THE RELATIONSHIP BETWEEN MACROECONOMY AND ASSET PRICES: LONG-RUN CAUSALITY EVIDENCE FROM LITHUANIA

. The purpose of this paper is to determine the long-run causal impact of various economic factors on Lithuanian stock, government securities and real estate prices, and to assess how accurately future asset returns can be forecasted based solely on economic information. Five macroeconomic indicators, namely, gross domestic product (GDP), foreign direct investment (FDI), consumer price index (CPI), money supply (MS) and Vilnius interbank offered rate (VILIBOR), were included in the model. The results of the created autoregressive distributed lag model (ARDL) revealed that a long-run causal relationship between Lithuanian assets and macroeconomic variables exists and that changing values of these indicators explain about half of the variability of assets’ returns. The results of ARDL model forecast showed that the most precise predictions are obtainable in real estate market, while forecasted returns of stock and government securities are not so accurate, especially the further forecast horizon. The possibility to understand driving factors behind changes of asset prices and to predict future return is of a particular importance not only for investors and businessmen, but also for the policy makers who are responsible for making substantiated decisions regarding monetary, macroprudential and fiscal policies they conduct.


Introduction
How to distribute one's funds successfully? is question arises to the majority of novice or even experienced investors. e search of few undervalued or fast-growing companies and the purchase of their shares or bonds with all available funds is the most commonly used approach. However, due to excessive non-systematic risk (i.e. risk that results from unpredictable factors and is unique to a certain asset or a company) such plain strategies mostly mis re in the long-run, so it is no surprise that the majority of individual or even institutional investors are unable to surpass broad market indices. According to Brinson et al. (1991) and Ibbotson & Kaplan (2000), an appropriate asset allocation rather than the stock or bond-picking strategies determines 80-90% of the variation in investment portfolio returns. In such a case an investor should strategically form a long-term investment portfolio from various assets, such as stock, bonds and alternative investments (e.g. hedge funds, privately-held companies, real estate). is can help to improve the risk-adjusted performance by increasing pro ts and/or reducing the investment risk.
But then another dilemma emerges -how and when to invest in di erent assets? One of the possible solutions to determine which particular asset class performs best under di erent economic conditions is to combine both macroeconomics and nancial theories. It is obvious that the change of economic situation has an impact on people's and company's behaviour which transmits to investors' projections of future asset returns. Moreover, macroeconomic factors, i.e. determinants that re ect the changing economic and nancial situation in a particular country or a region, have an e ect on the assumed risks and correlations between the returns of di erent assets. Due to these reasons, more and more researches about the link between the macroeconomy and asset markets have been performed regarding not only developed, but also emerging markets. Gan et al. (2006) analysed New Zealand, Anokye & Tweneboah (2008) -Ghana, Ibrahim (2011) -ailand, Golob et al. (2012) -Slovenian, Vejzagic & Zarafat (2013) -Malaysian markets. All these researchers found a cause-and-e ect relationship between macroeconomic forces and asset markets. e main purpose of this paper is to determine the impact of various macroeconomic factors on Lithuanian asset prices. Moreover, this paper tries to answer if it is possible to forecast future asset returns accurately and, as a result, prevent future asset bubbles and nancial turbulences, based solely on economic information. ree asset classes are examined: stock, government securities and real estate. e selection of these assets is not accidental: the rst two are the most important instruments of capital markets, while real estate is an alternative investment that can provide diversi cation bene ts, i.e. reduce the risk without decreasing portfolio returns. In addition, these three assets constitute the biggest proportion of local investors' portfolios. e historical analysis is conducted with quarterly data from 2000 until 2013, while the out-of-sample forecastfrom 2014 until 2016. e e ects of ve macroeconomic factors are explored: gross domestic product, foreign direct investment, consumer price index, money supply and interest rates. e novelty and relevance of this study is fourfold. First of all, almost all similar studies were carried out regarding only one Lithuanian asset class. is study, on the contrary, examines how the country's economic development simultaneously a ects all three Lithuanian assets. is is especially important in asset allocation and appropri-ate risk management. Secondly, due to the shortage of long-term historical data, there were few studies regarding causality relationships between macroeconomic factors and Lithuanian markets (particularly in the eld of government securities), and majority of the studies were conducted before recent nancial crisis that mightily disrupted such relationships. irdly, regression or correlation analysis were used in the majority of the researches regarding Lithuanian asset markets, while advanced studies about foreign markets were carried out mostly with relatively newer techniques, especially the cointegration method, which have greater explanatory power concerning causal links. Fourthly, the forecasting of prices and e cient rebalancing of investment portfolio is particularly relevant in today's context because the prices of all three assets have reached high values (local maximum), so further gains are strongly questionable and nancial stability (due to possible asset bubbles) may be impaired.
