess a heavy-tailed and skewed distribution, which results in underestimated risk or overestimated returns. 

In this paper, we rely on a distribution of different metrics other than returns to optimize our portfolio. In simple terms, we combine several parametric and non-parametric bandit algorithms with our prior knowledge that we obtain from historical data. This framework gives us a decision function in which we can choose portfolios to include in our final portfolio. Once we have our candidate portfolio weights, we apply the first-order condition over portfolio variances to distribute our wealth between 2 candidate set of portfolio weights such that it minimizes the variance of the final portfolio. 

Our results show that if contextual bandit algorithms applied to portfolio choice problem, given enough context information about the financial environment, they can consistently obtain higher Sharpe ratios compared to classical methodologies, which translates to a fully automated portfolio allocation framework.

Key results

We conduct the experiments on 48 US value-weighted industry portfolios and consider the time range 1974-02 to 2019-12; The table below reports extensive evaluation criteria of following strategies by order; Minimum Variance Portfolio (MVP), Constant Weight Rebalance portfolio (CWR), Equal Weight portfolio (EW), Upper Confidence Bound 1 (UCB1), Thompson Sampling (TS), Maximum Probabilistic Sharpe ratio (MaxPSR), Probability Weighted UCB1 (PW-UCB1). Below the table, one can observe the evaluation of cumulative wealth through the whole investment period.

Table 1. Evaluation Metrics

One thing to observe here, even UCB1 and PW-UCB yield the highest Sharpe ratios. They also have the highest standard deviation, which implies bandit portfolios tend to take more risk than methodologies that aim to minimize variance, but this was already expected due to the exploration component. Our purpose was to see if the bandit strategy can increase the return such that it offsets the increase in standard deviation. Thompson sampling yields a lower standard deviation because TS also consists of portfolio strategies that aim to minimize variance in its action set.

Figure 1. Algorithm Comparison

We also include the evaluation of cumulative wealth throughout the whole period and in 10 year time intervals. One interesting thing to notice is that bandit algorithms’ performance diminishes during periods of high momentum followed by turmoil. The drop in the bandit algorithms’ cumulative wealth is more severe compared to classic allocation strategies such as EW or MVP. Especially PW-UCB1, this also can be seen from standard deviation of the returns. This is due to using the rolling window to estimate moments of the return distribution. Since we are weighing UCB1 with the Sharpe ratio probability, and since this probability reflects the 120-day window, algorithm puts more weights on industries that gain more during high momentum periods, such as technology portfolio. During the bubble (1995-2002) period, UCB1 and PW-UCB1 gain a lot by putting more weight on technology portfolio, but they suffer the most, during the turmoil that followed high momentum period. One can solve this issue by using more sophisticated prediction model to estimate returns and the covariance matrix.

Figure 2. 1974-1994 Algorithm Comparison
Figure 3. 1994-2020 Algorithm Comparison

To conclude, our algorithm allows dynamic asset allocation with the relaxation of strict normality assumption on returns and incorporates Sharpe ratio probability to better evaluate performances. Our algorithm could appropriately balance the benefits and risks well and achieve higher returns by controlling risk when the market is stable.

Connect with the authors

About the Barcelona GSE Master’s Program in Finance

Stealth trading in modern high-frequency markets

Finance master project by Alejandro García, Thomas Kelly, and Joan Segui ’20

Photo by Aditya Vyas on Unsplash

Editor’s note: This post is part of a series showcasing Barcelona GSE master projects. The project is a required component of all Master’s programs at the Barcelona GSE.


This paper builds on the stealth trading literature to investigate the relationship between several different trade characteristics and price discovery in US equity markets.  Our work extends the Weighted Price Contribution (WPC) methodology, which in its simplest form posits that if all trades conveyed the same amount of information, their contribution to market price dynamics over a certain time interval should equate their share in total transactions or total volume traded in the period considered. Traditionally, the approach has been used to provide evidence that trades of smaller sizes convey a disproportionate amount of information in mature equity markets through the estimation of a parsimonious linear specification.


