Our research arises in a context where “free” services in one market cannot be understood without taking into consideration the other side of the market. The Spanish free-to-air TV industry is a two-sided market in which viewers demand TV programs (for free) and advertisers demand advertising spots for which they pay a price that depends mainly on audience. Our main contribution to the two-sided market literature is estimating both viewers and advertisers demand to be able to understand the interactions of both sides of the free-to-air TV market.
This analysis is carried out by developing an econometric analysis of the free to air TV market in Spain that captures the reaction of viewers to a change in advertising quantity and the effect on price of ads that this would bring. We specified Viewers Demand in the Spanish free-to-air TV through a logit model to analyse the impact of advertising minutes on the audience share and, we specified Advertisers Demand by an adaptation of the model of Wilbur (2008) to understand the effect of audience share and advertising quantity on prices of ads.
Conclusions
The results of the Viewers Demand model show an elastic demand and that viewers are averse to advertising regardless of the day but during prime time they are a bit more ad tolerant, especially from 10pm to 11 pm.
On the other side of the market, the Advertising Demand model shows that advertisers are relatively inelastic to both an increase of adds and an increase in audience share. This may be due to the fact that the data available for this project is precisely coming from the most viewed channels, for which advertisers would have more inelastic demand.
As expected, the results show that advertisers are more elastic with regards to audience share than to quantity of advertising.
In this study, we propose an approach for the extraction of a low-dimensional signal from a collection of text documents ordered over time. The proposed framework foresees the application of Latent Dirichlet Allocation (LDA) for obtaining a meaningful representation of documents as a mixture over a set of topics. Such representations can then be modeled via a Dynamic Linear Model (DLM) as noisy realisations of a limited number of latent factors that evolve with time. We apply this approach to Federal Open Market Committee (FOMC) speech transcripts for the period of Greenspan presidency. This study serves as exploratory research for the investigation into how unstructured text data can be incorporated into economic modeling. In particular, our findings point at the fact that a meaningful state-of-the-world signal can be extracted from expert’s language, and pave the way for further exploration into the building of macroeconomic forecasting models, and in general into the usage of variation in language for learning about latent economic conditions.
Key findings
In our paper, we develop a sequential approach for the extraction of a low-dimensional signal from a collection of documents ordered over time. We apply this framework to the US Fed’s FOMC speech transcripts for the period 08-1986 to 01-2006. We retrieve estimates for a single latent factor, that seem to track fairly well a specific set of topics connected with risk, uncertainty, and expectations. Finally, we find a remarkable correspondence between this factor and the Economic Policy Uncertainty Indices for United States.
In this thesis project I analyse labour flow networks, considering both undirected and directed configurations, and company control networks in the UK. I observe that these networks exhibit characteristics that are typical of empirical networks, such as heavy-tailed degree distribution, strong, naturally emerging communities with geo-industrial clustering and high assortativity. I also document that distinguishing between the type of investors of firms can help to better understand their degree centrality in the company control network and that large institutional entities having significant and exclusive control in a firm seem to be responsible for emerging hubs in this network. I also devise a simple network formation model to study the underlying causal processes in this company control network.
Conclusion and future research
Intriguing empirical patterns and a new stylized fact are documented during the study of the company control network, since there is suggestive evidence that the types and number of investors are strongly associated with how “interconnected” a firm is in the company control network. Based on the empirical data it also seems that the largest institutional investors mainly seek opportunities where they can have significant control without sharing it with other dominant players. Thus the most “interconnected”/central firms in the company control network are the ones who can maintain this power balance in their owner structure.
The devised network formation model helps to better understand the potential underlying mechanisms for the empirically observed stylized facts about the company control network. I carry out numerical simulations, sensitivity analysis and also calibrate parameters of the model using Bayesian optimization techniques to match the empirical results. However, these results could be “fine-tuned” at different stages further, in order to have a better empirical fit. First, the network formation model could be enhanced to represent more complex agent interactions and decisions. But also, the model calibration method could be extended to include more parameters and a larger valid search space for each of those parameters.