is paper consists of four main parts: the review of literature and analysis of theoretical approaches; the description and examination of the data and main econometric models that are most suitable for conducting such researches; the analysis of the ARDL model; the main ndings of the in-sample prediction and out-of-sample forecast for asset prices.

Literature review: the impact of macroeconomic factors on asset prices
Although di erent researchers analyse various macroeconomic factors, most of them examine the e ect of gross domestic product or personal income. is is due to the fact that these factors have an intuitively justi ed in uence on all assets. For example, due to the rise of GDP, the company's production, pro ts and, as a result, the prices of its shares in most cases increase (Singh et al., 2013). Moreover, almost all scientists (Apergis, 2003;Ong & Chang, 2013;and others) found statistically signi cant and direct impact of country's economic condition on real estate prices. Kohlert (2010) emphasized that GDP is an economic indicator mostly escalated in the mass media, so the change of GDP should have the biggest impact on people's future expectations and real estate prices. In extreme cases this can even lead to the formation of asset bubbles and tonancial instability. However, in the case of government securities, the e ect of GDP can be twofold: on the one hand, in the environment of deteriorating economic situation governments tend to increase the amount of debt and thus the supply of government securities, so the prices of these securities fall, but on the other hand, the prices of other assets during the economic downturn generally fall even more. e easiest way to investigate the in uence of interest rates on asset returns is by using the discounted cash ow model: interest rates a ect both the numerator (dividends, corporate pro ts, income from bonds or real estate) and the denominator (the discount rate). Due to the fact that many companies nance their purchase of new equipment or inventory by using borrowed capital, the decline of interest rates can cause the growth of corporate pro ts and the decrease of investors' required return (Chen, 1991;Vejzagic & Zarafat, 2013). Ultimately, it can even lead to stock market bubbles and pose threat to nancial stability. e majority of authors (e.g. Piljak, 2013) who analysed the cause-e ect relationship between interest rates and government securities prices found that the change of interest rates is the strongest force of all of macroeconomic factors.
is is due to the fact that interest rate is the component of nominal yields and, as a result, a ects government securities prices inversely. e change of interest rates should have a statistically signi cant and inverse e ect on real estate prices too, because the biggest share of bank loans are long-term and lent at variable rates. When interest rates increase, the periodic interest payments that are paid to the banks grow as well -so this is obviously a negative signal to the buyers of real estate. For the reasons outlined above, asset prices as well as nancial stability is heavily dependent on the monetary policy and sensitive to any, especially unexpected, change of interest rates or the volumes of quantitative easing.