The methodology is flexible enough to accommodate for a first set of key extensions in our work, which focus on studying the relative price contribution from trades initiated by high-frequency traders (HFTs) and on stocks of different market capitalization categories over the daily session. Nonetheless, previous research has found that short-lived frictions make the WPC methodology ill-suited for analyzing price discovery at under-a-minute frequencies, a key timespan when HFTs are in focus. Therefore, to analyze the information content of trades of different attributes at higher frequencies we use a Fixed Effects specification to characterize trades that correctly anticipate price trends over under-a-minute windows of varying length as price informative.

Key results

At the daily level, our results underpin prior research that has found statistical evidence of smaller trades inputting a disproportionate amount of information into market prices. This result holds regardless of the type of initiating trader or market capitalization category of the stock being transacted, suggesting that the type of trader on either side on the transaction does not significantly alter the average information content over the session. 

At higher frequencies, trades initiated by HFTs are found to contribute more to price discovery than trades initiated by non-HFTs only when large and mid cap stocks are being traded, consistent with prior empirical findings pointing to HFTs having a strong preference for trading on highly liquid stocks.

Connect with the authors

About the Barcelona GSE Master’s Program in Finance

Effects of Syndication on Investment Performance

Finance master project by Ozan Diken and Dominic Henderson ’20

Two people review reports together
Photo by bongkarn thanyakij from Pexels

Editor’s note: This post is part of a series showcasing Barcelona GSE master projects. The project is a required component of all Master’s programs at the Barcelona GSE.

Paper abstract

In venture capital, two or more venture capitalists (VC) often form syndicates to participate in the same financing rounds. Historically, syndicated investments have been found to have a positive effect on the investment performance. The paper provides insight into the effects of syndication on the likelihood of a successful exit for the venture-backed firm. It addresses the possible driving components such as the composition of the syndicates and, in particular, the internal investment funds being classed as external firms in two of the four models proposed, as well as a relaxation on the definition of investment round. One of the main conclusions is that in the analysis, using the chance of exiting and money in minus money out as success factors, syndication coefficients across all models are shown to have a higher chance of exiting. This supports the Value-add hypothesis and opposes the alternative, the Selection hypothesis, as it proposes that syndicated VC firms bring varying expertise to the project in order to increase the success factors post-investment. The paper advises to proceed with caution as the story is not consistent across the analysis.

Main conclusions

The paper aimed at looking to add to the literature of debates on reasons for syndication, such as the Valueadd vs Selection hypothesis as set out from various points of views. Uncertainty around profitability is the reason for syndication through the Selection hypothesis, however, the Value-add hypothesis suggests that VCs syndicate to add additional value to the venture post-investment. This is where the varying definitions of syndication we introduced, in order to draw inferences from the data. If the Soft definition of syndication (where syndication can occur across multiple investment rounds), was more successful, it may favour the Value-add hypothesis. However, in the initial test using “exited” as success, the Soft syndication models did not show a significant difference compared to the Hard syndication models.

bar chart

Using the chance of exiting as a success factor, syndication coefficients across all models showed a higher chance of exiting. Using this as a success factor, you could argue for the Value-add and against the Selection hypothesis, as syndicated investments across all models resulted in a higher chance of exiting the investment. Including the key controls, resulted in similar conclusions to be drawn, with syndication increasing the log odds of exiting. This does support the conclusions of Brander, Amit and Antweiler (2002) that highlight that the Valueadd hypothesis dominates.

Using Money Out minus Money In as a success factor it was shown syndicated investments increased this which would be in line with the Value-add hypothesis according to Brander, Amit and Antweiler (2002), however, this could be down to successful companies being input with greater investments which are already successful.