This project could also benefit from improvements to the utilised data. For example more granular data on the geographical regions could help to understand the different parts of London more and to have a more detailed view of economic hubs in the UK. Moreover, the current data source provides a static snapshot of the ownership and control structure of firms. Panel data on this front could enhance the analysis of the company control network, numerous experiments related to temporal dynamics could be carried out, for example link prediction or testing whether investors follow some kind of “preferential attachment” rules when acquiring significant control in firms.
Asymmetric pricing in the retail fuel market describes the situation in which retail prices are adjusted quickly in case of positive shocks in the wholesale costs, whereas the adjustment is much slower in case of negative ones. This asymmetry in the reaction of retail operators is captured by the well-known expression rockets and feathers. By relying on a reduced version of a database used in Moral and Gonzalez (2019) containing the series of diesel prices in Spain and Brent prices for the period 08/2014-06/2015, we address the following research question: how did the fuel prices of the retail gas stations in a subset of Spanish provinces react in this period to changes in the price of Brent? In order to answer this question, we construct a pricing equation that takes into account all the possible factors that can affect pricing with the aim of isolating the effect of negative shocks and the effect of positive shocks in the price of Brent on the price of gasoline of the various Spanish operators. Then, we check whether the difference between these two effects is statistically significant to see whether there were asymmetric reactions. Furthermore, since the common rocket and feathers phenomenon could be considered as a collusive device, and since in the period covered by the database a cartel was active among the main fuel companies in Spain, we also investigate the relation between asymmetric pricing and competition.
Figure 1. Spatial distribution of gas stations in Barcelona
Conclusions
The aim of our project was to capture the presence of asymmetric pricing in nine Spanish provinces between 2014 and 2015 by taking into account the fact that during the period considered the CNMC fined five of the largest oil companies in Spain for collusion. To do this, we estimated an Error Correction Model for each province by accounting for both panel heterogeneity and cross-sectional dependence to capture both the short-run and the long-run relation between the retail diesel prices and the Brent price.
Our results show that there exists a correction mechanism that pushes the retail prices back to the long-run equilibrium relation with the Brent in case of shocks, even if the magnitude of the correction may be overestimated potentially because of the pattern of the retail fuel price in the period before the fine of the CNMC became public.
Figure 2. Evolution of the Brent price and the average retail fuel price in Alicante in the period considered. Note that the CNMC fined the major oil companies in Spain in February 2015.
As far as the short-term adjustments are concerned, the results are less clear because of the lack of significance of most of the coefficients; this is potentially due both to the presence of imperfect collinearity arising from issues with the lag selection in each province as well as to the already mentioned patterns of the diesel prices. Furthermore, as to what concerns the effect of the fine of the CNMC, the results show that in many provinces there is some variability in the pricing of the gas stations after February 2015 that is not accounted for in the rest of the model. We may not confidently state that this is entirely due to the fine of the CNMC: in fact, the related coefficient may capture some variability due to the attempts of firms of recovering the losses incurred before the fine was issued. Consequently, we suggested that we may need to first solve the issue of the lag selection and then, if the effect of the fine is still significant, we may eventually add some control for the profitability of the firms, even if this would imply expanding the database because of the absence of variables capturing the evolution of profits of the firms observed.
To conclude, although our analysis may still need some refinement especially in the lag selection procedure, we suggest that the relation between asymmetric pricing and competition is worth exploring. In addition, it would be also interesting to understand whether aggregating the data in the database we used at a weekly level, for instance, would lead to different estimates and insights or would simply lead to biased findings as suggested in the literature.
The Global Financial Crisis prompted central banks to adopt unconventional monetary policies such as the asset purchase programs. In our thesis, we analyze whether securities purchases carried out by the ECB have had an impact on stock prices and whether these effects vary across sectors. We decompose the central bank announcement surprises into two opposing effects, a pure monetary policy shock and an information shock. We find that the pure monetary policy shock has indeed significant effects on stock prices across all sectors, suggesting that controlling for the information shock is important when analyzing the effects of central bank announcements.