e change of in ation should also have an inverse e ect on asset prices. First of all, corporate pro ts and dividends paid generally do not grow at the same pace as in ation: the costs that companies incur can increase immediately, while due to the longterm contracts many rms fail to raise their output prices quickly. is negative e ect of in ation was described in an o en quoted study of Calvo (1983). Moreover, in the light of growing in ation monetary policy tends to be tightened, so, as a result, nominal interest rates may be increased by the central bank. In the case of government securities, rising consumer prices should a ect the real return earned from government securities inversely. For instance, high and increasing in ation in developing countries o en indicates the likely crisis of the balance of payments and an eventual decline of government securities prices ( Jaramillo & Weber, 2012). e e ects of in ation on real estate prices are the most controversial among three asset classes. It is identi ed by many researchers (e.g. Tsatsaronis & Zhu, 2004;Tan & Chen, 2013) that investment in real estate sector is a good hedge against in ation and the depreciation of money. However, the rising in ation can have an opposite e ect if it increases periodic nominal interests paid to lenders. e returns from various assets are a ected by the change of money supply in several ways. According to monetarism theory (Friedman & Schwartz, 1963), the increase of money supply should improve country's economic determinants (e.g. output, employment) and reduce the costs of borrowing. In such a case, money supply should have a direct e ect on future asset returns. In addition, the increased amount of money can be directly channelled to various asset markets. However, a possible side e ect can arise: the growth of money supply increases in ationary pressures, which raises borrowing costs and may even reduce asset prices. e e ect of money supply can also be justi ed by the arbitrage pricing theory, formulated by Ross (1976): a whole range of risk factors (including money supply) are responsible for asset returns, so investors who are able to assess the value of the changing money supply can calculate the expected price of each asset, and, if it signi cantly di ers from its market price, earn an arbitrage pro t. Due to these reasons, the majority of the researchers (Hassan & Al, 2012;Vejzagic & Zarafat, 2013;Chowdhury et al., 2013) analyse the causal e ect of money supply on asset prices.
Foreign investment can have a direct impact on the national economy and asset prices. e ows of FDI are particularly important to small open economies because these countries o en lack local capital resources (Anokye & Tweneboah, 2008). is e ect is especially relevant to countries experiencing internal economic shocks. In Lithuania, FDI share in GDP exceeds 35%, so it is no surprise that Danilenko (2009) and Jasienė & Paškevičius (2010) found that the FDI ows are one of the main driving forces behind the change of the stock index values. However, this impact can be twofold on government securities prices: the improvement of country's investment environment usually increases the creditworthiness of such country and thus the yields of government securities decline, but on the other hand, this can lead to the increase of in ation, which has a positive e ect on nominal yields ( Jaramillo & Weber, 2012). Researchers (e.g. La Paz & White, 2012) who analysed the causal impact of FDI ows on real estate prices, mostly found a direct and strong link because FDI ows. is is possibly due to the fact that these ows o en correlate with portfolio investment that can be directly channelled to real estate market.
In summary, the change of several macroeconomic factors (foreign investment, interest rate) should have the same e ect or at least the same direction on the prices of di erent assets, while the change of others (GDP, in ation, money supply) may have strongly diverse e ects. is is due to the fact that all three assets are very di erent. For instance, the main features that distinguish real estate from other asset classes are the high cost of creation (constructing), longevity, heterogeneity (there are no two identical houses) and localized permanence (Durlauf & Blume, 2008). In addition, as compared to stock and real estate sector, the amount of studies regarding the e ects of macroeconomic forces on government securities prices is much more limited -many analysts a ribute the change of debt securities prices to some internal factors of debt securities market (e.g. yield curve or liquidity risk).
ere are few relevant studies about the e ect of macroeconomic forces on di erent asset classes in Lithuania. Laskienė & Pekarskienė (2007) analysed the link between 9 macroeconomic factors and the OMXV index from 2000 to 2006. e authors found not only a strong direct link between the values of the OMXV index and GDP, money supply and the construction cost index, but also an inverse link with the unemployment rate, yield of government securities and the exchange rate. Jasienė & Paškevičius (2010) found that the growth of GDP, FDI or in ation positively a ected the stock returns, but were negatively a ected by the growth of unemployment and government debt. Pilinkus (2010) analysed the period from 2000 to 2008 with the help of several timeseries models. However, this author found links that are di cult to support by various economic theories, e.g. the cointegration model revealed that interest rates and in ation had direct, while the money supply, investment and net exports -an inverse e ect on the OMXV index. Tvaronavičius & Tvaronavičienė (2008) analysed the relation-ship between xed investments and economic growth in Lithuania, while Galinienė & Stravinskytė (2016) found a strong correlation between the real GDP growth and the Bank of Lithuania's nancial assets/pro tability. Alexopoulou et al. (2009) examined the government securities markets from new EU members and found that the countries with the largest scal imbalances (Lithuania was no exception), su ered the biggest drop in debt securities prices and the rise of borrowing costs. According to them, in ation and the openness of the country were the main driving forces behind Lithuanian government securities prices. One of the most relevant researches regarding real estate market was made by Simanavičienė & Keizerienė (2011): GDP, in ation and investment in residential buildings had the biggest impact on the prices of old apartments in Lithuania, while investment had no signi cant e ect on the prices of new dwellings.