Using exit duration as a success factor, conclusions were unable to be drawn about syndication, as the syndication coefficients were not significant. A potential reason for this, as the literature suggests, Guo, Lou and Pérez-Castrillo (2015), highlight, that the type of fund the investment is being purchased for has an impact on the duration and amount of funding, therefore impacting the returns of the VCs. They find that CVC (corporate venture capital) backed startups receive a significantly higher investment amount and stay in the market for longer before they exit (Guo, Lou and Pérez-Castrillo, 2015). The data did not allow us to analyse the type of fund, meaning the investment strategy could differ from the outset. As no control variable exists for the type of fund it is therefore assumed this does not significantly impact the outcome. Controlling for the type of fund may have shed light on this aspect of the results.

Connect with the authors

About the Barcelona GSE Master’s Program in Finance

Does Fintech Contribute to Systemic Risk? Evidence from the US and Europe

ADBI Working Paper by Finance ’18 alumni Lavinia Franco, Ana Laura García, Vigor Husetović, and Jes Lassiter

A master project by four alumni of the Finance Program Class of 2018 is soon to be added to the working paper series of the Asian Development Bank Institute (ADBI).


Fintech has increasingly become part of the global economy with the evolution of technology, increasing investments in fintech firms, and greater integration between traditional incumbent financial firms and fintech. Since the 2007–2009 financial crisis, research has also paid more attention to systemic risk and the impact of financial institutions on systemic risk. As fintech grows, so too should the concern about its possible impact on systemic risk. This paper analyzes two indices of public fintech firms (one for the United States and another for Europe) by computing the ∆CoVaR of the fintech firms against the financial system to measure their impact on systemic risk. Our results show that at this time fintech firms do not contribute greatly to systemic risk.

Figure B.2: US Fintech: ∆CoVaR and Size
Figure B.3: US Fintech: ∆CoVaR and Beta
Figure B.4: European Fintech: ∆CoVaR and Size
Figure B.5: European Fintech: ∆CoVaR and Beta

Conclusions and key results

Our results show that, for the US, the payment and remittances and the market and trading support categories contribute the most to the VaR of the fintech industry. Instead, in Europe, fintech firms that provide software solutions and information technologies seem to be contributing the most to the risk of the sector. The estimation that includes fintech firms and the representative sample of the financial sectors show that fintech firms are not systemically important. Within the US financial system, the fintech companies that do contribute to systemic risk increase it by around 0.03%, while, in Europe, fintech firms contribute very little to the systemic impact (close to 0%). The Spearman’s rank correlation between a fintech firm’s ∆CoVaR and its respective size and between a fintech firm’s ∆CoVaR and its beta strengthens the importance of our estimations for a better assessment of systemic risk rather than just relying on the size and the beta of the firms to determine their likely contribution to systemic risk.

Some limitations of our study include the scope of our analysis method (∆CoVaR), the representation of the fintech sector, and the analysis of only two markets. However, micro-level data analysis focusing on each individual fintech category and changing the focus on emerging markets could reveal the specific risks, highlighting key research lines. 

About the authors

All of the authors are alumni of the Barcelona GSE Master’s in Finance, Class of 2018.

Making a Career in Private Equity: The Myths and the Opportunities

Jebb Peria ’10 (Finance), Associate at EV Private Equity

Jebb Peria ’10 recently answered some questions about careers in private equity in a post for his employer, EV Private Equity. Here are a few excerpts from the interview.

I’ve heard of private equity but how does it differ from, say, venture capital or fund management?

Fund management is basically a firm of money managers investing pooled funds from investors. The capital may be invested in traditional asset classes such as equities, fixed income and cash and alternative asset classes such as hedge funds, private equity, real estate, commodities and infrastructure. 

Private Equity (PE) is an active form of investment in privately held companies with the objective of growing them over a medium to long-term period. As active investors, PE firms work closely with management to increase and maximise the company’s value through financial engineering, improved governance and operational performance.

At EV Private Equity, we primarily invest in early-growth companies that have: a distinct product or service; the potential to grow rapidly; low levels of debt; and experienced management teams. We seek innovative and disruptive technology companies that can scale and drive superior returns.

