Corresponding author: Alexander Abramov ( ae_abramov@mail.ru ) © 2015 Nonprofit partnership “Voprosy Ekonomiki”.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BYNCND 4.0), which permits to copy and distribute the article for noncommercial purposes, provided that the article is not altered or modified and the original author and source are credited.
Citation:
Abramov A, Radygin A, Chernova M (2015) Longterm portfolio investments: New insight into return and risk. Russian Journal of Economics 1(3): 273293. https://doi.org/10.1016/j.ruje.2015.12.001

This article analyzes the impact of the increase of an investment horizon on the comparative advantages of the basic asset classes and on the principles of constructing the investment strategy. It demonstrates that the traditional approach of portfolio management theory, which states that investments in stocks are preferable over bonds in terms of their longrun risk–return tradeoffs, is by no means always consistent with empirical evidence. This article proves the opposite, i.e., that for longterm investors, investments in corporate bonds are more profitable in terms of the risk–return ratio than investments in stocks, arguing in favor of strategies pursued by pension funds and other institutional investors focused primarily on investments in fixedincome instruments, including infrastructural bonds. Emphasis is placed on the need for regular adjustments to longterm investors’ portfolios. As portfolios get older, those investors see a reduction in the returns’ dispersion, while differences in risk between various portfolios increase. This means that to maintain a fixed risk–return ratio for a portfolio as the horizon increases, an investor needs to increase the share of lowerrisk financial assets during asset allocation process. This thesis becomes especially relevant in the context of retirement savings management.
retirement savings, longterm investments, investment horizon, stock and bond returns, stock and bond investment risks, portfolio diversification
The Russian Government's decision to preserve mandatory retirement savings
The impact of the increase of the investment horizon on changes in the risk– return profiles of various financial instruments and portfolios has also become a topical issue. The existing research substantiates various assumptions regarding possible ways to improve a portfolio's risk–return profile by diversifying investments in various financial instruments and increasing the investment horizon. The classical papers by G. Markowitz (
A great deal of research is dedicated to the “return decomposition theory”, which studies the role of various factors in the risk–return profiles of institutional investor portfolios. In particular, Brinson et al. (
These papers introduced a rule in portfolio management practice that states that foremost attention should be paid to asset allocation rather than active management. Using the example of retirement savings portfolios for private Russian pension funds (PPF) and mutual funds,
One of the most thoroughly researched problems is that of the socalled premium on stock holding, which was first actively discussed in academic literature during the 1960s, almost concurrently with the efficient market hypothesis. Having analyzed longterm series of returns for various financial instruments, most researchers came to the consensus that stock holding, as a rule, provides a positive premium for investors, as opposed to returns on safe bonds.
However, the shortcoming for most of the above papers is their insufficient focus on the risks of investing in different financial instruments. A consistent comparison between stocks and bonds based on risk and return factors over different horizons was attempted by J.
We will underscore the following important aspects of Siegel's (2008) work. Increasing investment periods reduce the variation between average returns on financial instruments, while the difference between maximum and minimum returns decreases faster for stocks than for fixedincome securities as the length of holding increases (
Maximum and minimum returns for different holding periods, 1802 – December 2006.
Source: Siegel (2008, p. 25).
The risks inherent in financial instruments decrease as the horizon increases. According to Siegel, the standard deviation of average annual returns is negatively correlated to the holding period, provided that returns on assets are consistent with the random walk hypothesis. An analysis of actual series of stock, bond and treasury bill returns in the United States from 1802 to 2006 shows that starting from 20year holding periods, the standard deviation (risk) for stocks becomes lower than for bonds and even treasury bills.
Thus, having compared risk–return profiles for portfolios with different horizons, Siegel came to the conclusion that “the safest longterm investment for the preservation of purchasing power has clearly been a diversified portfolio of equity” (
Siegel's methods of analyzing the risks and returns of stocks and bonds in the U.S. and several other developed markets have also been examined for Russian stock market securities. Based on data for stock and bond returns in the U.S. market for the period 1928 to 2008,
Without contesting the correctness of these findings, we note, however, that they contain some assumptions that reduce their practical utility for institutional investors in building their portfolios. Moreover, they may lead to an incorrect understanding of the methods for building optimized portfolios. To substantiate his findings, Siegel used the following method to calculate average risks and returns for stock and bond portfolios over different horizons. Over a period spanning 205 years from 1802 to 2006, aggregate portfolios were built with different investment horizons, from 1 to 100 years.