However, fundamental forces not always play a crucial role in the formation of asset prices. Financial assets have a peculiar feature -the increase of their prices in most cases does not reduce the demand (which is the usual e ect in goods and services markets), but raises it (Case & Shiller, 1990). e increase of asset prices may a ract even more buyers, so the prices may continue their upward trend in future periods and, as a result, can make a huge threat to nancial stability. People's expectations are the principal determinants of real estate prices, so there is a clear inertia in this sector (Tupėnaitė & Kanapeckienė, 2009). While it is impossible to measure behavioural factors precisely, the previous returns of di erent assets are frequently included in similar models.
3. Data and construction of the model e rst step to identify the main driving forces behind the prices of Lithuanian companies stock, government securities and real estate, is to choose the most appropriate expressions of asset values. Researchers who analyse stock markets in most cases include stock indices in their models (e.g. Chen, 1991;Anokye & Tweneboah, 2008;Singh et al., 2013). Indices re ect not the state of individual company, but the dynamics of the whole market and its various systemic risks -this is justi ed by the Ross (1976) arbitrage pricing theory. It is most appropriate to examine the impact of macroeconomic factors on the NASDAQ OMX Vilnius index because it consists of almost all the shares listed on the Vilnius stock exchange. Moreover, the values of this index were included in the models of nearly all previous researches regarding Lithuanian companies stock. In the case of government securities, it is most meaningful to analyse the index calculated by the Bank of Lithuania (GS index) -it is the only publicly available index regarding Lithuanian government securities prices ( e Bank of Lithuania, 2013). Since there are no exchange-traded real estate funds in Lithuania and the values of the housing price index are provided by Statistics Lithuania only from 2006, it was decided to use the transacted real estate index (RE index) calculated by the Centre of Registers. e construction of this index highly resembles real estate price index that is most commonly used by other researchers in similar studies (e.g. La Paz & White, 2012;Galvao et al., 2011).
ere is no consensus among researchers on how many macroeconomic variables should be included in econometric models: some authors use just 1 or 2 variables (Fama & Schwert, 1977;Hou & Cheng, 2010), others -over 100 indicators (Ludvigson & Ng, 2009), but mostly -from 4 to 6 variables (Chen, 1991;La Paz & White, 2012;Singh et al., 2013). In the case of this study, it was decided to choose ve most frequently analysed macroeconomic variables: Lithuanian gross domestic product, foreign direct investment, consumer price index, money supply M2 and 6 month Vilnius interbank o ered rate (the description of these variables is provided in Annex 1). Although other macroeconomic factors may o en have a greater impact on certain assets (e.g. net exports or the exchange rate -on stock, country's de cit and debt -on government securities, the unemployment rate -on real estate market), it was decided to choose only those indicators that could be the driving forces behind all three Lithuanian assets. Moreover, the quarterly data was used in this analysis as there is a longer history for the variables of such frequency and it should be more stable than shorter-term data (e.g. quarterly GDP versus monthly industrial production). Also, this analysis focuses on longer-term dynamics of asset prices and e ects of macroeconomic variables, so quarterly data seems a suitable t. e quarterly frequency data was used by most of other authors (e.g. Apergis, 2003;Laskienė & Pekarskienė, 2007;Simanavičienė & Keizerienė, 2011;Ong & Chang, 2013;etc.). It is also important to note that the stationarity of the variables should also be checked by performing unit-root tests before constructing time-series models.