Conclusions
In our paper, we analyzed the effects of Quantitative Easing on stock prices in the Euro Area. Adding to previous literature, we not only analyzed the effect on the benchmark index but considered sectoral indices as well in order to allow for heterogeneous responses across different industries. Using the methodology of Altavilla et al. (2019), we first extracted the QE factor from each ECB press conference, starting from 2002. In a first exercise, we used the QE factor as a regressor to explain stock price changes on the press conference days. In line with asset pricing theory, we find negative effects of the QE shock on all sectoral stock price indices, yet, significance differs.
Overall QE Shock
In a second step, we decomposed the shock into two components, using sign restrictions. The two shocks are referred to as information shock and pure monetary policy shock and are characterized by positive co-movement and negative co-movement of interest rates and stock prices, respectively.
Information Shock
Pure Policy Shock
We looked at these two components separately in order to assess whether insignificant results obtained in the overall regression may be due to the two components off-setting each other, a presumption which was confirmed. Furthermore, we find that the pure monetary policy shock has significant effects on stock prices across all sectors, while the information shock appears to be more important on specific sectors, which are more related to financial markets. A more in-depth analysis of the reasons for this heterogeneity could provide further insight into the effects of QE on stock prices. Moreover, repeating this exercise with a larger sample and intraday stock price data might yield improved results. Other extensions could be the analysis of specific sectors for various countries.
Labor share, once thought to be a constant, has experienced a secular decline in many developed economies. We investigate whether adjustment costs to intangible capital can be used to explain this trend. We develop a simple partial equilibrium model with a profit maximizing firm that produces using a three factor CES production function and faces convex adjustment costs to intangible capital. We find an intuitive expression for the steady state labor share as a function of parameters and the steady state level of investment in intangible capital.
We then run simulations to better understand the behaviour of the labor share in our model. Somewhat surprisingly, we find that adjustment costs do not affect the steady state labor share for any given elasticity of substitution. However, their presence creates a strong relationship between the labor share and the elasticity of substitution. We also find a number of short-run dynamics that are affected by the level of adjustment costs.
Labor share trends over the last 60 years in the United States. Source: AMECO
Conclusions
We find that our model with adjustment costs leads to a very clear relationship between the elasticity of substitution and the labor share. Therefore, one could use it to explain the secular decline in the labor share as a result of a falling elasticity of substitution in presence of convex adjustment costs to intangible capital. However, in our simple model there does not appear to be a meaningful relationship between the level of convex adjustment and the steady state labor share. Moreover, adjustment costs affect a number of interesting short-run dynamics. The level of adjustment costs changes the responsiveness of the labor share to variations in the price of inputs. Lastly in our simple model the volatility of the price process does not alter the steady state labor share, even though it does matter for short-run dynamics.
We see room for further research in the following directions. Our analysis assumes perfectly competitive markets. A model of monopolistic competition in the goods market could lead to long-run effects of the level of adjustment costs on the labor share. Karabarbounis and Neiman, 2013 showed that in such a model price decreases can explain part of the decrease in the labor share. Therefore, analysing the effect of adjustment costs in the context of monopolistic competition seems promising. Another potential avenue is the generalization of the analysis to a general equilibrium setting.
Understanding endogenous changes in wages that were set to be fixed throughout our analysis, could be important in explaining the changes in the labor share.
Using a dynamic panel fixed effects model, we find that increases of ODA of above 2% of GDP have significant effects on the economic growth of African countries in the immediate aftermath of severe natural disasters. This is a surprising result because we do not find that ODA in times of relative stability has a significant effect on GDP. This suggests that debt relief, at least through the channel of significant increases in ODA, is an effective instrument in promoting post-disaster recovery, even though its effectiveness in raising economic growth more generally is limited. Since increases in ODA inflows of above 2% of GDP only occurred after 1/3 of the disasters we studied, we recommend that international financial institutions concentrate ODA flows on countries that had been afflicted by severe disasters.
Introduction
One of the biggest challenges facing developing Sub-Saharan African economies is their vulnerability to severe natural disasters such as droughts and floods. Not only do they face on average over 50 disasters a year, but their economies’ over-reliance on agricultural production and weak institutional capacity cause them to experience the effects of these disasters particularly acutely. Worryingly, this vulnerability is likely to rise in the coming years, as the earth warms and climate change increases the number and severity of extreme climatic events.