At the same time, those who actually manage longterm portfolios for pension and mutual funds will be surprised to learn that their real portfolios behave differently: as the horizon increases, the average annual return does actually decrease, whereas the standard deviation of the portfolio is, on the contrary, most likely to increase. For example, according to the 2014 annual report of GPFG (Norway), which is one of the world's largest government pension funds, the average annual returns on its portfolio for 1, 5 and 10 years was 7.58%, 8.61% and 6.14%, respectively, while the standard deviations for the same periods were 4.57%, 7.24% and 8.59%. As the horizon grew, the real portfolio of the pension fund showed a noticeable increase in the standard deviation, but by no means its reduction. Contrary to the assumptions about the benefits of longterm investment in stocks compared with bonds, one can note that in many countries, investments in bonds are the greatest in the structure of assets of pension funds. This fully applies to the portfolios of pension savings in pension funds and management companies in Russia (
This paper explores the impact of increased investment horizons on the effectiveness of asset management, based primarily on an analysis of the risks of longterm asset allocation strategies. The classical theory argues that risk is mitigated as the investment period increases. However, uncertainty about future returns (and, consequently, the ultimate return on the same portfolio) will only grow. The longer the investment period, the higher the probability of various extreme and rare events, such as a global crisis or a crash in a particular financial market. Such events may lead, for example, to shortterm negative returns on assets within a portfolio and to losses. This, in turn, may result in increased volatility of returns and ultimately reduced returns. The basic assumption examined in the analysis is that risks and returns behave differently rather than converge, as Siegel shows in his works.
In the empirical analysis, an example of the fullest global diversification of a portfolio was reviewed. To this end, we selected stocks for U.S. ETFs using different investment strategies as well as several stock market indices in a number of countries. This approach produced relevant and sustainable results, taking into account data from one of the most diverse samples of assets possible, along with the opportunities provided by various investment strategies pursued by ETFs and financial markets in developed countries and in Russia. We selected the following 19 instruments, for which we gathered historical series of their daily returns over 10 years (2004–2014), based on Bloomberg data:
The analysis covered three different investment periods: 1, 5 and 10 years. This enabled us to review changes in the intertemporal characteristics of potential portfolios over short, medium and long periods of time.
Sample returns on instruments for various horizons (% annually).
Thus, only approximately half of the sampled instruments showed a noticeable reduction in returns over increasing investment periods. The other indices and funds showed either no such trend or, in some cases, even showed an increase in the mean value. For example, the Russian and French indices (RTSI and CAC, respectively) demonstrated sharply negative returns in 2013 and 2014, which corresponds to an annual period in this analysis. However, they showed quite highly positive returns when the period was expanded to 2004–2014. Thus, we cannot assert any reduction in their returns. This result may be due to the market fluctuations that took place during the sample periods (2008–2009 crisis and the increased volatility of the Russian market during 2013 and 2014).
Sample standard deviations of instruments over various horizons (% annually).
Thus, the data from individual indices show that a longer investment horizon leads to wider potential fluctuations in returns and may result in an increased average annual risk. Over a longer period, returns on various instruments may have values that are extreme within the current historic range or may even break their historic records. This may lead to abnormally low returns for a portfolio with a fixed asset allocation throughout the investment period.
For a more thorough analysis of the hypothesis that as the investment horizon grows, differences in the risk rates of different asset allocation strategies increase, we analyzed the changes in opportunities for global diversification over longer investment horizons. This yielded a clearer understanding of the comparable advantages of longterm allocations of various asset classes belonging to different financial markets.
An empirical analysis of global diversification between various investment strategies (based on ETF data) and markets was carried out based on a sample of the 19 instruments listed in
Based on daily data, we estimated returns and risk rates for 1, 5, and 10year investment horizons. The average annual return on a portfolio with asset allocation (wi1, wi2, …, wi19) was determined as the average daily return ri on that portfolio over the entire investment period T, multiplied by 252 (the standard number of trading days in a year). The average annual risk rate of a portfolio with asset allocation (wi1, wi2, …, wi19) was calculated as the standard deviation of daily returns on that portfolio over the entire investment period T, multiplied by √252 (a standard transformation for a constant value as a part of a standard deviation). Defining portfolio characteristics in this way enabled us to take into account their fluctuations over the entire investment horizon and to reflect their volatility as a standard deviation in the analysis. This is especially significant when comparing various longterm investment strategies and researching opportunities for diversification and for improving the efficiency of longterm investments.