In order to evaluate the impact of various macroeconomic factors on asset prices simultaneously, the following function should be constructed: where: X t -OMXV, real estate or government securities index.
Various researchers use di erent methods to evaluate this function. It is important to note that several decades ago most examinations to capture similar links were carried out by using regression or other statistical analysis tools, but later on the use of timeseries models (vector autoregression for short-term and cointegration for long-term links) gained momentum. is can be explained by the fact that time-series models are used not only for capturing a statistical relationship between variables (which can be performed by simpler statistical methods), but also for the identi cation of causal e ects that macroeconomic forces have on asset prices. Moreover, the majority of timeseries models are multidimensional, so, unlike simpler econometrical/statistical methods, they help to examine the interactions between many variables simultaneously. However, while foreign researchers apply advanced time-series models for a long time, the majority of the authors who analysed Lithuanian asset markets still mostly use regression or correlation analysis (apart from Pilinkus, 2010;Dubinskas & Stungurienė, 2010). For all these reasons it was decided to ll this gap and to examine the causal relationships between variables using a long-term time-series model -cointegration.
Cointegrated variables are such variables that individually are not stationary (i.e. have unit roots), but their linear derivative creates a stationary process due to the common trends. If this is the case, then equilibrium exists, and over time variables do not move far away from each other and respond to each other's deviations from equilibrium. For example, the values of real GDP, money supply, price levels and interest rates are mostly non-stationary (should be di erentiated once or twice), but according to the theory of cointegration, their linear combination is stationary (Enders, 1995). e main advantage of cointegration models is that they (unlike other time-series models) help to determine the adjustment speed in which the system returns to its long-term equilibrium.
e most commonly used cointegration method is Engle & Granger (1987) and Johansen (1988) vector error correction model. However, when investigating the relationship between macroeconomic variables and assets, these two methods can be inaccurate due to the complexity of multi-equation function and endogeneity issue, so many authors (e.g. Maysami et al., 2004;Hassan & Al, 2012) prefer to employ a simpler vector error correction model -ARDL. is model is also a cointegration method and helps to asses causal relationships, but, unlike other methods, it is a regression model and more advantageous in small sample researches (such as in the case of this study).
is is due to the fact that the majority of time-series models (Engle & Granger, 1987;Johansen, 1988, are no exception) su er from the high number of lags included -when the sample size is small and the amount of variables used is quite high, every lag included in these models greatly increases the risk of multicollinearity. Moreover, the parameters of the ARDL model are estimated by ordinary least squares procedure, so it helps to avoid potential mistakes that occur in more complex vector error correction models. To add to the point, the majority of researchers in similar studies found out that not all macroeconomic variables were responsible for the elimination of the deviation from equilibrium, so multidimensional methods become excess and a simpler model -ARDL -could present more accurate and unbiased results. As a result, ARDL model can help to examine the causal e ect of macroeconomic forces on asset prices with a lower probability of error. e simplest form of ARDL model (with just three variables) has the features from both error correction and regression models: where: ΔZ t , ΔY t , ΔW t -the rst di erence of respectively endogenous variable Z and exogenous variables Y and W; ΔZ t-1 , ΔY t-1 , ΔW t-1 -lags of respectively Z, Y and W; α -the coe cient of the adjustment speed, which shows the time needed for the process to return to equilibrium; β -the set of coe cients that shows the cointegration links between variables and ensures that Z t returns to its constant status; δ -the coe cient that shows the e ect of di erentiated exogenous variables Y and W on variable Z. e coe cient of the adjustment speed (α) and estimates of the parameters of cointegration (β) are the most important elements in this ARDL model because only they reveal a long-term relationship between variables. If it is found out that the adjustment speed (α) is not signi cantly di erent from 0, it means that the variable is weakly exogenous and does not eliminate the disequilibrium. In order to determine the values of β, the normalization in relation to the endogenous variable should be carried out for all the parameters in the model. In addition, due to the fact that the assessment of ARDL model is performed using the least squares method, it is particularly useful in making short-term and long-term forecasts and might be less prone to errors due to the simplicity of estimation process.

