3.2 Testing the median returns for significance

Nevertheless, in order to test the significance of monthly mean returns, t-test is invalid and a different test should be performed. One can apply a one-sample sign test. It is a nonparametric alternative of the one-sample t-test because it does not require the data to come from a normally distributed population, as the t-test does. Using this test we can determine whether the median of a group differs from a specified value, which is equal to 0 in our case.

The median monthly period returns for all portfolios are represented in Table 2. It can be observed that profitability of portfolios hold for 3 months is higher than 1 month profitability. All pure portfolio median monthly returns are significant except for MWML3 portfolio and «loser» value portfolio for both holding periods. It should be noted that returns of momentum winners and losers for both holding period are much closer to each other than for value winners and loser portfolios. The reason for such difference may be that value effect is stronger than momentum effect if both are present at all. Besides, MWML1 is significant only at 10% level, which also provides us with information that zero-cost momentum strategies are unprofitable. We intend to test whether the findings can be explained by differences in risks. We cannot simply state that momentum effect is anomaly basing on poor significance of zero cost strategy. The thing is that loser momentum strategies can behave not as was expected due to the general upward trend prevailing in the market. A figure 3 represents cumulative returns of market and momentum strategy with 3 month holding period over the studied period of 15 years. It is clearly seen that both winner and loser portfolios outperform the market on average and follows its movements. Here are the correlations between the compared strategies and market: MOML3, Rm=0.49; MOMW3, Rm=0.30; MOMW3, MOML3=0.56. As we stated above alpha coefficient indicates the abnormal rate of return of our portfolio in excess of predicted returns by CAPM and dual-bets CAPM. Thus, we would still test momentum portfolios on the presence of abnormal return.

As the for profitability of combinations, all of medians are significantly different from 0. It is obvious, that median and mean returns of combo strategy will be within the interval form momentum returns to value returns, as we can observe that value outperforms momentum. Nevertheless, we cannot conclude yet whether value is better than momentum, or combination is outperforms both, until we calculate some widely used portfolio performance measures. Once we analyze the performance of our portfolios, then we will start the regression analysis of time series returns in order to estimate portfolio betas, alphas, check them for significance and finally conclude on solvency of tested hypotheses.

3.3 Performance measurement of constructed portfolios

There are several performance measure ratios which are commonly applied in modern portfolio management practice. These are Sharpe ratio, Treynor ratio, Jensen ratio (alpha) and information ratio. We would also estimate downside beta to capture the risk associated with potential for loss.

To begin with, it should be mentioned that performance is compared on an annualized basis. Therefore, we need to calculate annual returns of portfolios from monthly data using the following procedure. First, we found monthly arithmetic average for each year. Then, all values are multiplied by 12 to get annualized portfolio returns. To get average yearly returns for 15 years period we again simply take an arithmetic average. The obtained values for each strategy are represented in Table 3: Performance measure statistics.

The first performance ratio to be calculated is known as Sharpe ratio which measures performance in terms of both systematic and idiosyncratic risk. SR of portfolio is calculated as the excess return on investment divided by standard deviation of portfolio. To calculate the denominator, first we have to find standard deviation of returns for each year. To annualize standard deviation, we calculate standard deviations of each year from monthly values multiplied by the square root of 12. Then, the obtained figures are raised to the power of 2 in order to get yearly variances which are further summed and divided by 14 (15 years minus 1). The resulting values of variances for a sample of 15 years are raised to the power of Ѕ to get standard deviations.

Table 3 also represents these values for each strategy as well corresponding Sharpe ratios. The average value of 180 days-1year MIBOR (11.47%) is used for the studied period as a risk-free rate. The maximum SR (1.83) is attained by zero-cost value portfolio with 3-month holding return period, the minimum one (-0.3) is attained by loser value portfolio of the same holding period. The highest and lowest figures among combinations are 1.78 for 10/90 3-month period and -0.09 for 90/10 3-month period respectively, where the first weight stays for momentum strategy, the second for value strategy. It is clearly seen form the Table 3 that combined portfolios outperform pure zero-cost momentum but underperform pure zero-cost value portfolios if compare on the SR basis. However, we need to calculate some other ratios in order to make justified judgement on portfolios performance.