Of the 19 indices above, we obtained a set of portfolios by modeling over 14,000 possible combinations. This set of various asset allocations included the following types of portfolios: average weighted portfolio with the same weight of each asset and portfolios fully (100%) consisting of each individual asset. The remaining combinations describe most fully varied strategies for longterm asset allocation.
We emphasize some specific portfolios consisting of the stocks (units) of a single index. They include the following: SHY US Equity, as a proxy for the riskfree return rate of shortterm government securities; SPY US Equity, as an indicator of returns on the stocks of the 500 largest U.S. issuers listed on the S&P 500 index; LQD US Equity, as a benchmark of returns on U.S. investmentgrade bonds; the portfolio conventionally named “Full Diversification”, consisting of stocks (units) of all 19 index portfolios with the same weighting; and the RTS index portfolio.
Frontiers of portfolio sets from 19 equity investment funds (ETFs) and indices with 1, 5, and 10year investment periods.
Note: the numbers next to the asset names indicate the periods of investment in the portfolios fully (100%) consisting of those assets (1 year, 5 years and 10 years).
Source: authors’ calculations based on Bloomberg data.
The set of 5year investment period portfolios maintained a significant dispersion between minimum and maximum returns and risk values; however, the dispersion between returns became significantly narrower than for 1year portfolios. An efficient portfolio set consists of a set of fund combinations with annual returns between 0.2% and 27.8%. Portfolios used as benchmarks — SHY, LQD and SPY — are also approximately on the same line here.
As the investment horizon extends to 10 years, the difference between minimum and maximum risk values increases, while the difference between the maximum and minimum average annual returns of the portfolio set decreases. An efficient portfolio set consists of a set of portfolios with annual returns between 0.4% and 15.9%. None of the possible portfolios with 10year investment horizons has a negative average annual return, which per se demonstrates the advantage of diversifying portfolios over time. Portfolios used as benchmarks — SHY, LQD and SPY — are also approximately on the same line here. As the investment horizon increases, the impact of diversification on reducing the correlation between a portfolio's returns and risks falls significantly. Thus, for the risk–return ratio of a portfolio, the allocation of various investment asset classes becomes more relevant than the security selection within those asset classes, which determines to a great extent the portfolio risk and, to a lesser extent, its return.
The overlapping frontiers of portfolio sets and 1, 5 and 10year investment horizons clearly demonstrates that a longer investment horizon narrows the dispersion between portfolio returns while increasing the range of the standard deviation.
Summary data on returns and risks for portfolios with different investment horizons (% annually).
Thus, the research, which covered quite a large and representative sample of different investment strategies up to a 10year horizon, has shown that portfolio sets contract along the return axis and expand along the risk rate axis. This suggests that in longterm investments, the most important objective may be finding the target risk–return ratio of a portfolio and, first of all, the allocation of different classes of investment assets. To examine the sustainability of this hypothesis and to identify the comparative advantages of various asset classes, we will analyze longer investment horizons (up to 30 years) and change the sample of assets.
Returns and risks based on daily return data for portfolios from the MICEX index (stocks) and IFXbonds (corporate bonds) over longer investment horizons (% annually).
Source: authors’ calculations based on Bloomberg data.
To verify the above hypothesis that there is a potential comparative advantage of bonds over stocks over a longterm horizon, similar research was carried out based on longer series of U.S. indices. We used the S&P 500 as the stock index. As a proxy for bonds, we used the BofA Merrill Lynch US Corporate Index (C0A0), which tracks the trends in investmentgrade corporate bonds issued in the domestic U.S. market. Securities within it should:
The index did not include most hybrid corporate bonds. As of 2015, the index included approximately 6500 various bonds from all sectors of the economy, maturing in 1 to 25 years. The index was founded in December 1972 and has quite a long history of daily returns that were obtained from the Bloomberg database. All of the above facts allow us to consider the index as representative of this asset class and to include it in the analysis.