While it is difficult for countries to prevent natural disasters, since they tend to arise from exogenous climate conditions, they can take steps to mitigate these adverse consequences through post-disaster rehabilitation. To do so, governments require sufficient fiscal space so that they can borrow and spend without jeopardising budgetary sustainability. However, many African countries suffer from persistently high levels of debt, with 33 of the 39 countries in the Heavily Indebted Poor Countries scheme located on the continent. This constrains government spending on humanitarian relief and reconstruction, which can leave countries unable to recover from the devastation.
In view of these twin trends – African economies’ vulnerability to natural disasters and their crippling levels of debt – any channel that reduces a country’s debt burden and hence increases its fiscal space should theoretically encourage faster economic recovery. This suggests that debt relief can be a vital policy instrument in mitigating the negative effects of natural disasters. However, corruption and inefficient resource allocation mean that its effectiveness may be constrained in practice. To explore the role of debt relief further, we employ a dynamic panel fixed effects model across the most severe 25 floods and 68 droughts in Africa from 1978 to 2013. As a robustness check, we also include an Anderson-Hsiao style GMM estimation procedure. We define debt relief as any policy that reduces the need for governments to issue new debt or repay existing debt, particularly in the aftermath of a natural disaster. In the context of this paper, this includes debt forgiveness, debt rescheduling and/or increased official development assistance (ODA). Furthermore, we run two different specifications of debt relief: first, using a dummy variable which indicates any instance of the aforementioned forms of debt relief; and second, using a continuous variable for ODA inflows alone.
Main findings
Surprisingly, when we run our first specification, we find that debt relief in general does not have a statistically significant impact on economic growth. Additionally, ODA inflows in times of relative stability do not have significant effects on economic growth. Instead, they only reduce debt-to-GDP growth, suggesting that they are merely used by governments to pay off existing debt. This is in line with previous research by both Mejia (2014) and Raddatz (2009), who found at most weak evidence that either debt relief in the aftermath of disasters or ODA in general is effective in boosting economic growth.
In contrast, we find that increases in inflows of ODA of above 2% of a country’s annual GDP, when provided in the year of or immediately after severe disasters, do have statistically significant positive effects on economic growth (see Figure 1). These findings are similarly observed when we interact our ODA variable with the continuous measure of disaster severity. For a given level of ODA, the effectiveness of post-disaster ODA increases in the severity of the underlying disasters. Furthermore, ODA inflows no longer have statistically significant effects on debt-to-GDP growth. This suggests that, unlike in regular times, ODA flows are used fruitfully by governments after disasters to bolster economic recovery rather than to pay off existing debt.
Figure 1
This is a notable result because it suggests that debt relief, at least through the channel of ODA, is an effective instrument to promote post-disaster recovery. This result differs from that found by previous research because we focus on ODA increases that a) were larger than 2% of GDP and b) occurred in the aftermath of severe natural disasters. This helps us isolate the specific role of ODA in promoting post-disaster recovery from its general effectiveness as a form of economic stimulus to boost growth.
Policy implications
Our findings suggest that policymakers in international financial institutions such as the OECD or IMF should step up efforts to increase ODA inflows to developing countries when severe natural disasters hit. This not only has the direct effect of reducing the loss of lives, but is also vital for poverty reduction by ensuring that these countries return rapidly to their existing balanced growth path. Otherwise, countries risk experiencing persistent economic slowdown and skyrocketing debt due to the disasters, which would in turn lead to a vicious cycle of mounting debt and stagnant growth. Instead, increased ODA flows can substitute for the domestic shortfall in resources available to countries to rehabilitate the economy by providing emergency relief to citizens and rebuilding damaged infrastructure.