Venture Capital (VC) is a subset of PE which provides capital to early-stage businesses, usually in technology-based sectors. Venture capitalists normally invest in high-growth, high-risk, start-up or early-staged ventures, typically with a bias towards technology or innovation. PE tends to focus on later-stage investment in businesses that are more established and are generating cash. VC uses primarily equity while PE may use equity and debt (leverage).

Both PE and VC use a measurement known as MOIC (Multiple On Invested Capital) to calculate the returns they make from their investments. PE target returns range from 2x-5x while VC returns are expected to be higher. 

Do I need an MBA from Harvard, a mathematics degree or an accountancy qualification in order to be considered?

No, not necessarily. As a matter of fact, I don’t have any of those credentials. I graduated with a BA in Economics (with highest distinction) from York University in Canada, an MA in Economics from the University of Toronto, and an MSc in Finance from Barcelona GSE. I am also a CFA® charterholder. I guess this depends on which type of PE firm you want to work with as there are generalists and specialists.

As energy specialists, our team at EV Private Equity is comprised of people with substantial experience in the energy industry [oil and gas (O&G), oil field services (OFS)] as well as those from technical disciplines (reservoir, drilling, mechanical, chemical, and software engineering as well as geophysics and naval architecture). We also recruit candidates with graduate business degrees in areas such as MBA, finance, economics, strategy etc.

Is it true that private equity is very secretive and is not accountable to any regulators or governments?


EV Private Equity is regulated by the Financial Conduct Authority in the UK and the SEC in the US under the Investment Advisor Act of 1940.  

Like any other firm, EV Private Equity and its portfolio companies are obliged to abide by the laws and regulations of all countries we operate in. This is also part of the fiduciary duty towards the firm’s institutional investors, comprised mainly of large public and private pension funds, insurance companies, university endowment funds and sovereign wealth funds.

What is a typical day like in private equity?

I typically start the morning reading through the latest news and market trends. I skim-through DagensNæringsliv, Bloomberg, Financial Times and even LinkedIn to check on the latest oil price, mergers and acquisitions (M&As) and geopolitical news. Then, I read through my emails to check for any updates on the portfolio companies I’m involved with and any immediate requests from the partners.

My day is normally split between fixed deliveries and ad hoc tasks. My deliveries would range from weekly meetings and operational updates with portfolio companies to monthly, quarterly and yearly financial reporting to updating fair market values of portfolio companies to weekly meetings with the digital marketing team. I would also participate in quarterly investor meetings, board meetings as well as annual strategy meetings with my portfolio companies.

If there’s a deal I am involved in, I would build the financial model, perform valuation and sensitivity analysis and support the drafting of the investment paper. I would also be participating in weekly call updates with the due diligence providers regarding any red flags and show stoppers (in other words, developments that may affect our decision to invest).

If one of my portfolio companies is preparing for an exit, I might be having calls with the management and the financial advisors discussing the potential buyers, the market sentiment and the status of the Information Memorandum (IM), the document we share with prospective buyers.

There is not much slack time. If I do have some spare time, I can always find something to work on: a process to simplify and make more efficient; a model to automate; improvements to our social media presence; or offering support to other office locations. 

What are the rewards?

Helping to create value for the company and produce superior returns for investors is rewarding and gratifying.

I also get to work with different partners, management teams, board members and technologies. These teach me different insights, strategies, and management styles.

It is very rewarding to work with the smart, entrepreneurial and down-to-earth group of individuals at EV Private Equity. They make the workplace fun and invigorating.

Of course, the job is also financially rewarding. I would like to believe that I am fairly and reasonably remunerated given my performance and contributions, the skillset I bring to the table, and my dedication to my craft.

Intrigued? Read the full interview with Jebb on EV Private Equity’s website!


Jebb Peria ’10 is an Associate at EV Private Equity in Norway. He is an alum of the Barcelona GSE Master’s in Finance.

LinkedIn | Twitter

Estimating Time-Varying Network Effects with Application to Portfolio Allocation

Finance master project by Daniel A. Landau and Gabriel L. Ramos ’19

Editor’s note: This post is part of a series showcasing Barcelona GSE master projects. The project is a required component of all Master’s programs at the Barcelona GSE.