Using data from the two indices, we analyzed the trends for the main indicators of stock and bond portfolios against changing investment horizons from 1 to 30 years, based on daily data from the beginning of 1985 to the end of 2014.
Parameters of portfolios consisting of a corporate bond index and a U.S. stock index (% annually).
Source: authors’ calculations based on Bloomberg data.
The results are the opposite for stocks. The return rate decreases after a 6year investment period and then fluctuates around a 5–7% average annual return.
At the same time, the risk rate grows considerably and, after a 7year period, evens out at a considerably high level compared with the return rate. This means that stocks do not become less risky assets over longer investment horizons. The analysis has demonstrated that this portfolio has a rather low risk–return ratio, i.e., below 1.
A comparative analysis of the risk and return trends for stock and bond portfolios confirmed the above findings. We can see that the average annual returns on portfolios differed considerably over shortterm periods of 1 to 6year investment horizons. At the same time, quite logically, stock returns exceed bond returns. However, returns on the portfolios under review became much closer over longer periods. Moreover, there are periods where bond returns have exceeded stock returns (14, 15 and 16 years). This suggests that the difference between stock and corporate bond returns disappears over sufficiently long investment horizons.
Of greatest interest is a comparative analysis of portfolios in terms of the risk rate, which was calculated as a yearly standard deviation based on historical daily data for the respective period. We can see that the risk rate for the stock index portfolio grew at first for investment horizons of 1 to 7 years and then, following a slight decrease, remained almost flat. This runs contrary to Siegel's results (
As shown above, the risks and returns of different financial instruments (stocks and bonds) behave differently over time. Returns on different asset classes become closer, while differences in the risk rate grow rapidly. This suggests that over a longer horizon, stocks do not necessarily become more profitable for an investor in terms of the risk–return tradeoff. It has been shown that situations are possible where over long investment horizons (from 15 years onward, as well as 10 years for the Russian market), corporate bonds provide a comparative advantage over stocks in terms of returns and risk rates. This means that this asset class can be viewed as the most promising and preferable for longterm investors with long investment horizons. Moreover, we can recommend increasing the share of bonds in portfolios over longer investment horizons.
Long investment horizons were analyzed based on a different sample of financial instruments. Increasing the horizon to 30 years required daily data of comparable depth. Only a few stock indices at the financial markets of developed and developing countries possessed this quality.
To carry out an intertemporal analysis, we used a sample of 10 assets that represented global indices with the longest series of data (
Index list.
In a similar manner, based on daily data, we calculated the respective series of risk–return pairs for portfolios held by an investor with constant weighting during t years (t=1, …, 30).
For the widest review possible, we compiled various weighted sets for over 10,000 portfolios (10,672 portfolios). This enabled us to more completely evaluate possible asset combinations in investor portfolios and to evaluate the effectiveness of most possible asset allocations. The sets included the “Full Diversification” portfolio, where each of the 10 assets has the same weighting. Additionally, the analysis included portfolios fully (100%) consisting of each particular asset to be able to evaluate the limits of a portfolio set and pinpoint the location of full diversification in the risk–return space. The remaining weighting sets — various linear combinations of assets in a portfolio — were generated using a random number generation algorithm with the condition that their sum equaled 100%. The large number of portfolios enabled us to present the fullest possible picture of the differences between various asset allocation strategies and to analyze the changes in their comparative advantages over longer investment periods.
The model is presented in
Portfolio set with an investment period of T years in risk (σ, %) and return (r, %) coordinates.
Note: the ‘Full Diversification’ portfolio is marked with a white square.
Source: authors’ calculations based on Bloomberg data.
As the investment period increases, the portfolio set for the same selection of portfolios contracts vertically. This means that differences between portfolios diminish slightly as the length of time the portfolio is held grows. However, it should be noted that there is no full vertical contraction, even for the longest 30year period. The dispersion between return rates stops shrinking roughly after the 20year mark, which may be due to the cyclical nature of the financial market. For example, decreasing volatility and, as a consequence, the decreasing dispersion between the return–risk parameters, can be explained by transitions of the markets (or some markets out of those reviewed) to the allocation stage. It is characterized by mixed investor sentiment, leading to a reduction in the price amplitude. Hypothetically, this longterm cyclical pattern may be a consequence of long waves in global economic trends, which have a considerable influence on the trends and structures of national financial markets. Returns on a fully diversified portfolio are almost constant for most periods and fluctuate around approximately 6% annually.