Current attempts at mitigating such disasters are relatively limited: in our sample of 92 severe disasters in Africa between 1978 and 2013, large increases of ODA greater than 2% of GDP only occurred after 32 of these disasters. This is surprisingly infrequent, especially considering that we focus only on the largest of disasters which should have ample international media coverage. As highlighted above, larger increases in ODA have greater cumulative effects on the economy, especially for more severe disasters. As this effect is not observed when we study ODA inflows in times of stability or inflows below 2% of GDP, we recommend that existing ODA programmes prioritise large flows to countries which have just suffered from severe natural disasters. This is because the marginal benefit of these targeted flows in promoting development is likely higher than general flows to countries that are relatively stable.
Finally, although our paper focuses on floods and droughts in Africa, we believe that our results can be generalized to other types of disasters. Although further research is needed to fully establish the causal mechanism by which debt relief improves post-disaster outcomes, it is likely that it will have a similar positive impact in rehabilitating economies that face disasters which leave them with high levels of debt and significantly lower budgetary revenue. Most notably, it suggests that significant increases in ODA flows can play a vital role in helping developing economies devastated by the COVID-19 pandemic by allowing them to mitigate its adverse effects.
Mejia, S. A. (2014, July). Debt, Growth and Natural Disasters A Caribbean Trilogy (IMF Working Papers No. 14/125). International Monetary Fund. Retrieved from https://ideas.repec.org/p/imf/imfwpa/ 14-125.html
Our paper examines the wages and career prospects of employees in flexible work arrangements (FWAs). Using the British Household Panel Survey, we analyse the effect of being in a FWA on hourly wages and the likelihood of promotion. We use the occupational share of employees in FWAs before and after the introduction of “Right to Request” (R2R) legislation as an instrument to control for sample selection. Applying our instrument in pooled OLS and linear regression models, we find that flexible workers, particularly women, may receive higher wages than their non-flexible counterparts. This supports theoretical arguments that FWAs could increase labour productivity.
Conclusions
Our findings imply that there may be no penalty associated with workers adopting flexible working practices. Our instrumental variables wage model implies there could in fact be a reverse effect: coefficients changed from negative. In particular, the effect of FWAs was significant and large for women, leading to an approximately 9 percent increase in their wages. Those in FWAs have higher wages than those in conventional working arrangements, controlling for variables such as occupational choice, hours worked, and personal circumstances (including number of children and educational background). Similarly, we cannot reject the hypothesis that FWA has no impact on career progression, when modelling promotions as a 10 percent pay rise versus the previous year.
Income Distribution and FWA
We do find some evidence that working flexibly decreases the difference in wage outcomes between men and women. The approximately 9 percent increase in wages associated with our FWA variable in our women-only specification compares to a 5 percent increase in our men-only specification. We cannot reject the hypothesis that FWAs have no effect on men’s wages. We find evidence women in FWAs are paid significantly more than their non-flexible counterparts.
This begs the question: why do those in FWAs appear to achieve better labour market outcomes than those not in FWAs? This appears to contradict some findings of economic theory on compensating wage differentials and the effects of similar working arrangements, such as part-time work. Further, the fact that our wage findings were highly significant for women (and not for men) appears to go against the gendered difference in how men and women use flexible working; men are more likely to use FWAs to improve their career outcomes, whilst women use FWAs to accommodate care needs.
First, we could have captured a range of productivity benefits that often come alongside flexible working practices. The increase in schedule control may improve worker satisfaction and hence productivity in itself, but is also often associated with better workplace practices such as improved management (Bloom et al, 2010). The increase in flexible working seen across many sectors (such as services) following the R2R reforms may have disproportionately benefited them ahead of other, less “flexible” sectors. The UK, with more than two-thirds of its labour force in the service sector, may have seen a productivity rise associated with more employees having greater scheduling control. Increases in productivity may then have been passed on to flexible-working employees in the form of pay rises above the mean.
Second, our model may neglect important social trends. The R2R legislation may have accompanied shifting attitudes towards flexible working, which spurred an increase in the compensation afforded to flexible workers. Future research examining historical trends in the remuneration of employees in FWAs could provide more detail on this.