One more widely used ratio is Treynor ratio which measures the performance only in terms of systematic risk. TR is calculated as the portfolio excess return divided by portfolio beta. Again, we used yearly returns and calculated yearly betas as well simply as covariance of yearly returns of a certain portfolio and market divided by annualized market variance for the 15-year period. Also we have computed Jensen ratio and Modigliani risk-adjusted measure. The former is also known as alpha as we discussed previously, showing the abnormal return on investment, where the last is measured in units of per cent return and cab be calculated as the difference between Sharpe ratio of active and market portfolio multiplied by standard deviation of market return. All figures can be observed in Table 3.

The tendency is still the same: combo portfolios tend to outperform momentum portfolios but underperform value portfolios. There are negative betas for some portfolios meaning investment tend to decline when market rises, while increases when market falls. Only two portfolios have betas bigger than 1 (valw3 and valw1), while the rest have betas lower than 1. The lowest positive betas are 0.03 for 50/50-1 and 0.02 for 90/10-3, implying these portfolios are very defensive. However 90/10-3 has negative SR, which is not impressive. Overall, the strategies 30/70-1, 30/70-3, 50/50-1, 70/30-1, 70/30-3, can be considered as the most conservative strategies, due to they have relatively low betas, and thus are less exposed to market fluctuations.

We do not intend testing whether alphas and betas are significant or not, as 15 observations are not sufficient to explain the robustness of the model. Nevertheless, these figures provide us with some basic information about performance on annualized basis.

3.4 Regression analysis (CAPM)

Now we are going to run regression analysis in order to test the significance of constants (alpha), betas (measure of systematic risk) on monthly data, check the overall robustness of the models and finally conclude on significance of the studied strategies.

First, we applied standard CAPM model. We have performed regressions both with and without risk-free rate. Moreover, autocorrelation was examined in order to satisfy Gauss-Markov conditions. If Durbin-Watson (D-W) statistics is close to zero, then positive autocorrelation is present in the model. It can be eliminated by autoregressive transformation, adding new variable AR(1) into the regression equation. If D-W is still smaller than 2, then add AR(2). Once the D-W statistics is close to 2, we may claim that the problem of autocorrelation is solved.

Table 6 represents estimation output of regression analysis. To simplify our analysis we use only one macroeconomic factor represented by the rate of return of MICEX index. As the aim of our work is to detect the abnormal return (alpha) of studied strategies, there is no need to use a lot factors that may influence our portfolio returns. Since alpha is a measure of risk-adjusted return to a market index and shows the under - or outperformance compared to market, it is sufficient to use only one factor. Nevertheless, we may face the problem of poor R², meaning that market return is bad proxy for predicting returns. Let us discuss the main findings of regression analysis.

As can be seen from the Table 6, there is no evidence of abnormal returns of all momentum strategies applied, as the constants of each constructed momentum portfolios are insignificantly different from zero. Moreover, momentum strategies yield almost the same results for 1 and 3 month holding period. Figure 4 shows average annual returns of each portfolio over the studied period. It is clearly observed that portfolio mom12X3 and mom12x1 have similar pattern in returns. Figure 3 represents the cumulative returns over 15 years. Zero-cost momentum strategies are deeply below the market return. Thus, we can finally conclude, that momentum and contrarian affects are absent in Russian stock market as no abnormal return can be attained. Nevertheless, we can still compare results of winner and loser momentum portfolios with market return. As we can see from Figure 3, momentum winner and loser separately tend to outperform cumulative market return., If an investor had followed a strategy of taking a long position of winner momentum stocks starting in 2001, he would have gained more than simply copying the market over 15 years. In other words, we cannot claim that this strategy is unjustifiable only due to it does not produce abnormal return besides market premium. So, the performance of the strategy must be explained not only by alpha but also by premium for risk. The difference between portfolio return and the market return is known as arithmetic attribution. A table 7 represents the attributions for all constructed portfolios and corresponding alphas. It is clearly observed that attribution for winner momentum portfolios is larger than estimated alphas. Even though we found no evidence of momentum effect, we managed to construct portfolios momw1 and momw3 that outperform the market on average.