In this paper, we characterize a variety of international financial markets as partially correlated networks of stock returns via the implementation of the joint sparse regression estimation techniques of Peng et al. (2009). We explore a number of mean-variance portfolios, with the aim of enhancing out-of-sample portfolio performance by uncovering the hidden network dynamics of optimal portfolio allocation. We find that Markowitz portfolios generally dissuade the inclusion of central stocks in the network, yet the interaction of a stock’s individual and systemic performance is more complex. This motivates us to explore the time-varying correlation of these topological features, which we find are highly market dependent. Building on the work of Peralta & Zareei (2016), we implement a number of investment strategies aimed at simplifying the portfolio selection process by allocating wealth to a targeted subset of stocks, contingent on the time-varying network dynamics. We find that applying mean-variance allocation to a restricted sample of stocks with daily portfolio re-balancing can statistically significantly enhance out-of-sample portfolio performance in comparison to a market benchmark. We also find evidence that such portfolios are more resilient during periods of major macroeconomic instability, with the results applicable to both developed and emerging markets.

Conclusion and Future Research

In our work, we represent 4 international exchanges as individual networks of partially correlated stock returns. To do so, we build a Graph, comprised of a set of Vertices and Edges, via the implementation of the joint sparse regression estimation techniques of Peng et. al (2009). This approach allows us to uncover some of the hidden topological features of a series of Markowitz tangency portfolios. We generally find that investing according to MPT dissuades the inclusion of highly central stocks in an optimally designed portfolio, hence keeping portfolio variances under control. We find that this result is market-dependent and more prevalent for certain countries than for others. From this cross-sectional network analysis, we learn that the interaction between a stock’s individual performance (Sharpe ratio) and systemic performance (eigenvector centrality) can be complex. This motivates us to explore the time-varying correlation ρ between Sharpe ratio and eigencentrality.

Optimal Weights for Tangency Portfolio Strategy.

Overall, we show that in considering the time-varying nature of partially correlated networks, we can enhance out-of-sample performance by simplifying the portfolio selection process and investing in a targeted subset of stocks. We also find that our work proposes a number of future research questions. Although we implement short-sale constraints, it would also be wise to introduce limits on the amount of wealth that can go into purchasing stocks, as this would help to avoid large portfolio variances. Furthermore, our work paves the way for future research into the ability of ρ-dependent investment strategies to enhance portfolio performance in times of macroeconomic distress and major financial crises.

Authors: Daniel A. Landau and Gabriel L. Ramos

About the Barcelona GSE Master’s Program in Finance

Option Pricing in the Heston Stochastic Volatility Model: An Empirical Evaluation

Master project by Patrick Altmeyer, Jacob Daniel Grapendal, Makar Pravosud, and Gand Derry Quintana ’18

Editor’s note: This post is part of a series showcasing Barcelona GSE master projects by students in the Class of 2018. The project is a required component of every master program.


Patrick Altmeyer, Jacob Daniel Grapendal, Makar Pravosud, and Gand Derry Quintana

Master’s Program:


Paper Abstract:

There exists a substantial body of literature concerned with the calibration of the Heston model for pricing financial derivatives under stochastic volatility, many of which rely on computationally expensive algorithms. Our paper evaluates a calibration method of the Heston model proposed by Alòs, De Santiago, and Vives (2015), which can be used to price derivatives with little computational effort. The calibration method is innovative in the sense that it considers only the three most critical regions of the implied volatility surface. The regions where the underlying option is, firstly, at-the-money, secondly, close to maturity and lastly, far away from maturity. Although their procedure is parsimonious and very easy to implement, they calibrate a model whose empirical applicability is contested.

The main contribution of our paper is the evaluation of their model in an extensive numerical exercise as well as an application to real data. Collecting empirical option data has been one of the main challenges with respect to this work, since historical data on financial derivatives is not accessible to the public. Faced with this issue we have written a script that allowed us to automatically scrape option data at a high frequency over just a couple of weeks. Thus, we build our own extensive data base. Also, we have made the data and code available on and, respectively.