In contrast, the differences in the risk rate in the form of standard deviation grow as the investment period increases. The cloud becomes horizontally wider with each 5year increment. Over the 1year period, only a few individual portfolios were on the righthand border of the risk rate. However, as the period grows, more dots appear on the cloud's border. That is, their density increases and, thus, quite a number of portfolios bear increasingly higher risks.
A calculation of the variance between the data series obtained for each investment period duration allowed us to estimate the degree of the dispersion of the portfolios along the X and Y axis for each investment period. For example, the variance of the average annual return for 5year investment period portfolios is characteristic of the dispersion between the average annual returns for all of the 10,672 portfolios obtained in the model. Here, dispersion characterizes the presence and extent of differences in returns on portfolios with completely different longterm asset allocations. Similar calculations were made for the risk rate, i.e., the standard deviation for each of the portfolios for each investment period duration. Dispersions of the risk rate were calculated for each t investment period. The calculation results are presented in
Dispersion of the average annual return and risk rate for all portfolios and different investment periods (%).
Source: authors’ calculations based on Bloomberg data.
The return dispersion (parameter of the vertical width of a portfolio set in the previous figures) falls considerably beginning with the 18year investment period and is generally negatively correlated with the investment period. This fact clearly confirms the hypothesis that the dispersion of the average annual return falls as the portfolio investment period increases. Thus, if investors each held one portfolio from the set for one year, their effectiveness would differ dramatically. This was previously demonstrated in the figure containing a respective portfolio set. The analysis helped us verify the previous quantitative hypotheses. For 1year investment period portfolios, dispersion reaches 7.5%, while the average (not shown in the graph) is approximately 4.0%. This means that, on average, most dots (returns on different portfolios) fall within the following interval according to the “three sigma” rule: [4 – 3×√7.5, 4+3×√7.5]=[–4.22, 12.22].
The dispersion of returns for portfolios with a 30year investment period is not the least among dispersions for all periods under review, as was expected according to the dispersion contraction hypothesis. However, it is still representative. The dispersion of returns on portfolios with a 30 year period is approximately 2%, with an average of 7%. Thus, with moderate growth in the mean interval value of all returns obtained for all portfolios under review, we observed a sharp decline in dispersion between these returns around an average value for all types and asset allocations. Here is an evaluation ofthe interval according to the same “three sigma” rule: [7 – 3×√2, 7+3×√2]=[2.76, 11.24]. Negative returns are no longer seen, while the return dispersion interval had its low limit shifted upward by more than 6 percentage points compared with the 1year portfolios.
The risk rate shows a positive trend. The quantitative analysis has confirmed the results of the graphical analysis. Longer investment periods for the same portfolios lead to a growth in risk rate differences between them. Thus, over short periods, dispersion of the risk rate may play a secondary role in determining the optimal strategy of asset allocation. However, beginning from the 16year horizon, one should take into account the comparative advantages of various portfolios in terms of the risk rate on par with the other factors.
As shown above, differences in average returns across portfolios decrease as the investment period grows, while differences between the risk rates of portfolios with different asset allocations increase. Asset allocation in this analysis is a sample set of weightings for a longterm period.
According to the findings regarding the longterm attractiveness of corporate bonds, we analyzed the joint hypothesis about the growth in differences between risk rate values for asset allocation strategies with increasing investment periods as well as the hypothesis about the comparative advantage of stocks over bonds in the long run. These hypotheses were tested using the same set of 10 assets listed in
The modeling results for over 10,000 different asset allocations for various sample investment horizons (1, 5, 10, 20, 25 and 30 years) are shown in
The portfolio set including corporate bond index with a T investment period in risk (σ, %) and return (r, %) coordinates.
Note: the white circle marks the corporate bond index portfolio; the white triangle marks the S&P 500 Index portfolio.
Source: authors’ calculations based on Bloomberg data.