Peer-to-peer home-sharing platforms such as Airbnb are a new phenomenon which many researchers consider to be responsible for significant disruptions in the housing market. Prior to the introduction of these platforms into the rental market, hotels were the primary supplier of short-term rentals, while residential properties almost exclusively operated on the long-term rental market. The introduction of short-term rental platforms like Airbnb, allows homeowners to choose either to supply on the short-term or the long-term rental markets. As a result, when residential properties are moved to the short-term rental market, the quantity of housing supplied on the long-term rental market decreases, inducing an upward pressure on long-term rents.
In our paper, we offer a novel approach to investigate the extent to which the expansion of the sharing economy is responsible for increases in long-term rents and prices on the housing market. To this end, we construct a theoretical framework for the housing market that allows for spillover effects between neighborhoods, and other local externalities caused by tourism. The model allows for the short-term housing market devoted to tourism to impact both long-term rental rates and housing prices. Using a panel of quarterly data on newly signed rental contracts and transaction prices in Barcelona from 2015-Q2 to 2018-Q4, we implement a fixed-effects spatial 2SLS method allowing for endogeneity in the variable which measures the presence of Airbnb.
Airbnb listings in Barcelona (2018-Q2)
Barcelona, which hosts the sixth largest concentration of Airbnb listings in the world, serves as a prime case study to investigate these effects because our dataset covers growth rates in contractual rental rates, transaction prices and the number of active Airbnb listings of 27.42%, 27.41% and 29.38%, respectively.
Key results
The theoretical model predicts that a change in the level of Airbnb activity might affect both long-term rents and housing prices. In fact, if negative externalities generated by tourists are sufficiently small, Airbnb leads to increases in long-term rental prices. Yet, these effects ultimately depend on the values of parameters such as the size of the stock of housing units and the level of externalities emerging from tourism. In addition, the model bears upon the effects of Airbnb on gentrification and displacement: we find that for a positive increase in the negative externalities generated by tourism, the proportion of homeowners renting in the short-term market will increase. As the degree to which residents are harmed by negative externalities increases, more of them will decide to abandon their neighborhood, reducing the local demand for long-term housing. As a result, rents will suffer a downward pressure, increasing the relative profitability of the short-term rental market for homeowners. Besides, this effect will be aggravated if the degree of inter-neighborhood dependence generated by externalities is high. Residents will be prone to move to other neighborhoods in which not only the presence of Airbnb is low, but also in which the penetration of this marketplace is low in the surrounding areas.
We refer to this process as Airbnb-induced gentrification. Similarly, if the profitability of renting a property on Airbnb increases, a similar process as the one we have just described above would arise, which would also lead to gentrification.
For another thing, our main empirical results show that Airbnb positively and significantly affects rents, even when accounting for spatial dependence and inter-neighborhood spillovers. In a given neighborhood (as classified in this paper), for every additional 100 Airbnb listings, rents increase by an average of 2.1% when indirect spillovers coming from adjacent neighborhoods are included. In particular, the direct effect of Airbnb within a given neighborhood accounts for much of this effect: the own-neighborhood effect is to induce a 1.7% increase in rents. The maximum average indirect effect found in the sample data accounts for 35% of the total effect. The implications of these findings are far reaching and suggest that spillover effects can indeed explain a large portion of rent increases. Likewise, we identify a potential bias in the previous literature in that the total effect is falsely interpreted as the direct effect, thereby misinterpreting the direct effect of Airbnb on long-term rents.
Empirical Results: Main Impact Measures
In contrast, our empirical results show that Airbnb has had no significant effect on transaction prices. The most plausible explanation for the non-significant results for prices is that homeowners do not believe that Airbnb is sustainable in the long-run, and therefore they do not adjust their predicted future cash flows when valuing their properties.
Finally, we believe that future research could delve into more detailed theoretical models, especially with respect to the price setting by homeowners in light of the establishment of Airbnb. Additionally, we think that making a distinction between direct and indirect neighborhood effects is vital in order to truly understand the dynamics of the housing markets, especially in the growing metropoles. Accordingly, we encourage scholars to further apply and develop spatial econometric methods that measure indirect spillover effects in studies related to housing markets.
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 dot.com 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.
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