In terms of our results, we find that whilst the calibration method has solid theoretical foundations and produces satisfactory estimation results within the theoretical Heston universe. However, it fails in practice. Specifically, for the numerical exercise we find that out of all simulations the maximum average error across the entire volatility surface is 0.999 percent while the mean error across simulations is only 0.481 percent. In sharp contrast to that, absolute percentage errors for our empirical data are on the order of 30-40 percent in many cases. In the following figure, we present our findings for intra-daily data from May 16, 2018. The left column shows empirical implied volatilities for a European call option on Facebook Inc. (FB) stocks. From top to bottom volatilities are shown for the opening, lunch and closing sessions. The central column shows the fitted volatility surfaces while the right column shows absolute percentage differences between empirical and estimated values. The finding that errors are particularly high for at-the-money options with short times to maturity is robust across the entire data sample.

Conclusions and key results:

In light of these results, we conclude that inherent limitations of the Heston Model disqualify the calibration for practical use. Nonetheless, we believe that similarly simple calibration methods as the one examined here should be used in combination with more sophisticated option pricing models.


Alòs, Elisa, Rafael De Santiago, and Josep Vives. 2015. “Calibration of Stochastic Volatility Models via Second-Order Approximation: The Heston Case.” International Journal of Theoretical and Applied Finance 18 (06). World Scientific: 1550036.

Download the full paper [pdf]

More about the Finance Program at the Barcelona Graduate School of Economics

Economics articles by BGSE alumni at CaixaBank Research

Ricard Murillo, Marta Guasch, and Mar Domènech in front of Caixabank. Photo by Marta Guasch.

We’ve just come across some articles written by several Barcelona GSE Alumni who are now Research Assistants and Economists at Caixabank Research in Barcelona. New articles are published each month on a range of topics.

Below is a list of all the alumni we found listed as article contributors, as well as their most recent publications in English (click each author to view his or her full list of articles in English, Catalan, and Spanish).

If you’re an alum and you’re also writing about Economics, let us know where we can find your stuff!

Gerard Arqué (Master’s in Macroeconomic Policy and Financial Markets ’09)

The (r)evolution in the regulatory and supervisory framework resulting from the crisis

Mar Domènech (Master’s in International Trade, Finance, and Development ’17)

Registered workers affiliated to Social Security: situation and outlook across sectors

Active labour market policies: a results-based evaluation

Equal opportunities: levelling the playing field for everyone

Cristina Farràs (Master’s in Macroeconomic Policy and Financial Markets ’17)

The financial situation of Millennial households in the US and Spain: will they catch up with previous generations?

Measures to improve equality of opportunities

Marta Guasch (Master’s in International Trade, Finance, and Development ’17)
and Adrià Morron (Master’s in Economics ’12)

Jay Gatsby’s American Dream: between inequality and social mobility

Ricard Murillo (Master’s in International Trade, Finance, and Development ’17)

Inflation will gradually recover in the euro area

Millenials and politics: mind the gap!

The sensitivity of inflation to the euro’s appreciation

Ariadna Vidal Martínez (Master’s in Finance ’12)

Situation and outlook for consumer financing

Source: Caixabank Research

Can misguided monetary policy explain the European housing bubble?

Patrick Altmeyer (Finance student ’18) who has an interest in monetary policy, shares his work on whether misguided monetary policy can explain the European housing bubble.

Property prices surged throughout Europe in the early 2000s before collapsing during the crisis and causing tremendous welfare losses. This dissertation uses Structural Vector Autoregression (SVAR) to analyse the role of house prices within the monetary transmission mechanism in Europe over the past decades in order to understand whether lax interest rate policy had caused the bubble. Quarterly observations of inflation, output, consumption, real estate prices and mortgage variables for eight European countries were used. Sample periods vary by model specification but generally four decades.