As for value portfolios, the results are more satisfactory. Table 6 reports that all alphas, except vall1, are significant, meaning that there is a value effect in Russian stock market. The largest alphas are achieved by valw3 (4.24%) and valw1 (3.22%). Zero-cost value strategies produce 3.86% and 3.21%. Looking at the Figure 3, zero-cost value cumulative returns are appreciably above the market and momentum zero-cost portfolio returns. Moreover, there are observed different from momentum portfolios patterns of average yearly value returns across 1 and 3 month holding period. Figure 4 shows that returns of 1 and 3 month value portfolios were declining from 2001 to 2003, then rising up to 2006. Value performs slightly better than momentum in 2008, bur worse in 2012. Both value zero-cost strategies benefit from diversification, as a result the average annualizes standard deviations obtained are 26.34% of vwml3 portfolio and 29.03% of vwml1, which are lower the market risk of 31.11%.

The combined portfolios were formed from weighting zero-cost value and momentum portfolios. Since we provided an argument for insignificance of momentum strategy, there is no rationale behind combining significant and insignificant strategies. But we are still interested whether such a combination can yield a higher risk-adjusted return than each separately. We also run a CAPM for combo portfolios and check their significance. Table 6 also represents the regression output for each combined portfolio. Portfolios 50/50 (1), 50/50 (3), 70/30 (1), 30/70 (1), 10/90 (1), 10/90 (3), 20/80 (1), 20/80 (3), 40/60 (1), 40/60 (3) and 60/40 (3) produce positive significant alphas, meaning that combined strategies can bring abnormal return. These alphas are greater than momentum portfolio alphas, whereas lower than value portfolio alphas. Relating to Table 4, none of the combined portfolios outperform the value component separately analyzing different measures of performance. The potential of combined strategies to outperform value and momentum is solid diversification. As we can see form the Table 5, momentum and value strategies are negatively correlated implying that both strategies can offset each other during market disturbances. Thus, a combination of value and momentum portfolios can be considered as a hedging strategy.

3.5 Dual-beta CAPM

We performed dual-beta CAPM in order to check whether it has stronger explanatory power and estimate downside and upside betas. We report regression output only for zero-cost portfolios in Table 8 as the results obtained are not as expected. R² in most cases remained unchanged, but also decreased for some portfolios. The constants of momentum portfolios remain insignificant as well as under standard CAPM. Finally, estimated upside and downside betas are also insignificant.

3.6 Summary

On the grounds of conducted research, we may draw a conclusion of the strength of the raised hypotheses.

H1: Momentum effect exists in 1 and 3 month perspective, and following the strategy can bring abnormal returns.

The hypothesis is rejected as no evidence of momentum effect in Russian stock market found. However, the constructed winner portfolios with one and three month holding period, and based on the stock selection criteria of best past performance for previous 11 months skipping the recent month, has outperformed the market over the 15 year observation period. But still, the strategy failed to bring abnormal return.

H2: Value effect exists in 1 and 3 month perspective, and following the strategy can bring abnormal returns;

We do not reject the hypothesis, as there was found strong evidence of value effect in Russian stock market. The strategy generates significant positive alphas.

H3: Combined portfolio can bring abnormal returns in 1 and 3 month perspective.

Finally, we do not reject this hypothesis even though combined portfolios did not manage to outperform corresponding zero-cost value portfolios. Most of the combinations show significant abnormal return, outperforming market and separate momentum strategy.

Conclusion