Changes in the characteristics of a portfolio fully consisting of the S&P 500 Index over a longer investment horizon can also be seen in
As the period is extended, extreme values in daily returns increased their range and occurred more often. This had the effect of increasing dispersion and risk rates. Over a longterm period (
The shape of the portfolio set is more oblong than in
The portfolio set over a 5year horizon is more oblong, but to the left and to the right there are still significant differences in the average annual returns between portfolios within the same risk zone. An even more oblong shape is characteristic of longer investment horizons, while in the lefthand part of the cloud, consisting of portfolios with minimum risks and different weightings (≫0) of corporate bonds, differences in the average annual returns decrease sharply as T grows. This results in the almost triangular shape of the cloud on the left. On the right, as the horizon grows, the spokes protruding in the direction of the edges take on more pronounced shapes (the right edges of the cloud represent portfolios fully (100%) consisting of the various global stock indices from
The visual presentation of the results can be seen in
The dispersion between the average annual returns and the risk rates for all portfolios and different investment periods, taking into account corporate bonds (%).
Source: authors’ calculations based on Bloomberg data.
The trends for both series differ significantly in amplitude from
The trends for a diversified portfolio with equal weightings on all 10 assets (full diversification: 10% in the corporate bonds index, 10% in the S&P 500 Index and 10% in 8 stock indices of various countries) are shown in
Identifying a pattern in the behavior of diversified portfolios leads to a number of practical conclusions. In contrast with the traditional approaches of portfolio management theory, assuming that over longterm investment horizons stock investments are more preferable than bonds in terms of the risk–return ratio, the method used in this article has proven the opposite assumption. As horizons increase, stocks and bonds become closer in terms of returns, while stock risks increase faster than bond risks. This means that for longterm investors, investments in corporate bonds are more profitable in terms of the risk–return ratio than investments in stocks. At the same time, the sustainability of these findings has been confirmed both in the case of the Russian financial market with shorter horizons and in the case of developed markets with a longer history.
In the case of diversified portfolio sets, we proved the assumption that over increased investment horizons, investors must pay with a significantly larger increment of the risk rate for each incremental unit of return. This suggests that portfolio management should pay the most attention to risk mitigation. When deciding on a longterm investment strategy for a period of more than 20 years, one should consider the inherent risks in each potential asset class within a portfolio. For a long investment horizon (10 years or longer), while building an investment strategy, longterm investors should focus more on the asset allocation structure than on selecting particular investment and trading strategies or on particular issues of securities representing respective asset classes. The asset allocation structure should provide for achieving a desired level of return while taking reasonable risks.
The specific behavior of a portfolio set and diversified portfolios over time are the contraction of returns with substantially larger differences in the risk rates. Therefore, we can recommend that longterm investors (government as well as private) periodically restructure their diversified portfolios as the holding period grows. The share of risky assets should be reduced, as their heavy weighting in a longterm portfolio may actually lead to maintaining the same rate of return with a constant, disproportionate increase in the risk.
In our opinion, these assumptions justify the expedience of focusing retirement savings portfolios and private pension funds reserves mostly on the bonds of various issuers, including infrastructural bonds, which are also more in line with the nature of the obligations of this type of institutional investors. Taking into account the problem of the influence of investment horizons on the risk–return profiles of a given portfolio and its ambiguity as perceived by investors and academic circles, regulators should improve disclosure practices regarding the risks and returns of retirement savings portfolios and reserves as well as the particular corresponding asset class components within, including longterm historical indicator data series. This will foster research in this field and, consequently, help justify applied solutions for portfolio investments.
At the session of the Russian Federation Government on April 23, 2015, Prime Minister D. Medvedev made an official statement that “the decision has been made: the saving component stays.” See shorthand notes of reports from this session at http://government.ru/meetings/17789/.
This viewpoint has been formulated by Fisher and Lorie (1964), Mehra and Prescot (1985), Poterba and Summers (1988), Siegel (1992, 1999, 2005), Robertson and Wright (1998), Ibbotson and Chen (2003), Ilmanen (2003), DeLong and Magin (2009), etc.
For the period from 1802 to 2006, 200 5year, 185 20year and 105 100year portfolios could be built.
The Bloomberg Professional service (the Terminal). Official website: http://www.bloomberg.com/.
The calculations use the values of respective indices for the French, German, Japanese, UK and Russian stock markets, due to the limited historical data of the respective ETFs.