4. Empirical Results
4.3 Comparing TVTP Models with FTP Model in Practical Performance
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4.3 Comparing TVTP Models with FTP Model in Practical Performance
Since the above nine models are all significant, this paper will examine their practical performance during the data period. In addition to the nine TVTP models, the FTP model are also considered in this part, and this paper will compare the performance of TVTP models with FTP in order to test whether the nine TVTP models incorporating exogenous financial variables really performs better in practice than the FTP model without extra information even though the statistic results have showed the significance in the TVTP models. The process is as follows.
First, this paper identifies which state each trading day is during the sample period from April 15, 2002 to March 29, 2013 through state probabilities the model generates. The probability threshold is 0.5, which means this paper will identify the state of the day is tranquility if the probability of state 1 is more than 0.5, or crisis when the probability of state 2 is over 0.5. The state probabilities at time t are determined by the time-varying transition probabilities and the state probabilities at time t-1. Thus the state-switching days during the period can be observed. When the state changes from 2 to 1 which also means the crisis state ends and tranquility state begins, I will buy one unit SPDR S&P 500 using the close price on the first day of tranquility state; when the state changes from 1 to 2 which means the tranquility state ends and crisis state starts, I will short sell one unit SPDR S&P 500 using the close price on the first day of crisis state. After constructing position whether it is long or short, I will hold the position until the next state-switching day, and then buy to cover (sell) the position if it was a short (long) position at the previous state-switching day.
In other words, I will close an old position and build a new position meanwhile at each state-switching day besides the first and the last state-switching days.
This paper does not consider any transaction cost or margin for short sell in the
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process because the most important purpose for examining each model’s performance is to measure which one is better among the nine TVTP models and compare the effectiveness between TVTP model and FTP model by concrete return figures. Thus, considering transaction cost may cause a complicated result related with other factors so that it is not easy to explore the root performance of each model clearly.
Thus, this paper will calculate the return in a familiar method to simplify the process. When a long position is closed, I calculate the difference between selling price and buying price, and divide the difference by the buying price. On the other hand, when a short position is closed, I divide the difference between selling price and buying price by the selling price. Finally, I accumulate the return and transfer to the yearly rate of return for comparing the performance between all models.
The performance of each model and result description is as follows. The yearly rate of return is 7.16% for FTP model, and there are six TVTP models which have higher yearly rates of return than the FTP model excluding the model with spot and 2 periods of lag SPY (5.54%), with spot and 2 periods of lag SPY and Credit10Y (5.57%), and with spot and 3 periods of lag SPY and Credit5Y (5.69%). The model with spot information of Credit5Y is the best among all models because of the highest yearly rate of return of 7.81% and absolute total return of $136.14.
From the cases of three models with lower return than FTP model, this paper infers that significant models in statistical analysis do not always mean the good performance when applying practically. Because the three models which have lower return than FTP model are all statistically significant in the LR test in previous analysis.
During the same period, the yearly rate of return of SPDR S&P 500 is 3.22%, the yearly rate of return of DJIA index is 3.4%, and the yearly yield rate of 10-year BBB corporate bond is 6.2%. Comparing the models’ performance with these benchmarks,
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worse than FTP also surpass the stock market benchmarks. Therefore, this paper can conclude statistically and practically that the time-varying transition probability Markov regime switching models incorporating the information contained in SPDR S&P 500 or credit spread perform better than the fixed transition probability model which is without exogenous information. In addition to the statistical significance test, following the timing of state shifts identified by the TVTP model concluded above and investing in SPDR S&P 500 can also make more profits and even transcend the benchmarks of stock market and the BBB corporate bond market.Table 9. Performance in return of each model
Variable Lag
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This paper also shows some graphs about the smoothed probability of crisis state (state 2) and the level of VIX index at each time t during the sample period in Figure 4. This paper takes the FTP model, the model with spot information of Credit5Y, and the model with spot and 2 periods of lag SPY for examples because they cover extreme performance. In Figure 4 (a)(b)(c), all of blue lines indicate the VIX index (refer to left vertical axis), and the other line indicates the probability of crisis state (refer to right vertical axis). It is clear to see that when the VIX index has strong responses or rocket sharply, the probability of crisis state almost reaches very high level even 1 timely, and help us detect the crisis. And when the VIX index becomes smooth relatively, the probability also decrease to very low level even 0. Identifying state switching is the main feature of the Markov switching model, and it seems to work well in this paper because the timing of crisis state reflected by the TVTP and FTP models seems to be consistent with the timing VIX index jumps up in all graphs of Figure 4. Actually, the differences between these graphs are the state-switching days, state probability of each day, and the number of transition, which are the keys causing different performance of each model. In Appendix C there are large and clear graphs directly comparing the TVTP model’s crisis state probability with the FTP model’s; thus, it may be easier to observe the differences between them.
In previous paragraphs, the reasons why SPY, Credit10Y, and Credit5Y are significant variables have been mentioned. By checking and comparing the practical performance of each model, this paper finds the model with spot information of Credit5Y is the best and the model with spot information of Credit5Y and Credit10Y is only worse than the best one. It supports the inferences again that credit spread is very useful in detecting the market instability like VIX because credit spread also reflects the investors’ sentiment and confidence for future market condition, so the model incorporating credit spread information will better identify state switching in
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VIX index and earn more profits.
4-(a) FTP model
4-(b) TVTP model with spot information of Credit5Y
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4-(c) TVTP model with spot and 2 periods of lag SPY
Figure 4. Smoothed probability of crisis state for various models
From Table 9, this paper also finds that the return for short selling only is always less than the return for longing only for each model. This paper infers it is related to the nature of VIX index. The VIX index is asymmetric when reflects the market downturn and upturn. The previous sections have showed that VIX is very sensitive to market instability so that it will rocket intensely when the crisis occurs. But the feature of mean reversion makes the VIX index decrease gradually after reaching relatively high level. However, the crisis state in VIX will persist until not only the VIX level lowers but the volatility of VIX index also becomes smaller. In other words, though the VIX index lowers, the crisis state keeps if the VIX still fluctuates strongly.
Only when the level of VIX lowers and its volatility gets smooth both, the state will switches from crisis to tranquility. The price of SPDR S&P 500 moves negatively with the VIX, but the price will stay high as the VIX jumps up dramatically. Then the price of SPDR S&P 500 starts to fall while the market is in crisis state. When the VIX begins falling but keeps strong volatile, the price of SPDR S&P 500 will turn to
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short sell SPDR S&P 500 at a higher price when the VIX switches from tranquility to crisis state, the persistency of crisis state will cover part of rising SPDR S&P 500 so that I cannot buy to cover at the lowest price level timely. However, though I may not buy SPDR S&P 500 at the lowest price from crisis state to tranquility, I will sell at a relatively highest price when the VIX jumps up dramatically. Moreover, the duration of tranquility state is longer than crisis state observed from the model estimation, so the degree of price increase for long position may be larger than price decrease for short position. That’s why the return for short selling only is always less than the return for longing only.
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