Empirical ndings of the autoregressive distributed lag model
Before the construction of ARDL model, the stationarity of the variables was examined. When additional lags due to possible autocorrelation were included in the unitroot tests, all variables (even interest rates) were found to be non-stationary by three tests: Augmented Dickey Fuller (ADF), Phillips-Perron (PP) and Zivot Andrews (ZA) (see Annex 2). As the majority of the variables were integrated by the rst order, and in order to be consistent with interpretation of the results, the ARDL models were constructed with the rst di erences of each variable. e results of created ARDL models (le columns of Annex 3, 4 and 5) prove that all three assets are cointegrated in respect to macroeconomic variables -this is evident from the coe cients of the adjustment speed (α). ese adjustment speeds are statistically signi cant and equal -0.24, -0.26 and -0.5 respectively in the case of stock, government securities and real estate. It takes from about two (real estate) to four (stock and government securities) quarters for the asset index to eliminate completely the disequilibrium that occurs in t-1 period. e residual standard error reveals that the model ts the data pre y well and is estimated reliably. e coe cients of determination of ARDL models are equal to 46% (in the case of stock), 57% (in the case of government securities) and 59% (in the case of real estate), i.e. about half of the variability of indices values can be explained by the changing values of macroeconomic determinants. It becomes clear that the predictions based on macroeconomic factors are the least useful in the case of the stock market and the most useful for the real estate market. A er the normalization of all the parameters, the following equations of long-run relationship between the variables were derived: In the long-run the changes of macroeconomic factors have strong and long-lasting e ects on the OMXV index, though the directions of various drivers are di erent. OMXV index values increase by nearly 2% when FDI ows or money supply grows, and declines from 3 to over 4% when GDP, in ation or interest rate increase by 1%. Even though these impacts are strong, the direct e ect of FDI ows and money supply, as well as an inverse impact of in ation and interest rates should not be surprising -the majority of other researchers obtained similar results. e long-term and strong inverse impact of GDP on the OMXV index is more di cult to explain: various economic theories prove that the production directly a ects the expected cash ows and stock prices.
is result probably con rms that investors can predict the prospective GDP gures by interpreting, for instance, data of monthly production indices and export-import volumes, so they manage to reallocate funds before the publication of the quarterly GDP indicator.
Although many analysts a ribute the changes of debt securities prices to various bond-speci c factors, this ARDL model proved that in the long-term macroeconomic factors also a ect (for the most part -inversely) Lithuanian government securities prices. In particular, in ation and interest rates have strong e ects -when they increase, the prices decrease by respectively 0.92% and 1.85%. Such conclusions were made by almost all researchers who analysed the link between the in ation, interest rates and the debt securities prices, though Alexopoulou et al. (2009) found that the rise of in ation in Lithuania increased government securities prices. Inverse, but much weaker e ect (amounting to less than 0.5%) is noticeable from two other macroeconomic factorsoutput and foreign investment. is suggests that the improvement of macroeconomic situation worsens the prospects of debt securities market and makes riskier investments look more a ractive. From all macroeconomic determinants only money supply can have a direct impact on government securities prices -when it increases by 1%, government securities prices grow by 0.2%. e increase of the values of macroeconomic indicators, contrary to the case of government securities, has a positive e ect on real estate prices. For instance, index values increase by 0.39%, 0.63% and 1.07% respectively when FDI, money supply and GDP grows. is is compatible with the results of other studies regarding Lithuanian real estate sector (Simanavičienė & Keizerienė, 2011;Tupėnaitė & Kanapeckienė, 2009). However, it is surprising to notice that the real estate in Lithuania is a very poor protection against in ation in the long-run (when it grows, real estate prices decrease by almost 3%), so rapidly increasing consumer prices can lead to the instability of real estate market and, as a result, can even disturb the nancial stability in Lithuania. Moreover, in contrast to the results obtained by the majority of other researchers, there is a direct impact of interest rates on real estate prices -the e ect is strong and amounts to more than 1%. So growing interest rates do not distract investors and they continue purchasing property even with higher costs.