Impulse response functions for the baseline SVAR suggest that real estate prices did indeed respond positively to dovish monetary policy and thereby amplified conventional effects on consumer spending. However, the interpretation of these preliminary results is complicated by explosive house price dynamics during the early 2000s. The linear vector autoregressions fail to fully capture these non-linear elements of the time series. A statistical test developed by Homm and Breitung (2012) is therefore used to identify bubble periods in the various countries analysed. Explosive house price dynamics are found in all countries but Germany as shown in Figure 1.

Figure 1: House price trends in European countries. Shaded areas indicate bubble periods.

Information about house price bubbles is subsequently used to augment the baseline SVAR in various ways. Consequently, the measured effect of a decrease in interest rates on house prices remains positive, but to a lesser extent. Overall, evidence found here suggests that interest rate policy alone was not responsible for the European housing bubble. Rather, it appears that the boom could be better explained by joint effects of loose monetary policy, financial liberalisation and associated mortgage market innovations. Note, for example, that total securitisation activity measured in terms of the number of euro-denominated asset-backed securities outstanding increased six fold from 2000 until the credit bubble burst in mid 2007. Unsurprisingly, many have drawn a connection between monetary policy and securitisation commonly arguing that the latter amplified the conventional credit effects of the former. Information about mortgage rates and lending activity is used as a proxy for mortgage securitisation and added to the SVAR in the final section of the empirical part. Indeed, these variables are found to have high explanatory power with respect to house price trends in most countries as evident in Figure 2, which plots forecast error variance decompositions for each country under the preferred model specification.

Figure 2: Forecast error variance decompositions.

The paper therefore concludes that stricter interest rates more closely aligned with policy rules could not have entirely avoided the bubbles, hence this approach is not recommended for the future. Putting more focus on asset price stability and thereby departing from the policy rate’s traditional role of smoothing consumption and consumer prices would be too complicated and is therefore not advisable, either. In light of the finding that financial innovations have greatly contributed to bubbles, policy makers should continue current efforts on imposing stricter regulation through macroprudential measures.

The full article can be read here.

Partial Adjustment in Policy Functions of Structural Models of Capital Structure

Editor’s note: This post is part of a series showcasing Barcelona GSE master projects by students in the Class of 2017. The project is a required component of every master program.


Mattia Bongini

Master’s Program:


Paper Abstract:

We present a tradeoff model of capital structure to investigate the sources of adjustment costs and study how firms’ financing decisions determine partial adjustment toward target leverage ratios. The presence of market imperfections, like taxes and collateral constraints, is shown to play a decisive role in the behavior of the policy function of capital and leverage. By means of a contraction argument, we are able to show the existence of a target leverage towards which optimal leverage converges with a speed of adjustment that depends on a firm marginal productivity of capital. Our predictions are consistent with the empirical literature regarding both the magnitude of the speed of adjustment and the relationship between leverage ratios and the business cycle.


In this work we showed how financial and economic frictions are able to generate a partial adjustment dynamics in leverage policy functions. In the model we studied, the key factors of this phenomenon are collateral constraints (which strike a balance between tax benefits of debt and distress costs) and firm productivity of capital. The latter, in particular, determines the speed of adjustment towards the (state-dependent) target leverage ratio.

Our model fits well several stylized facts of leverage dynamics established by the empirical literature: an example is given by the magnitude of the speed of adjustment, which falls into the confidence intervals estimated by several authors. Another one, is the countercyclical behavior of leverage dynamics with respect to the business cycle, which is due to the fact that in recessions it is easier for the collateral constraint to be binding.

Future work should first address the translation of the hypotheses of Theorem 5.4 on the Lagrange multiplier into assumptions on the components of the model (the production function and the various market frictions). The next step would then be to extend the model to a full general equilibrium model to study thoroughly the effects of preference and monetary shocks on leverage dynamics. Pairing consumers’ utility maximization with firms’ financing problem would also allow to study the interaction between expected returns and partial adjustment: in such framework, the collateral constraint should probably be replaced by several credit rating inequalities determining both firm specific discount rates and target leverage ratios.