From the obtained results it becomes clear that the changes of various macroeconomic factors can have an uneven impact on di erent assets, so investors may exploit this opportunity by reallocating their funds. When the country's economic situation and people's expectations improve, it is likely that in a long term real estate prices will increase the most. Almost identical conclusions can be drawn with respect to interest rates -it can have a direct impact only on real estate prices. In the case of deteriorating economic situation, the best investment is the least risky asset, i.e. government securities. e change of money supply can have a direct e ect on all assets, but the biggeston stock prices. When choosing investments based only in terms of FDI indicator, the changes of stock index are best re ected by this factor, while government securities prices o en react inversely. e rise of in ation is negative for all asset prices, but the least -for the government securities prices.
In addition, two di erent robustness exercises were performed to check the stability and reliability of the ndings obtained with ARDL model. First of all, two variables were separately added to the model: money supply M3 versus M2 and industrial productions versus GDP. Inclusion of another money supply indicator had only marginally a ected model results (middle columns of Annex 3, 4 and 5). Although the e ect of money supply decreased somewhat, the main conclusions remain the same for all other variables and the adjustment speed. Meanwhile, industrial production, probably due to higher variability than GDP, a ected model results more signi cantly (right columns of Annex 3, 4 and 5): the value of intercept increased, impact of industrial production (compared with the case of GDP) -decreased, multiple R 2 squared become somewhat lower, etc. Still, the main ndings of the e ects of macroeconomic variables remain almost unchanged, so the constructed ARDL model seems to be quite stable. e Johansen vector error correction model was also performed to examine if the conclusion of the causality links hold not only for the created ARDL model. e trace and eigenvalue tests (without linear trend and constant) revealed that at least two stationary combinations of cointegrated vectors exist. e coe cient of the adjustment speed for the Johansen model with two cointegrated vectors (Annex 6,7,8) showed that asset prices react to the dis-balance that originated between asset prices and macroeconomic variables in the previous periods, though in di erent magnitude and scale.
So the long-term equilibrium links between asset prices and macroeconomic determinants seem to prevail, meaning that asset prices react to the changing macroeconomic environment. However, not all determinants were responsible for the elimination of the deviation from the equilibrium, so Johansen cointegration procedure might be redundant, especially in small sample researches. As a result, a simpler single-equation model, i.e. ARDL, might be a more useful tool for examining historical and future links between asset prices and macroeconomic determinants.

5.
Results of the forecast model for asset returns e biggest issues for the reliability of the created model arise when the results of identi ed causal relations are used for the short-and, especially, long-term forecasts. Many models which are suitable for capturing only the past links between variables become imprecise in predicting future changes (Goyal & Welch, 2008). In this study, an a empt was made to identify the accuracy of predicted asset returns until the end of 2013 (insample testing), as well as the precision for the period between 2014 and 2016 with the inclusion of the latest available macroeconomic data in the ARDL model (out-ofsample testing).
Until the end of 2013, the predicted returns quite accurately re ected the actual changes of the OMXV index values (Fig. 1)  tionship between variables. However, the forecasts for the period of 2014-2016 were too pessimistic with the inclusion of the latest available data: investors were receiving higher returns than the ARDL model indicated, especially in the latest periods. A possible explanation is that there were many determinants that were not included in the model (e.g. global factors, speculations, expectations) that potentially have an in uence on the behaviour of individual and institutional traders who invest their funds in Lithuanian stock market. Similar conclusions can be drawn with regard to the predictions of government securities returns. Although the correlation coe cient (0.72) is even higher, the forecasted growth rates were lower than actual ones since 2014 (Fig. 2). is discrepancy can be a ributed to the fact that the macroeconomic situation in Lithuania had been steadily improving and, more recently, the monetary policy has become more accommodative, and thus had a positive impact on government securities prices, while the model did not capture these e ects. It is also important to note that the further the forecast horizon, the bigger di erences were recorded, so the model-based forecasts should be employed only for the near future. e forecasts based on the identi ed links between variables were the most accurate for the real estate prices. Until 2006 the actual real estate prices were much more variable than predicted estimates, but a erwards the explanatory power of the model increased (Fig. 3). Although the correlation coe cient (0.75) is only slightly higher than in the case of the government securities or OMXV index, the forecasted real estate returns from 2014 quite accurately re ected the actual gains, possibly due to highly inert real estate prices. However, actual real estate prices have increased much faster during the last couple of quarters. It should be mentioned that successful identi cation of causal links and predictions faces a number of practical challenges. First of all, although the created ARDL model revealed that the changes of macroeconomic factors account for about a half of variability of asset returns, it is obvious that asset prices are also a ected by other factors (e.g. market liquidity, speculative forces, various risk factors, unconventional monetary policy measures). Secondly, the Lithuanian companies stock, government securities and real estate markets are relatively small, thus sensitive to the changes of global macroeconomic conditions. irdly, not all macroeconomic indicators or index values are announced at the same time, e.g. values of FDI ows and real estate index are announced more than half a year later. us, in order to increase the accuracy of asset price predictability, it could be helpful to include more frequent periodicity, a higher number and more various types of global and local macroeconomic and microeconomic factors, as well as to perform a sensitivity analysis of these changes.

Conclusions
e literature review carried out in this paper revealed that authors justify their selection of macroeconomic determinants by many di erent theories, e.g., the arbitrage pricing theory, the discounted cash ow model. On the basis of these theories, ve macroeconomic indicators that have an intuitively justi ed e ect on Lithuanian companies' stock, real estate and government securities prices were selected: gross domestic product, in ation, interest rates, money supply and foreign investment.  Although regression and other statistical models (e.g. correlation analysis) were the most commonly used methods for the identi cation of inter-dependencies, the autoregressive distributed lag model was chosen in order to nd causal e ects that macroeconomic factors have on asset prices. is method also overcomes the problems of other cointegration methods due simplicity of the estimation process and suitability for researches with small sample sizes.
e constructed model revealed that in the period from 2000 to 2013 the Lithuanian government securities, real estate and companies' stock prices were cointegrated with all ve macroeconomic factors and that could explain about half of the variability of asset prices. Previously announced macroeconomic data can be used for the prediction of future stock returns: foreign direct investment and money supply have a direct, while in ation and interest rates -inverse impact on the stock prices of Lithuanian companies. It is odd that the growth of gross domestic product can lower stock prices. Rising values of macroeconomic indicators should reduce prices of Lithuanian government securities, while only the change of money supply can have a direct impact. e dynamics of real estate prices are most closely related to the changes of macroeconomic factors: gross domestic product, foreign investment and money supply in Lithuania have a direct impact on real estate prices. In contrast to the results of similar studies, the rise of interest rates can have a positive impact on real estate prices in Lithuania, and in the background of rising in ation real estate can be a poor investment. e additionally performed robustness checks broadly con rmed the main messages of the constructed models.
e results of the forecasts of autoregressive distributed lag model revealed that the most accurate predictions (with high coe cients of correlation) were obtainable in real estate market, while the forecasted returns of stock and government securities were much lower than the actual ones, possibly due to the many determinants not included in the model. Also, the out-of-sample forecasts were becoming more inaccurate the further the start of forecast period. In order to improve these results, it would be useful to experiment with a more frequent periodicity of data and a wider variety of di erent global and Lithuanian indicators. Moreover, according to the rules of strategic asset allocation, the success of investment performance is not only dependent on the earned pro ts, but also on the assumed risks. So, in the future it would be useful to examine how various factors a ect price variances and the correlations between the returns of di erent assets.